rowanstree-blog

[rowanstree-blog]

Day #180

This school year, I learned a lot. Not just academically but personally and emotionally. I learned to work hard, for it would benefit me later in life. I learned to convey my thoughts because I know that my voice should be heard. And I learned to keep my chin up, no matter what obstacle knocks me off my path.

For a good portion of the year, I believed that I couldn’t do it, that I was learning nothing because I wasn’t being publicly taught and felt that somehow that was superior to homeschool. also thought that my “lack” of an eight grade education wouldn’t be good enough for my future superiors and that I would be held back. Towards the final months, I cam to realize that I was wrong. I have worked hard and have learned an abundance of academic subjects as well as uncovering traits of my own that I didn't know I had in me. I always liked school and applied myself but not to this extent. I have learned that I can motivate myself to work six hours a day, just doing academics.

Around January, I lost that confidence I had gained over those five months. My dad left and I felt it was because of me. I didn’t and still don't understand why he did it but I am stronger than I ever was before. My mom and I became homeless (and still technically don’t have a home of our own) but caring friends and family have loved us and cared for us and were willing to let us into their homes and give us food and a warm bed to sleep on. From this, I have also learned to “just keep swimming” no matter how strong that current gets. And from that, I have learned resilience.

I have not only learned about myself but also about women in history whose accomplishments have been subverted by the historically biased patriarchy. The women suffragists, Susan B. Anthony and Elizabeth Cady Stanton, fought long and hard in the battle for equal rights, proving to society that women are capable of so much more than they were given the chance to prove. They also fought for safety legislation, better wages and the right to vote. When the nineteenth amendment was ratified, they realized it was just the beginning of a much broader war, that included better wages and working conditions, and child labor laws.

And due to the system of the electoral college, it doesn’t really matter that women were given the right to vote in a presidential election, during the 2016 election, presidential candidate Hillary Clinton won by the popular vote but Donald Trump became the president of the United States  by the electoral college and his wealth that promoted him to a heirarchy through money and businesses that won over the vote of privileged, rich, white males that were declared delegates of the united states. I have also learned about the allocation of contraceptives to allow women maternal freedom rather than becoming a proxy for others patriatchial expectations. I have also learned how women were burned, drowned and hanged during the Salem Witch Trials in the 1600’s just because of “suspicious behavior” or using medicine to either cure themselves to others of diseases that were very common during that. I have also learned about women who have fought for education for all colors and genders, because no one person, group, gender, religion, race or ethnicity is either superior of inferior to one another. The courage, determination and strength of these women have fortified my opinion about feminism and determination, we deserve better.

This year I have also learned about personal finance and global warming, things I knew nothing about before this year. I feel that this year and this experience has prepared me for life later on; college, taxes, jobs, a home. Thing Is definitely need to take into consideration in the following years. I feel that the corrupt public school system has failed to teach students things that they will and instead teach them to follow a curriculum rather than their mind. I can’t say that I haven’t done that though. I have learned stuff like personal finance and women’s history but my love of school and homeschooling later on in my academic life made it hard to let go of my old academic schedule. I have learned to somewhat adjust according to the circumstances but I wish to be more flexible. I know I can and will work harder to do so through summer, high school, college and beyond. This year has taught me so more more than to just solve for the pH of a system using the Henderson-Hasselbalch equation or derive the values of trigonometric functions. It has taught me to focus on the now, but think holistically. And to also study and insert myself into things that make me happy and are beneficial to my following years, as I age both physically and emotionally.

In conclusion, I have learned to be more confident whether it be my education, decisions or educational decisions. I have learned to keep fighting, to fight for what’s write and to do what makes me happy. I feel that is what my mom has been trying to teach me all year and I thank her for giving me this opportunity that I would never take back.             Have a good summer :)

[rowanstree-blog]

Day #179

          Today I started with a Math class on factoring the difference of two squares as a product of two binomials. In this video, I went over that the equation for the difference of squares is equal to a^2-b^2 and when factored as a product of two binomials is equal to (a+b)(a-b) or (a-b)(a+b) as long as their are tow different signs, it doesn't matter what order it is in. I also learned that there are two very important things to consider when factoring the difference of two squares, you have to see if their is a common factor that can be factored out of the problem in order to make the coefficient and the constant term less than its original form. Also, you must read “factor” as “factor completely.” When factoring the form a^2-b^2, first, check for GCF, if there is none, than square both variables and then write the square root of the first term in the beginning of the two parenthesis and the square root of the second term in the end of the two parenthesis and included both a positive and a negative sign in between the terms within the parenthesis. I also learned another very important rule that you can never factor a sum of squares when factoring the difference of them. After that, I did a few practice questions and then took a practice test on that followed by a video on factoring the difference of squares with two variables. After that, I took a quiz on factoring the difference of squares with the leading coefficient not equal to one so you would therefore have to factor out the greatest common factor of the two terms. I then took another practice test in finding the difference of squares followed by a video on factoring perfect squares with a negative common factor so that you then factor the negative sign out o the parenthesis when you write it as a product of two binomials. After that, I took a Chemistry class on buffer capacity. As a review, buffer capacity is how much acid or base you can dd before there is a change in the pH of a system. The pH, pKa and the ratio of the concentration of the conjugate base over the weak acid can help us determine the behavior of our buffer and who strong or weak it is. I then compared two buffers after calculating the initial pH of one system. In both buffers, I added a base so that it would subtract from the conjugate acid and decrease that concentration and add to the concentration of the base. After doing this, I found that the pH was changed but only by 0.06 and that the second buffer system changed by .9 so therefore I determined that the first buffer system has a higher buffer capacity and that as you add more either acids or bases, the pH increases but not as exponentially as the second buffer system hence, it has a lower buffer capacity. When determining what buffer to use in a solution, it is important to note that the concentrations of the weak acid and the conjugate base must be between 0.10 molar and 1.0 molar because you don’t want it to exceed its buffer capacity. I then took a space science class on Einstein’s modern theory of relativity which is basically stating that our observations of velocity on earth is related to the earth’s constant state of motion and that nothing is absolutely in motion or absolutely stopped. After that, I took an environmental science class on locally support of organic agriculture growing as consumers are becoming more aware of the burning of fossil fuels and petroleum for food production and transport that can have tremendous effects on our environment. The CSA program provides funds from consumers to the farmers in order for the consumers to get healthier food and make a smaller ecological footprint and gives profit to the farmers. After that, I did a quick exercise followed by a half-hour lunch. After that, I took a women’s history class on Aspasia who was known for knowledge and outspokenness and was against confining laws placed on women and supported better education for women. Next, I took an economics class on a video on what microeconomics is which is the study of economics as a whole and has to do with big economic decisions that can affect the economy. After that, I took a grammar class on plural possession with is when you would just use an apostrophe to denote possession. Then, to finish off the day, I read some of “The Beauty Myth” on false claims made by beauty firms that take the money out of the wallets of hard working women for a substance that will supposedly make them beautiful.

