#solving exponents

[math-journal2]

<— x —>

Unit 10: Part 4

Application Problems

*each pic own problem

.

Exponents

Investment exponent problem

Increase of 1.35% interest per year

f(x) = a(1.0135)^x

Or a(1 + 0.0135)^x

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Compound Interest

Always simplify the (1 + r/n) part

Will lose credit otherwise if equation is an answer

Exponent Normal

Exponent e^x

-Half Life

Newton’s Cucking Law of Cooling

Be very aggressive in labelling

It may look like this..

Or it may decide it wants to stab you and look like this

Key:

Determine known variables

Whatever is left is unknown

Unlike with Decibel and Richter test, you don’t need to keep 2 different equations in your head.

Think: PROCESS OF ELIMINATION

.

.

.

LOGS

Richter and Decibel (Lv2)

Richter Scale

2 things in mind

It’s a hot mess.

Remain calm, it’s like any other new equation. This takes time to sort out. Then you’re like AHA!

.

Note: 10^-4 on bottom

Variables set up:

Example 1: know mag, want strength ratio

m (sub 1) = magnitude of ocean

m (sub 2) = magnitude of city

I (sub 1) = intensity of ocean ??

I (sub 2) = intensity of city ???

Strengh ratio = ???

_

Equation: Richter scale and..

ratio of strength =

I (sub 1) / I (sub 2)

Strategy:

Want: strength ratio

Problem: no intensity #’s

Solution: solve for intensity

Later: solve for strength ratio

.

.

Example 2: know 1 mag + strength ratio, want other mag

m (sub 1) = magnitude of ocean ???

m (sub 2) = magnitude of city

I (sub 1) intensity of ocean ???

I (sub 2) intensity of city ???

strength ratio = #

_

Equations used: same + …

I (sub 2) = I (sub 1) * strength ratio

Then solve for m (sub 2) with that

Aka. Solve for easy stuff the work up

.

Solve for magnitude

Decibel

Example 1: 2 diff decibels, want ratio of intensity

B (sub 1) = sound of drill

B (sub 2) = sound of whisper

I (sub 1) = intensity of drill ??

I (sub 2) = intensity of whisper ??

Strength ratio = ???

_

Equation: normal one

Strength ratio = B[1] / B [2]

_

Strategy: Similar to richter scale

Think: what do I want

Then: what’s in my way

Last: how do I get past it

These are multi part problems that look overwelhming at first seeing all the missing variables. The key is solve what’s easy, then try the tricky stuff. Sometimes you can bs your way through these problems.

Note: 10^-12 is good for helping you find the intensity.

Note: solve what variables you can before popping in numbers.

Page 31

[two-calicos-in-a-trenchcoat]

Because I just saw that post again and im still mad about it

[gothicprep]

i also don't mean to be harsh, but i don't think you guys have the grasp on the order of operations you think you do :/

[brandboosterx]

In this video, we delve into the art of solving logarithmic equations with different bases, demystifying the process for you step by step. Whether you're a student brushing up on logarithms or someone facing more complex problems, we've got you covered. Understanding how to work with different bases is crucial when faced with logarithmic equations. We break down the techniques, providing clear explanations using frequently used words to ensure that you grasp the concepts effortlessly. No more getting stuck on those seemingly perplexing logarithmic problems!

[charmingcritter]

This is a call for help

If any one knows about college algebra please hit me up. My first unit test is coming up and I live in fear now

[thevoicefromanotherworld]

"PLEASE, DON'T STOP"

Another fic with Dave, cause I need him so bad every day, every night from the kitchen door to the bathroom seat love him

I hope you like it!

WARNING : EXPLICIT SMUT UNDER THE CUT

Dave walked into the library to study for Algebra, a subject he had an exam on next week. He looked around to see where there was an open spot. Then he saw you. You were in the same class as him, and he was 100% sure that you hadn't noticed him.

I mean, he always went unnoticed by everyone, especially by girls. You were his crush, that unattainable person he'd never talked to. He and you belonged to a totally different league: he was the nerd, and you were the typical girl who always gets invited to parties first.

All these thoughts were mixing in Dave's head, while his legs moved towards where you were.

Your mere presence made him very nervous, but the spot next to you was the only free one at the study table, so he gathered his courage and placed himself next to you, holding on tightly to the strap of his backpack.