[rowanstree-blog]

Day #178

           Today I started with a Math class on factoring quadratics by grouping, with a common factor. I started off with watching a video on factoring quadratics with a common factor and by grouping. To do so, you must derive the common factor out of the quadratic and put it outside of the parenthesis so that when you multiply that number by another number in the parentheses, you will derive your original first, second and third term. After doing that, you have to multiply your leading coefficient by the constant term and find what two numbers are a factor of that number and add to the middle term. After that, take those two numbers and have them replace the middle term and continue to simplify. To finish it up, take the common binomial, in the parentheses and multiply it by the two numbers outside the parentheses as well as bringing down that constant term we derived in the beginning and writing it outside the first set of parentheses. After that, I watched another video on factoring quadratics by grouping with a common factor. Except this time, the leading coefficient is negative so therefore the common factor is also. I then did a practice test on that followed by a video on factoring 2-variable quadratics. All you have to do is if the leading coefficient is not equal to one, then make it one and then take that variable and put it at the beginning of the parenthesis and put the second variable at the end of the parenthesis while writing the two numbers in the parentheses who's sum is the middle term and who's product is the constant term. Next, I watched a video on factoring two variable quadratics by grouping followed by a challenging practice test on factoring quadratic polynomials. I then took a French lesson on Duolingo followed by a Chemistry class on the relationship between the pH and the acid dissociation constant for buffers, relative to the ratio of the concentration of the conjugate base over the concentration of the weak acid. As a review, a buffer contains an aqueous solution that has a weak-conjugate, acid-base pair that can fix the pH of a system when the equilibrium is disturbed. The Henderson-Hasselbalch equation can be rearranged in order to derive different information relative to the pH, acid dissociation constant, conjugate base and weak acid. When the pH is equal to the pKa, then the [A-]/[HA]=1 which states that [A-]=[HA]. If the pH is greater than the pKa, then the [A-]/[HA] is > 1 which states that the [A-]>[HA]. And that if the pH<pKa, then the [A-]/[HA] is < 1 which states that the [A-]<[HA]. I then took an environmental science class on how organic agriculture is booming due to higher consumer demand of organic products and that organic agriculture causes farmers to experience profit losses in the short run but in the long run, the same as conventional agriculture but less inputs and industrialized methods are replaced with organic ones. Because demand is now so high, subsidies are being provided to farmers using organic agricultural methods. I then took a 15 minute break followed by a women’s history class on Catherine the Great who overthrow her husband of the Russian empire and brought better education and modern laws to govern the empire BUT she also ruled with absolute authority which was not necessarily favored. I then took a quiz on microeconomics which is the study of individual relationships followed by a grammar class on possessives for names or words ending in s which is the same a words not ending in s, it is still ‘s.

[rowanstree-blog]

Day #177

          Today I started with a Math lesson on factoring quadratics which are also referred to as quadratic polynomials or second degree polynomials. Quadratics are written in the standard form, x^2+(a+b)x+ab. When factored, they are put unto the form (x+a)(x+b). This is how you will factor a quadratic with a leading coefficient equal to one. If the leading coefficient of a quadratic is not equal to one, than there is a different way of factoring it in which I will articulate in a little bit. In order to factor a quadratic with the leading coefficient equal to one, you have to find two numbers that you can add to get the second term and multiply to get the third, that is why the second and third terms are written ad (a+b)x and ab. I then started off the lesson with a video on factoring quadratic into the form (x+a)(x+b). I did a few examples followed by a video on more examples of factoring quadratics. After that, I took a practice test followed by a video on an introduction to factoring by grouping which is helpful with a leading coefficient not equal to one. When you have a quadratic with a leading coefficient not equal to one, you have to factor out a number that is divisible by all of the coefficients and the constant term in the quadratic. You then multiply the leading coefficient by the content and find two numbers that multiply to that number and add to the middle term. Once you have that, have those two numbers, as a coefficient of x, replace the middle term and continue to factor. To finish it up, you then take the common factor in the parentheses and the numbers multiplying those terms to conclude factoring a quadratic with the leading coefficient not equal to one. I then took a French lesson on Duolingo followed by a Chemistry class on more on the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation helps to determine which buffer system to use in a solution with a specific pH. For this video, I looked at the derivation of the Henderson-Hasselbalch equation. It started off with the weak acid dissociation constant being equal to the dissociated acid over the undissociated acid because when a weak acid is put into a solution, it doesn’t completely dissociate. On the top of the ratio, it is the concentration of the protons multiplied by the concentration of the conjugate base over the concentration of the weal acid. You can then take the log of both sides and then separate the proton concentration and the conjugate base over the weak acid on the right side of the equation. After that, change the logarithm of the weak acid dissociation constant and the concentration of protons to the negative acid dissociation content and a negative pH. After that is done, flip those two to the other side of the equation and you will be left with the Henderson-Hasselbalch equation. When deciding which buffer works the best, because the weak acid donates protons and the conjugate base accepts them, it is good if their concentrations are equal so then the pKa=pH. After that, I took an environmental science class on how organic agriculture has different definitions and systems but are all aimed at converting industrialized agriculture to a more, organic compound centered energy source that poses a better ecological outcome. I then did an illustration of Mercury’s precession around the sun caused by the severe curvature of the space-time continuum that was determined by Einstein’s Modern Theory of Relativity for my space science class. I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Queen Liliuokalani who was the last reigning monarch of Hawaii before it was claimed by the United States. She fought for native hawaiian independence and the preservation of their native culture and land. I then took an economics class on monopolies which have one seller, high prices, products with no close substitutes, and high barriers to entry caused by patents and sole ownership of resources. Because a Monopoly is one firm, any losses or gains experienced by the firm is experienced by the industry and consumers don’t prefer monopolies because of their high prices and would rather competitive markets where the price isn’t so high. After that, I took a grammar class on the possessive ownership and how ‘s denotes ownership and is not used only with pronouns. Then, to finish off the day, I read some of “The Beauty Myth” on how the “holy oil” is falsely advertised and has been proved by biochemists that the things that “holy oils” have in them will not stop aging, nothing will and the beauty industry is therefore exploiting consumers into thinking they will stop aging but really, its not doing anything.

[rowanstree-blog]

Day #176

         Today I started with a math class on understanding the binomial theorem. I started off with a video on binomial expansion and combinatorics. In this video, It explained how combinatorics is included in the binomial theorem when expanding binomials. This video was about the n choose k values as the coefficient of the two binomial terms. In order to visually represent the terms order of degrees. I take a scale and one side is plainly lighter than the other, x. Therefore, its side of the scale is at a steep incline, relative to the y value. If you were raising a binomial to the third power, than the x value would be a three and the y value would be at zero. As the expansion progresses, the x-values decrease ad the y-values increase and the final state is that y is now at 3 and x is now at zero. This can be represented by the expanded binomial form, (3/0)x^3y^0+(3/1)x^2y^1+(3/2)x^1y^2+(3/3)x^0y^3. Once you use the binomial theorem and simplification, the expansion simplifies out to x^3+3x^2y^1+3x^1y^2+y^3. You can use either Pascal’s triangle or the binomial theorem to derive the coefficients, given n and k. After that, I watched a video on Pascal’s triangle and how it is related with combinatorics. It is related because it can help determine the coefficients of an extended binomial and based on the pattern of Pascal’s triangle, can also help determine the variables as well. I then watched another video on binomial expansion and combinatorics followed by a quiz on expanding binomials in which I used combinatorics, Pascal’s triangle and the Binomial theorem to solve the questions. Next, I took an Algebra I class on plotting inequalities who's starting point is dictated by whether the term is either <-or>- and its direction is indicates by < or >. I then took a French lesson on Duolingo followed by a Chemistry class on the Henderson-Hasselbalch equation which can help to find the pH of a buffer system and find the ration of conjugate base to conjugate acid of a buffer. The Henderson-Hasselbalch equation is equal to pH=pKa+log(base/acid). pKa is the acid dissociation constant and is needed when calculating the pH of a buffer system or deriving the ratio. I then did a couple practice problems on that followed by an environmental science class on sustainable agriculture. Sustainable agriculture is any form of agriculture that does not cause environmental or social problems and can benefit people in the long run. They also decrease fossil fuel inputs and therefore decrease the pollution cause by those outputs.  There are different kinds of sustainable agriculture including low-input agriculture which decreases antibiotics, pesticides, herbicides. insecticides, fossil fuels, etc., that causes harm to our environment. Also, organic agriculture uses organic alternatives to environmentally threatening practices. Industrial agriculture has had many environmental and social impacts that can be avoided using sustainable agriculture and scientist feel that is we want to benefit ourselves in the long run, we should switch to sustainable agriculture before its too late. I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Harriet Tubman who helped enslaved African Americans find their way to freedom while gaining an abundance of recognition, trust, and loyalty along the way. Ten years before the civil war, she had brought 300 slaves to freedom! After  that, I took an economics class on Oligopolies. Oligopolies have a small number of sellers,  which means that any individual firm can impact the rest with their cessions so all of the oligopolistic firms keep a close eye on everyone. Also, their products are both homogeneous and differentiated and there are also high barriers to entry, unlike monopolistic competition and perfect competition but it is not impossible, like a monopoly. Also, an Oligopoly is considered complex because of how hard it is to maintain a steady market while one small move of one firms means the sacrifice of the rest. After that, I took a grammar class on apostrophes and plurals. Apostrophes are only in pluralizing when it is doing to so to a lower cases letter, to avoid misinterpretation. Then, to finish off the day, I read some of “The Beauty Myth” on how the “cult of the fear of age” has developed a language that articulates to women their “unappealing appearance” and advertises the “need” for creams and serums to help their aging skin, even on a molecular level.

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Day #175

A          Today I started with a Math on more on binomials. I started off with a video on Pascal’s triangle and binomial expansion. The numbers in Pascal’s triangle can help articulate the coefficients of binomials raised to the nth power and once you fill in the a and b terms and their coefficients, you can also determine what power the binomial terms are raised to depending on what  power the term as a whole is raised to. I then watched a video on expanding binomials In which there were numerous greater than one as the coefficients of the terms in the binomial. Once I either use Pascal’s triangle or the binomial theorem, I can then multiply that leading coefficients by the other coefficients to get the final number for the term. After that, I took a quiz on binomial expansion using combinatorics (the binomial theorem) and Pascal’s triangle. Next, I watched a video on expanding binomials without Pascal’s triangle in which I used an algorithm for mentally computing binomial expansion coefficients. What you can do is that for each successive term, you have to multiply the exponent of x by the coefficient of the previous term and divide it by two in order to get the coefficient of the other term; Instead of using (n choose k)= n!/k!(n-k)!. After that, I took a French lesson on Duolingo followed by a Chemistry class on solubility and the common ion effect. Like I stated in the previous blog post, the common ion effect is when a soluble compound, like for example Silver Chromate, is added to a solution, that in this case includes silver nitrate, the common ion is silver in this case and the common ion effect will occur between the two chemicals. In this case, Silver Cromate is on the product side of the reaction and according to Le Châtelier’s principle, the reaction will shift to the product side of the reaction to in this case make more mols of Silver and Chromate. I then watched a video on Solubility which is when a solute is dissolved in a solvent to form a solution. This is a reversible reaction and therefore has its own equilibrium constant, ksp which is the constant of solubility and products. For example, when NaCl is added to a solvent, H2O, the ionic bonds in the table salt are broken into Na and Cl, sodium and chloride, which is ushered away by the water molecules. If I were to add more salt to the solution, then the bonds will form and go back into solid-state particles. This can be determined by Ksp, if the Ksp value is small, then it is most likely to be more in the solid form. After that, I took an environmental science class on the negative impacts of aquaculture. When farm animals are kept in dense populations, it is prone to disease, which lowers food security, which increases antibiotic treatment and is very expensive. It also increases waste such as feces or uneaten fish meal. Fish meal consists of other fish which is less energy efficient and creates a larger ecological footprint. Also, If farmed animals go into non-native ecosystems, then they may outcompete the native organisms. If they are transgenic, then the male dominant fish will reproduce will the other fish and spread the transgenes through the population. After that, I did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Wilma Mankiller who was the first woman to lead the Cherokee nation and used her leadership to advocate Native American causes and protection of their land and culture. After that, I took an economics class on entry and exit decisions in the long run in a perfectly competitive market. Entry is the long run process of firms anteing an industry in response to industry profits. And exit is the long run equilibrium where all firms earn zero economic profits producing the output where P=MR=MC and P=AC. Perfectly competitive firms are price takers so once they enter the market, they must keep the prevailing market price and can neither increase nor decrease the price so eventually, through various transactions of entry and exit, the perfectly competitive firms’ profits will equal zero. After that, I took a grammar class on contractions which is another use for the apostrophe and can use the apostrophe to contract two words together and denote the missing letters. Then, to finish off the day, I read some of “The Beauty Myth” on how beauticians act a lot like cult members and hypnotists when telling a person about their wrinkles and fragile skin and to advertise skin creams and oils that will “help” them but eventually just become another bottle of goop that will supposedly make you beautiful.

[rowanstree-blog]

Day #174

          Today I started with two Math quizzes as a review of what I did yesterday. I did one quiz on constructing sinusoidal functions, derived from their graph. And then I took a quiz on modeling with sinusoidal functions. After that, I started a lesson on the Binomial theorem. I started off with an introduction to the binomial theorem. As a review, binomials are two term equations that can get quite difficult to calculate as the exponents that you might raise it to become exponentially larger. The binomial theorem helps to lessen the amount of time it takes to expand a binomial as the exponents become exponentially higher. The Binomial theorem states that (n choose k)a^n-k b^k (K is equal to zero, up to what ever n is equal to. The Binomial theorem also states that (n choose k)=n!/k!(n-k)!. The pascal triangle can also help when expanding binomials but can become painstakingly long to fill out as the rows become more and more abundant. In this case, “!” stands for factorials which are the number multiplied by every number below it, stopping at (+)1. For example, 3!=3*2*1. And after filling out (n choose k), in this situation, n=3 and n=1 would be (3 choose 1)=3!/ 1!2! which would all be equal to three. This would then be the coefficient of your binomial term that you would have to multiply with any other number in the binomial. Finally, a Pascal triangle is an array of numbers, relative to the binomial theorem. If I were to fill in the first three rows of the Pascal Triangle, I would get one on top, 2 ones below that and a one, a two, and then another one after that. This works by taking the number next to one on the left-hand side of the triangle and adding it to the number next to it to get the number under them. The ones left out of the addition will just carry down. I then took a French lesson on Duolingo followed by a space science class on how precession causes perihelion. Precession is the slow movement of an axis of a spinning body around another axis due to a torque (for example, a gravitational force) This changes the direction of the first axis. Perihelion is the point of the orbit of a planet, asteroid of comet at its closest point to the sun. Mercury has a very mysterious orbit because its elliptical orbit precesses around the sun causes a perihelion where it is closest to the sun at one of those points. Mercury’s precession is very slow but has been realized by many astronomers. When Einstein wrote the theory of relativity, E=Mc^2, he articulated space and time as a fabric and gravity as the curvature and movement of that fabric that controls the movement of spacial bodies. It is thought that one of the deep curves in the space-time continuum in which the sun is in, Mercury is said to be in the same plane in the vicinity of the sun which explains its precession around it. I then took a Chemistry class on the common ion effect which is when a soluble compound (which is able to dissolve in a solution) is added to an equilibrium solution that has an ion  precipitant (which can derive a solid from a solution). After that, I took an environmental science class on the benefits of aquaculture which include the energy efficiency, decrease in fossil fuels, decrease in commercial fishing and fishing pressures. This can help alleviate some of the given environmental impacts that occur with commercial fishing. It can also replenish the aquatic population as their is an ever-increasing demand for seafood that could cause harm to fish and shellfish populations. After that, I did a quick exercise followed by an hour long lunch. Next, I took a women’s history class on Simone de Beauvoir who wanted to be an independent woman rather than the inferior parter to a dominant male. She was also sensitive to the fact that women are considered to be the subordinate or “second” sex to men. She published many books, one of which was “The Second Sex” which articulated the fact that men considered themselves the more superior gender and more essential to humankind. Her book brought both genders together to “affirm brotherhood” and regain the proper social recognition that one gender is neither inferior nor superior to the other. I then took an economics class on efficiency in perfectly competitive markets which has to do with Allocative efficiency which is the state of an economy when production equals consumer preference and the goods and services are produced up to the point when the benefit to the consumers equals the marginal cost of production. And Productive efficiency is where the market must keep the production of goods and services on the production possibilities frontier in order to reach efficient productivity to assure that it does not go below that. After that, I took a quiz on apostrophes which help dictate whether something or someone belongs to someone or something. It could also articulate the state in which something is. Also, It helps shorten a sentence while still conveying the same message. Then, to finish off the day, I read some of “The Beauty Myth” on  how eve’s sin is related to skin aging and how women look at and compare themselves to photographs that are unrecognizable to the original model because of all the light touch ups that is thought to be vital for women beauty as well as the fact that women’s worth is not dictated by what they say but what they look like.

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Day #173

           Today I started with a Math class on construction sinusoidal functions based on their graph. I started off with a video on deriving sinusoidal functions from its graph. In this, I added the maximum plus the minimum values and divided it by two in order to get the midline. I then derived the amplitude an then  took the period of the function and put it under 2pi. I then took a quiz on constructing sinusoidal and cyclical functions. In this quiz, I learned that if the function intercepts the midline at x=0, then it is a sinusoidal function. If the one of the functions extremums are at x=0, then it is a cyclical function. Based on given information, I could derive if the function was flipped. If it was, then I would have to make the amplitude a negative value to indicate its flip. I then found the midline and and then the amplitude of the function. After that, I derived the period of the function. Once I knew all of that information, I wrote the function with all of the correct inputs. I then watched a video on a trigonometric word problem on modeling the daily temperature. I take the maximum temperature and write that as my maximum point and then I take the minimum temperature and write that as my minimum point. I can then derive my midline and amplitude from that and because the period in which the function lasts until it repeats is 24 hours, I then put 24 under 2pi and simplify it to pi/12. After that, I did a trigonometric word problem on modeling annual temperature, I did the same exact thing as the previous video except the period is written as 2pi/365. Then, to finish off the lesson, I took a quiz on modeling with sinusoidal and cyclical functions. I then took a French lesson on Duolingo followed by a Chemistry class on Buffers and how they help to lessen the effects of acid rain. Acid rain occurs when fossil fuel emissions release sulfur dioxide which react with water in the atmosphere to make sulfuric acid. Buffers help retain pH balance in a system that requires a set pH like blood, reservoirs, soda, pools, etc,. In this whole video, I learned that in conclusion, a buffer solution resits change in its pH and that a buffer system is a mixture of weak bases and its conjugate acid and weak acids with its conjugate base. The weakness of the acids or bases help to either sink or secure the amount of protons in a song acid or base in order to neutralize it. But, buffers do have an end point in it's capability to return a reaction to its original pH balance when the equilibrium in interrupted. This is called a buffer capacity and is when the maximum amount of Hydrogen ions that a buffer system can neutralize. When you put a pH indicator into a buffer system, once the system changes color, the end point in the pH indicator is reached and the system has exceeded its buffer capacity. I then took an environmental science class on aquaculture which is the cultivation of aquatic organism  in a controlled environment. When managed in a large-scale, industrialized fashion, it can pose environmental impacts but when managed in a small-scale, community fashion, it can be efficient. Due to our ever increasing demand of seafood products, the large-scale management of aqua farms has become more abundant which can harm the environment. After that, I did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Corazon Aquino who led a peoples revolution to end the 20-year dictatorship of Ferdinand Marcos. After knowing a lot about global current events, she became very in-tune with what was going on around the world at that moment. She became the first women to lead the Philippines and focussed on benefitting the public. I then took an economics class on how perfectly competitive firms make output decisions. Because a perfectly competitive firm must retain the prevailing market price of the product that they are selling, if they wish to be profit maximizing, then they can increase their output to make total revenue greater that  total cost at the greatest amount or have total revenue be less than total cost by the smallest amount to benefit the firm while staying the the perfectly competitive market. After that, I took a government class on how U.S Supreme court justices are appointed which goes by three steps. 1) The president nominates a candidate 2) The senate must approve nomination and 3) The president must formally dress the candidate to court. Next, I took a quiz on commas in dialogue, tag outs, dress, and yes and no responses for my grammar class. Then, to finish off the day, I read some of “The Beauty Myth” on how the “beauty” in the world is defined by women’s looks and how much they change their physical appearance to be considered “beautiful.”

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Day #172

          Today I started with a Math class on graphing sinusoidal functions. I started off with a test on deriving the period from the graph of a sinusoidal function. After that, I watched a video on transforming sinusoidal graphs by adding a vertical stretch and a horizontal reflection to the base equation      y=sin (x). In this function, the visual graph ranged form -2pi to 2pi. Before I graphed the function, i wrote down all of the coordinates. I used the x values between 2pi and -2pi and then graphed it on a cartesian plane. I then graphed the function y=2sin(x). Because the 2 was added to the equation, the function experienced a vertical stretch as the amplitude stretched by a factor of two. After that, I graphed the function y=sin(-x). This caused the function to experience a horizontal reflection as it moves, approaching positive infinity on the x axis. Then, I graphed the whole function, y=2sin(-x). Relating to the original y=sin(x) function, the function as a whole experiences a vertical stretch and a horizontal reflection as I add coefficients and negative signs to the equation. Next, I watched a video on transforming cyclical graphs with vertical and horizontal stretches. I started with the equation y=cos(x), which starts at one and continues from there. I then changed the function to y=cos1/3x. By using KCF, the period increases by a factor of 3, this causes the function to experience a horizontal stretch because the period expands. I then altered the function even more by changing it to y=-2.5cos1/3x. because it is a negative 2.5, the function is flipped and instead starts at -1. The amplitude then increases by a factor of 2.5 concluding that there is a significant difference between the original cyclical function. I then watched another video on graphing sinusoidal functions and how to find the phase shift and vertical shirt of a sinusoidal function. All you have to do to find the P.S., you must take -c/d and simplify if needed. In order to find the V.S., all you have to do is take d in the equation. After that, I did a French lesson on Duolingo followed by a Chemistry class on Buffers. Buffers help to maintain and restore the pH balance where it it necessary. Buffer solutions consists of weak bases and acids to react with strong acids and bases when introduced to a reaction. This is beneficial to all mammalian systems. For example, human blood pH must range from 7.35-7.45. When there is an influx of hydronium into the blood, using Le Châtelier’s principle, the reaction will compensate for that influx, they are generally incorporated in a buffer solution. The same can happen when there is an influx of bases, the reaction will simply move to the right and restore proper pH or else the blood may become too alkaline or acidic. I then took a space science class on a history of Earth’s climate. When Earth first came to be, there was an abundance of ammonia and methane which caused it to be very hot. Once Oxygen-Production Cyanobacteria was introduced, the Earth cooled and life was capable of sustainability by Oxygen. Once these new elements were introduced, the Earth became practically a big snowball. These polar opposite states of the Earth are called the Greenhouse climate and the Icehouse climate and have become less extreme over the years. Our huge contribution to global warming is creating our current Icehouse state to move to the Greenhouse state early on which can have severe environmental impacts. Earth has sustained itself through many hard times and can most likely recover from our impact but the question is, can we recover from our impacts? After that, I took an environmental science class on how livestock agriculture contributes to air and water pollution. Manure and Urine are high in Nitrogen and Phosphate which can end up in ground water and surface water systems which can lead to eutroficaiton and contaminated water. Also, chemicals, hormones and antibiotics are being applied to the animals but their microbial resistance has strengthened and therefore has little to no effect on them but certainly the environment. Animal waste and metabolism exerts gases that contribute to global warming such as Methane. Feedlots can minimize environmental impacts, if properly managed but it is very hard to do so. I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Martha Graham who contributed a lot to modern, twentieth century dance through her expression of emotion. Her movements conveyed emotion that had not been articulated in ballet before, abdominal contractions articulated inner tension that was foreign but intriguing to audiences. After that, I took an economics class on perfect completion and why it matters Perfect competition is when there are many sellers with the same product, there is easy entry and exit in and out of the market and the sellers cannot raise prices or else they won’t get any sales. Perfect competition matters so that the perfectly competitive markets can thrive and provide a very limited amount of freedom to the sellers which is beneficial to the consumers. After that, I took a grammar class on the Oxford comma which is used as punctuation in long lists to steer clear of confusion. I then read “The Beauty Myth” on how many women live to look a certain way and remove certain aspects of themselves to please the Patriarchy.

[rowanstree-blog]

Day #171

          Today I started with a Math class on finding the period of sinusoidal functions. Firstly, I started off with a video on deriving the period of a sinusoidal function from its graph. In order to do so, I took the minimum x-value and subtracted the maximum x-value from it. Based on the graph, I can conclude whether the given amount of time in the function is either complete or not yet. if it is only 1/4 of the way until the function repeats itself, then I take the number I got and multiply it by 4. If the function is only 1/2 of the way there until it completes one full cycle before repeating again, then I take the number I got and multiply it by 2. I did this operation with decimals and radians. After that, I watched a video on finding the amplitude and period of a sinusoidal function from its equation. A sinusoidal function is based on the equation y=asin(bx-c)-d.  The amplitude of a sinusoidal function is the coefficient of the sine function, a, in absolute value. In order to derive the period from a sinusoidal function, you must look at the coefficient of x, b, and find the absolute value of that. Once that is done, you must put it under 2pi and simplify if needed. I then took a practice test on finding the period of sinusoidal functions from their equations. Then, to finish up the Math lesson, I did a review on the midline, amplitude, and period which can all be derived not only from a functions equation but also its minimum and maximum values as well as other things. I then did a French lesson on Duolingo followed by a Chemistry class on comparing the reaction quotient, Q and the equilibrium constant K. In this video, I took a reaction and after given the molar concentrations of the reactants and the products, I was asked if and how the total pressure would change as the system approaches equilibrium at a constant pressure. First off, I calculated the reaction quotient of my equation and then compared it to the equilibrium constant. In this case, the reaction quotient was smaller than the equilibrium constant so the reaction would have to favor the products in order to reach the equilibrium concentration. In this case, there is three mols of reactants to form one mol of products so because I must favor the products to reach equilibrium, the total pressure would decrease considering all of my products and reactants are in the gas phase and the total pressure of a reaction is determined by the mols of gas in the system. In conclusion, for the given reaction, the total pressure decreases as it favors products and approaches equilibrium. I then took an environmental science class on how high meat consumption yields an ever-increasing amount of feedlot agriculture. Feedlots are either huge warehouses or pens that help deliver energy-efficient foods to livestock in extremely high densities. As industrial agriculture expands, so does the use of feedlot agriculture which confines animals to a smaller amount of space in order to create lower grazing impacts and become more economically efficient as well as increase the overall food production. This has had some benefits but intensified animal production through feedlots model other environmental impacts including air and water pollution, just to name a few. I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Rose Schneiderman who rose to leadership on the movement of labor unions. She promoted better education, hours, wages, protection laws and respect to the working woman, including immigrants. Being a woman immigrant herself, she experienced these things first hands and felt it is necessary for the women of the world to have these things. I then took an economics class on Why parties in a cartel will cheat. A cartel’s goal is to increase prices and therefore economic gain while decreasing overall competition. Many cartels cheat in order to succeed this but can result in violence. The equilibrium scenario is in which marginal revenue equals marginal cost but they hope to increase the cost to provide them a greater benefit in the long run. I then took a grammar class on Appositives which are noun phrases that clarify or redefine its antecedent. In the sentence, “My older sister, Jenny, is starting college in the fall.” The appositive is Jenny which shows who my older sister is, the appositive clarifies its antecedent. I then read some of “The Beauty Myth” which articulated how women are expected to look a certain way and hate certain parts of themselves in order to please society. They are expected to torture themselves into starting a diet or even stop eating to get that “idealistic” body type that they think they need to have in order to be happy. 

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Day #170

          Today I started with a math lesson on an introduction to amplitude, midline and extremes of sinusoidal and cyclical functions. I started off the lesson with a video on the features of sinusoidal functions. The midline of a function is a horizontal line where exactly half of the function is on top and half i is on the bottom. The distance between the maximum point and the midline and the midline and the minimum point is called the amplitude. And order to find the midline of a sinusoid given the maximum point and the minimum point of the function, you must add them and divide them by two. In order to find the amplitude given the maximum point and the midline, you must subtract the amplitude from the maximum value and divide it by to. In order to find the amplitude given the minimum point and the midline, you must subtract the minimum point from the midline and divide that by two. I then took two quizzes, one on finding the midline of sinusoidal functions, and one on finding the amplitude of sinusoidal functions. I then watched a video on finding the midpoint and amplitude from the equation of a sinusoidal function. The equation of a sinusoidal function is equal to y=asin(b(x-c))+d. In order to find the amplitude, all you have to do is find the absolute value of the number before sin. When finding the period, which is how long of a change in x to you have to go to repeat the cycle, you have to use the formula 2pi/b. All you have to do is substitute in b, and simplify if needed. When finding the midline of a sinusoidal function, you have to look at d and write it as y=d. Also, when finding the frequency of a sinusoidal function, you must take the reciprocal of the period. When finding these in a cyclical function, do the same exact thing you would in a sinusoidal function except the graph is a cyclical graph. I then took a short French lesson on Duolingo followed by a Chemistry class on the reaction quotient Q. The reaction quotient Q is the measure of the products and the reactants at any given time. What this means is that you can use the reaction quotient for a reaction in or out of equilibrium and even if you don't know. How you solve it is the same exact way you would solve for the equilibrium, constant, K except once you solve the equation, you must compare the concentrations for both Kc and Qc. If Qc=Kc than the system is in equilibrium, and the equilibrium concentrations are the same. If Qc>Kc, then the products are more favored in the reaction and in order to get the reaction to its equilibrium concentration, you must favor the reactants, i.e react in the reverse direction. If Qc<Kc, then the reactants are more favored than the products and in order to get the system to its equilibrium concentration, you must favor the products, i.e react in the forward direction. I then did an environmental science class on how our food choices indirectly correlate with with our energy choices. For example, considering when we eat, 90% of the energy derived from the thing we consume is lost through cellular respiration. If you take a cow, fore example, and feed it a piece of grain, and then you eat the cow, the energy derived from the grain was lost through cellular respiration and the cow’s metabolism. Eating things higher up the food chain take up more resources i.e growing plants, allowing grazing area for the animal that eats that plant etc,. Therefore, eating lower on the food chain can result in a smaller ecological footprint, more solar energy is put to use, is more energy efficient and Earth can eventually increase its carrying capacity because we are having less environmental impact. I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Marie Curie who was the first world-famous woman scientist and first women to win two Nobel Prizes, one in physics and one in chemistry. She devoted her life to radioactivity and discovered polonium and radium. Her high exposure to radioactivity resulted in her death of lukemia. I then took an economics class on monopolistic competition which is similar to perfect competition and is a mix of perfect completion and a monopoly. In a monopolistic competition, there are many sellers with easy access and exit to and from the market but their products are slightly different which can result in a bit of price control but no too much or the consumers will switch to a close substitute. After that, I took a grammar class on punctuating a list to make sure that items are separated to avoid confusion. Then, to finish off the day, I read some of “The Beauty Myth” on how age, size and diet are types of sin that should be covered up from society because “it is something so be ashamed of.”

[rowanstree-blog]

Day #169

          Today I started with a math class on on the Pythagorean identity. The pythagorean identity is derived from the Pythagorean theorem which is derived  from the equation of a circle. The Pythagorean identity is the pythagorean Identity with the hypotenuse is equal to 1. Once you change the x and y variables to cosine of theta and sine of theta, this identity, the Pythagorean identity can be applied to trigonometric identities of special angles in a unit circle. Because the hypotenuse is equal to one, it is easy to derive either cosine of theta or sine of theta once you know sine of theta or cosine of theta. Once you know what one of them is equal to, you can either add or subtract it from one after squaring it to get either cosine^2 theta or sine^2 theta. You then take the positive or negative square root of this answer and once you fins out what quadrant it is in, you can find out if your answer is either positive or negative. To start off the lesson, I watched a video on the proof of the Pythagorean identity. I then watched another video on using the Pythagorean trigonometric identity with a few examples. After that, I did a practice test on the Pythagorean identity  In this, I derived that fact that if your terminal ray is in the first quadrant, both sine and cosine are positive. If your terminal ray is in the second quadrant, your cosine is negative and your sine is positive. If your terminal ray is in the third quadrant, then both your sine and cosine are negative. And if your terminal ray is in the fourth quadrant, then your sine is negative and your cosine is positive. I then took a quiz on that and then watched a video on how to memorize trigonometric identities of special angles, from yesterday. After that, I took an Algebra I class on testing solutions for inequalities. Next, I took a french lesson on Duolingo followed by a Chemistry class on a worked example of Le Châtelier’s principle. In this lesson, I used the reaction CaCO3(s)-\-/CaO(s)+CO2(g) and applied different scenarios in which I had to determine if it would skew the reaction out of equilibrium. First, I was asked if I added CO2(g) then would it skew the equilibrium? Yes, it does, in order to restore the equilibrium, I would have to favor the reactants and go in the reverse direction to fix the concentrations. Because CO2 is the only gas, the equilibrium constant of this reaction is determined by the concentration of CO2 in the reaction. I then was asked the question is changing the volume would skew the equilibrium, If I increased the volume, then the pressure would decrease so therefore the forward reaction would be favored to restore the system’s equilibrium. Other things like adding a catalyst or an inert gas would not alter the equilibrium, because it is not a determinant of either the equilibrium constant of the expression or the partial pressure of CO2. I then took a space science class on the Milankovitch cycles which are three changes to the Earth’s cycle that would have dramatic effects on our climate, seasons, insulation, etc,. These include the 95,000 year stretch, the 42,000 year tilt and the 21,000 year wobble. After that, I took an environmental science class on how domestication and consumption of animal products has risen significantly as there has been an increase in wealth of developing nations. This can have a variety of impacts our environment, population etc,. I then did a quick exercise followed by an hour long lunch. After that, I took a women's history class on Lakshmi Bai who was a Rani of Jhansi in India and was an early heroine as she fought to release India from Britain’s rule. She sought independence while married and once her husband died, took the job of recruiting armies and risked her life for India’s freedom. After that, I took an economics class on the prisoner’s  dilemma and Nash Equilibrium which is when the interaction between two participants determines their choice in a certain scenario. This is also used in game theory which is completion an how businesses decide to change their prices to benefit their economy while keeping necessary competition. I then took a grammar class on 3 ways to end a sentence which an articulate the emotion, urgentness, unknowingness, etc,. Then, to finish off the day, I read some of “The Beauty Myth” on how the beauty myth is derived a lot from Judeau-Catholisism which articulates that women are “imperfect” and “In need of fixing” and that “their means to live is to please the patriarchal society’s view of them.”

[rowanstree-blog]

Day #168

        Today I started with a math class on trigonometric values of special angles. I started off with a video on trigonometric values of special angles. In this lesson, I went over the radian measures of different terminal rays on the unit circle. I then derived an equilateral triangle of an angle with theta equal to 45 degrees which is pi/4 radians. I used that information to derive the angle measure of another part of my triangle and then used the pythagorean theorem to find out the side lengths of the triangles. After that, I found the sine, cosine and tangent of theta. I then watched another video on that with all different types of special triangles including equilateral, scalene and isosceles. I then watched a video on finding the sine, cosine, tangent, cosecant, secant and cotangent of special angles. After watching those videos I found that the sine of pi/4 (45 degrees) is equal to 1/sqtr(2). Therefore the cosecant of that is sqrt(2). Because cosecant, secant and cotangent are the reciprocals of sine, cosine and tangent. Also, the cosine of pi/4 is equal to 1/sqrt(2) and the secant is therefore equal to sort(2). The tangent of pi/4 is equal to 1 and cotangent would also be equal to one because the reciprocal of one is one. Then, the sine of pi/6 is equal to 1/2 and cosecant is equal to two. Cosine of pi/6 i sequel to sqrt(3)/2 and secant is equal to 2/sqrt(3). The tangent of pi/6 is equal to 1/sqrt(3) and the cotangent is equal to sqrt(3). The sine of pi/2 is equal to 1 and cosecant is equal to one as well. Also the cosine of pi/2 is equal to 0 and therefore secant for this angle is undefined. The tangent of pi/2 is undefined so therefore the cotangent is equal to 0. Lastly, the sine of pi/3 is equal to sqrt(3)/2 and the cosecant is equal to 2/sqrt(3). The cosine os pi/3 is equal to 1/2 and the secant is 2. And the tangent of pi/3 is undefined so therefore the cotangent is equal to 0. I then did a French lesson with my grandmommy followed by a French lesson on Duolingo. I then took a Chemistry class on Le Chàtelier’s principle which is an equilibrium law that is applied to reversible reactions when its equilibrium is disturbed. Because of this disturbance, the reaction will move either left or right in order to counteract that disturbance. A disturbance in equilibrium can be a result in either a change in pressure, volume or temperature. It could also be the result of a dilution of either a product or a reactant or the addition or subtraction of chemicals. I this video, I went over all of the possible equilibrium disturbances that can occur in a reversible reaction. For example, if I take the Haber process which is when one mol of nitrogen reacts with three mols of hydrogen to create 2 mols of ammonia, all in the gas phase. If the amount of Hydrogen increases in the reaction, then both hydrogen and nitrogen will go down as the amount of ammonia goes up because the reaction is occurring to create a higher molar concentration of the products and lowering the molar concentration of the reactants to therefore reach a new equilibrium. In conclusion, If the reactants are more abundant than the products, then mover the reaction to the  right and if the products are more abundant than the reactants, than move the reaction to the left. I then took an environmental science class on how the debate over genetically modified foods includes more than science. Genetic modification gives people opposed to it less control over what they can eat due to global food supply being dominated buy agrobiotech companies that corrupt the independence  and freedom of small farmers. Much of the research done to test the safety of genetic modification has been either overrun or funded to protect such institutions. Due to genome invasion and contamination of native crops, patented genetic sequences are unintentionally ending up in farmers cops who then are sued by big corporations like Monsanto for “taking their product.” I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Tz’u hsi who was the empress of China. Her intelligence and literacy quickly promoted her from concubine to empress. She had abused her power but established many rules and regulations that impacted the lives of several women then and now. I then took an economics class on economic growth which is when there is an increase in goods and services that can improve an economy and cause it to thrive. After that, I took a government class on McCarthyism which is when a suspected communist is summoned before a government without either a committed crime or a convicted one. They are asked to incriminate friends, deemed disloyal and questioned. If they do not  cooperate, they are either imprisoned or lose their jobs. I then took a quiz for grammar on commas and introductory elements followed by reading “The Beauty Myth” on how the beauty myth has become a religion with dieting sins, idols, beliefs, rituals etc,.

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Day #167

          Today I started with a math class on the graphs of the trigonometric functions, sine, cosine and tangent. I started the lesson of with a video on the graph of the sinusoidal function, y=sin(x). I started with a question asking what the domain of the sinusoidal function was. The domain is all sets of valuable inputs for the function. I used the unit circle and a y, theta graph to wrote and plot the sinusoidal equation. Once I did all of that, I concluded that the domain of this function is (-1,1) including -1 and 1. I then watched a video on how to construct the graph of y=tan(x). I concluded that the graph would have a vertical asymptote every five radians and approach positive snd negative infinity while doing so. Considering the tangent of theta is the slope of the terminal ray, I just had to take the sin of theta over the cosine of theta to find out the tangent of several pi radians. I then watched a video on intersection points of y=sin(x) and y=cos(x). In this video, I wrote terms of the table in terms of radians for both the cosine of theta and the sine of theta on the unit circle and graphed accordingly. After that, I watched a video on basic trigonometric entities involving symmetry. In the lesson, I drew several terminal rays in all four quadrants of a graph in a unit circle. I then wrote down which sine and cosine functions were equivalent and then followed it up with a video on tangent identities which is the proportion of a sin function over its equivalent cosine function. Next, I watched a video on sine and cosine identities involving symmetry in which I took random sine and cosine functions and determined if they were equal to each other. I then watched a video on tangent identities periodicity. In this video, I did pretty much the same thing except I determined if its slope, or tangent was equal to 1/2. After all of that, I took an Algebra 1 class on the Quadratic equation sample problems as a refresher. I then took a French lesson on Duolingo followed by a Chemistry class on how to fill in an ICE table according to the equilibrium constant expression of a reaction. I stands for initial concentration which should be given in order to calculate E which stands for equilibrium concentration which can be found after adding or subtracting I and C which stands for change in concentration. First, you must write all of your initial concentrations If your equilibrium constant is larger than or equal to 10^4, then your products are favored. If Kc is less than or equal to 10^-2, then your reactants are favored. This information can help you figure out which side is equal to zero which will later determine how you fill in your ICE table. Depending on which side is favored, you must add or subtract the molecules stoichiometric coefficient of x. Add, subtract and solve for x to find out your equilibrium constant. After that, I took a space science class on a simulation video of Earth’s tilt and rotation which determines its season. This information can contribute to the reasoning behind why the equator doesn't have seasons. It is because it is never turned away from the sun, like us hence our four seasons as we turn towards and away from the sun. I then took an environmental science class on various studies launched and questions asked on the transgenic contamination of Mexican maize. Even though there have been both false positives and false negatives in order to protect and expose the firms causing this transgenic contamination. It is true that transgenic contamination is becoming more and more abundant and the effects are still unknown. I then did a quick exercise followed by an hour long lunch. After that, I took a women’s history class on Mary Harris “Mother” Jones who was a labor organizer who played an outspoken role in the world that was mislead by her appearance. She was a passionate and resilient woman that fought for what she believed in and due to that, became known as “the most dangerous woman in America.” I then took an economics class on Allocatice efficiency which is when the marginal cost is equal to the marginal benefit and I did an example that showed this both literally and graphically. Next, I took a grammar class on commas and introductory elements which are followed by a comma and are placed in the beginning of a sentence. After that, I read some of “The Beauty Myth” on how markets rely so much on feminine appearance more that the actual product to “appeal” to the reader while they are actually making them more self conscious.

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Day #166

          Today I started with a math class on an introduction to radians, using the unit circle. The unit circle is a circle that has a radius of one and a circumference of 2pi. You can divide your unit circle by varying numbers togged the number of radians equal to the number of degrees. 2pi radians is a full rotation around a unit circle which is equal to 360 degrees. I then watched a video on converting radians to degrees. Because 180 degrees is equal to pi radians, what you have to do is multiply your given radian measure by a ratio of degrees per radian and then multiply that by 180/pi. After multiplying, dividing, and canceling common factors, if needed, you then have the number of degrees equivalent to a certain number of radians. After that, I watched a video on converting degrees to radians. Because pi radians is equal to 180 degrees, you must multiply your given degree measure by the number of radians per degree and then multiply that by pi/180. Once again, multiply, divide, and cancel common factors, if needed, to get the number of radians equivalent to that number of degrees. Next, I watched another video on converting radians to degrees followed by a practice quiz on conversions between both of them. After that, I watched a video on radian angles in quadrants followed by a lesson on the unit circle definition of sine, cosine and tangent. As I stated earlier, the unit circle has a radius of one and its angle=theta. Using the pneumonic SOH CAH TOA, sine is equal to opposite over hypotenuse, cosine is equal to adjacent over hypotenuse and tangent is equal to opposite over adjacent. Relating to the unit circle, the cosine of theta is equal to the x coordinate where the terminal side of the angle intersects the unit circle. The sine of theta is equal to the y coordinate where the terminal side of the angle intersects the unit circle. Finally, the tangent of theta is equal to the sin of theta/cosine of theta which is equal to the y coordinate over the x coordinate. I then took a practice quiz followed by a review on the unit circle definitions of sine, cosine, and tangent. After that, I took a French lesson on Duolingo followed by a Chemistry class on the small x approximation for a large equilibrium constant, meaning that equilibrium is about 100% favored on the product side which therefore means that Kc >~ 10^4. I followed the four steps to calculate the small x approximation and calculated for x. In this video, it articulated the importance of following each step or else your answer is incorrect. After that, I took an environmental science class on what the benefits and impacts are of genetically modified crops. As genetic modification becomes more common and biotechnology expands, people are becoming more wary of the danger that may follow due to genome alteration. If a plant is genetically modified to resist insect harm, then the use of insecticides will go down, but, if a plant is genetically altered to resist a certain herbicide, then herbicide use will flourish. This part clearly exemplifies a cause for worrying but what about the actual impacts of genetically altered DNA. Well, people believe that as genetic modification expands further and further, our native genetic diversity will be lost which may be necessary to have one day in the nearby future. In conclusion, altering the genomes of crops on a large scale has been fairly recently applied and the increase in herbicide application is clearly bad for our environment. Genetically modified organism’s altered genetic code can spread across vast amounts of land and therefore lower biodiversity and genetic variation of native plants. In Britain, they launched several studies to figure out the impacts of genetic modification which was conclude to be complex but there needs to be a precautionary principle applied to biotechnology advancements until we clearly know its long term affects. I then did a quick exercise followed by an hour long lunch. I then took a women’s history class on Toni Morrison who was an editor and author of several works of literature on the lives of African Americans in the highly segregated South. Through this, she won various awards and recognition and conveyed to the black community to know what the past was like in order to benefit themselves today. I then took an economics class on increasing opportunity cost which is when you get more of a certain product and therefore the opportunity cost for the other product is becoming exponentially larger. I then took a grammar class on commas used in space and time, addresses and dates, to formally address a matter. Then, to finish off the day, I read some of “The Beauty Myth” which articulated how “beauty advertisements” bring women together and tear them apart, all because of the “beauty myth.”

[rowanstree-blog]

Day #165

          Today I started with a Math class on graphs of rational functions. I started with a video on graphing rational functions according to their horizontal and vertical asymptotes. Like I had articulates in my previous blog post, In order to find the horizontal asymptote, you must multiply the numerator and the denominator by the highest degree term in the function and simplify from their while stating the limit as x approaches positive and negative infinity. Then, you must simplify from there. To find the vertical asymptote, you must factor the numerator and denominator and cancel out like factors. If a term cancels out, it is therefore a removable discontinuity or a “hole.” After that, you can look to find out the vertical asymptotes and make sure you include your point of discontinuity when stating the simplified function. I then watched a video on graphs of rational functions: deriving the y intercept. In order to find the y intercept, you have to set all x terms equal to zero and calculate what is left to find out the y-intercept. This point is where the line cuts across the x-axis. After that, I watched a video on the graphs of rational functions: deriving horizontal asymptotes which you can do with the method I articulated a few sentences ago. Next, I watched a video on graphs of rational functions: vertical asymptotes when the numerator isn’t stated. When finding the graph of this function you can take your factored denominator and find a graph that either has two vertical asymptotes or one vertical asymptote and one vertical discontinuity. After that, I watched a video on graphs of rational  functions: zeros. Zeros are a point that crosses any axis and can be found when both the numerator and denominator is found so we can cancel out the removable discontinuity from the possibilities. Next, I watched a few videos on graphing rational functions which can be done by finding all of the things that I was learning how to find in the previous videos. I then took a French lesson on Duolingo. After that, I took a Chemistry class on the Small x Approximation for a small equilibrium constant derived from the equilibrium calculation. The Small x Approximation is an approximation method that is used to solve the equilibrium concentration problems. This approximation works best when the reaction is more favored on one side, either the products or reactants. The reaction is more favored on the product side when Kc is greater than or equal to 1,000. The reaction is more favored on the reactant side when Kz is less than or equal to 0.001. The step by step process for solving the small x approximation is 1) Assume reaction is 100% favored on one side of the reaction 2) write and fill in an ICE table (initial concentration, change in concentration, and equilibrium concentration.) 3) Solve for x, assuming x is really small. 4) CHECK YOUR ANSWER. I then did a practice example on this followed by an environmental science class on how biotechnology is transforming the products around us. Genetic modification is fairly new to scientists and once scientist proved that in this short run, it is not harmful it dominated our agriculture. Recombinant DNA in plants and animals helps to prevent against disease, resist pesticides, grow faster etc,. This can help in the short run but once all crops and livestock are genetically altered with recombinant DNA, there is no, currently known, way to reverse that process to restore the native genome and our genetic diversity. I then went for a bike ride and then had an hour long lunch. Next, I took a women’s history class on Deborah Sampson who entered the U.S  Continental army after becoming a school teacher and dreaming of traveling the country, meeting new people, and receiving a higher compensation. Unlike many women during that time, Deborah decided to fight for independence and entered the war as Robert Shurtoff. She had fought long and hard but and unhealed wound led her to a terrible fever and her identity was discovered. She was honored and then discharged and sent her latter years traveled around New England, astounding people with her adventures in war. I then took an economics class on opportunity cost which is the loss of potential gain of one product for the advantage of another. I then took a grammar class on salutations and valedictions which is where you place commas to either separate the greeting from he body text or from the goodbye from the sender. I will later read some of “The Beauty Myth.”

[rowanstree-blog]

Day #164

          Today I started with a math class on discontinuities of rational functions which can be derived from a function after factoring and simplifying it. I started with a video on discontinuities, vertical asymptotes and zeros of a rational function. If you have the function f(x)=x^2-2x-24/x^2+10x+24,  you would simplify the numerator and denominator to f(x)=(x-6)(x+4)/(x+6)(x+4). Once you cancel out the x+4′s, you know know your removable discontinuity that when graphed, is shown by a circle on the line to show where the graph is undefined, at x=-4. In order to find out what term makes the expression equal to zero, all you have to do is look at what is left in your numerator, in this case, x=6 would be our zero. Finally, in order to find your vertical asymptote, you must look at what is left in your denominator and in this case it is x=-6 which is when x approaches positive or negative infinity and asymptotes our vertical asymptote. After that, I took a practice quiz followed by a video on analyzing the graphs of rational functions in order to describe a statement that articulates the asymptote. I then watched two videos, one on how to find the vertical asymptote and one on how to find the horizontal asymptote. In the video on how to find the vertical asymptote and graph the functions by that asymptote, I learned that by taking your rational function, you must take the denominator to find your asymptote and graph it and then substitute different possibilities for x. In order to find and graph a horizontal asymptote, you must take the highest degree term in either the numerator or the denominator and then multiply every term of the numerator and the denominator by one over that degree. After completing that, cancel out the remaining numbers over the term to zero and write what is left as your horizontal asymptote. Also, remember to always right your limit as x approaches positive or negative infinity. If the highest degree term of the function is in the denominator than y=0. If the highest degree term in the function is in the numerator than there is no horizontal asymptote. Lastly, if the numerator and denominator both have the same highest terms, than y=whatever the leading coefficients are. I then did a French lesson on Duolingo followed by a Chemistry class on calculating the equilibrium constant, K with partial pressure which is denoted as Kp. Kp i the ratio of product and reactant concentrations in terms of partial pressure. It is written as the equation Kp=(PC)^c(PD)^d/(PA)^a(PB)^b. You can look up the partial pressures to find out what it is and to solve the equation. When finding out the relationship between Kp and Kc, use the formula Kp=Kc(RT)delta(n). Delta(n) is the molarity of product gasses minus the molarity of reactant gasses. I then did a few examples followed by a Space Science class on the Mohorovicic seismic discontinuity which is the boundary between the Earth’s crust and its mantle. When he discovered that the seismograph that was 200 kilometers away from an earthquake, and that its linear graph shifted from time=distance to distance exceeding time. He was the first to find out that the Earth had different layers and therefore different densities. When this was graphed, he came to the conclusion that as seismic waves travel downwards, they get refracted and gain velocity and therefore exceed the original liner slope of y=x or time=distance. I then took an environmental science class on how genetic engineering is like and unlike traditional breeding. Traditional breeding combines two of the same or similar species to reproduce and organism with desired traits. In genetic engineering, the proceeds in unnatural and needs actual displacement and placement of genetic code to create the desired organism and can combine extremely different species. Traditional breeding also takes organisms as a whole but genetic engineering takes the DNA of an organism. But they are similar because they combine desired traits to create something whether having to do with disease resistance, fast-growth or whatever it may be. I then took an hour long lunch followed by a women’s history class on Marie Mitchell who was the first woman astronomer and she lived vicariously through her students throughout the science realm. I then took an economics class on the Production Possibility Frontier which articulates different choices you can make and the outcomes. Once graphed, any point outside the graph is impossible and any point inside the graph is possible but inefficient. After that, I took a grammar class on if it is okay to start a sentence with a conjunction. And, yes it is ok, as long as you link them, being a dependent clause, with an independent clause in order to make the sentence grammatical. Then, to finish off the day, I read some of “The Beauty Myth” which talked about how magazines are guiding peoples lives in how they live, dress, diet, clean etc,.