You looked up at him, your eyes locked with his with curiosity and something else he couldn't quite place.

-H-hey –he greeted, swallowing hard- we're going to algebra together, I sit two seats behind you –he shook his head embarrassed- maybe this sounds a little weird, but would you mind if we studied together? These last few problems are costing me, and I need help to raise my average grade… -he paused for a moment before adding- although w-well, if you're studying with someone else or you're not taking algebra right now, I can go

-Relax, I'm not taking algebra right now, but I'll help you anyway –you said, smiling kindly-

-Really? –he asked surprised- Thank you very much! –he exclaimed before turning to the rest of the students at the other tables- I guess I should lower my voice –he laughed nervously- wait, I know a place where we can be where we can talk normally –he looked at you attentively- Do you want to…?

-God, yes –you murmured- I'm sick of talking in whispers –you said beginning to gather your things- let's go

Dave nodded and led you to a room where there were a couple of bookshelves on the sides and a large table in the center. He closed the door behind him when you entered and put the “quiet, we're studying” sign on the outside so no one would come in.

-This is better –he looked around the room- we still have to speak quietly because we're in a library, but not too much because this is a more private room –he cleared his throat at your curious gaze, while he took out the book and notes from his backpack- okay, let's start –he said, but when he went to grab a pencil he frowned while cursing under his breath- shit –he growled- I forgot my pencil case –he complained- What kind of person goes to study and forgets their pencil case? Can I borrow a pencil? –he asked- I promise I'll give it back to you when we're done

-Sure –you said handing him the one you always carried as a spare-

-Thanks –he murmured, a slight blush flooded his cheeks, making you smile- okay, the exam is supposed to be on topics three through five, right?

-Yes - you said after checking the agenda where you had written it down-

-Okay - he opened the book and pointed to a couple of operations - this is what I have been having the most trouble with these last few weeks - he indicated, resting the pencil on the exercise, he looked at you out of the corner of his eye, the light in the place made his intense blue eyes shine brightly - Do you think you can help me?

-Of course – you said, taking a separate sheet of paper to do the necessary calculations-

-Great – he murmured, watching you approach him, your shoulders brushing-

-You should start by solving the parentheses – you began, pointing to the symbols as you spoke- then, the exponents, then, the multiplications and divisions, and finally the additions and subtractions

-Okay, this makes a lot more sense – he murmured, observing the calculations you were doing on the sheet of paper in your notebook- you are very intelligent – ​​he said, gradually overcoming his shyness- we should study more often – he said, leaving the question hanging in the air-

-That would be nice – you said, and Dave almost fell off his chair in shock-

Was that really happening? “Please, someone pinch me,” he thought

-Okay… mhmm, could you…? You could give me your number, w-to keep in touch and all that -he said taking his phone out of his jeans pocket, you noticed he had a book placed on his lap -Here -he said handing it to you -

You took it and went into contacts to save your number, before handing it back to him.

-Why do you have that there? -you asked pointing at it with your head, his face turning scarlet due to the embarrassment he felt- No reason -he murmured shaking his head -It's just that… I'm very sensitive to touch and when our fingers have touched, I think…-he swallowed hard- I think it turned me on -he confessed making you smile. God he was so cute that you wanted to pull him towards you and never let him go- Please don't think I'm disgusting or weird or anything like that -he murmured hastily-

-I think it's hot -you said approaching him, making him open his mouth wide-

-Hot? –he repeated, you nodded- I didn't expect that –he confessed-

Slowly your hand went down to the place where he had placed the book, to remove it slowly. The shape of his hard cock was revealed against the front fabric of his jeans.

You rested your hand on his thigh, getting dangerously close to him without actually touching him. A gasp came out from between his lips when he felt your touch.

-I don't think that… -he muttered- we should be doing this here -he said- anyone could find out -another new gasp- and let's be… let's be honest I-I'm a virgin, I-I don't know what I'm doing, I don't know if…

-Dave -you stopped him kindly, he made the effort to look at you- it's okay

-You know my name -he said making you smile-

-Of course I know your name, we go to class together -you murmured tracing the outline of his cock with your index finger, making him hold on tightly to the arms of the chair-

-Nobody ever comes to this place -he continued saying- but what if they do today? What if someone comes…?

-Nobody's going to come, Dave -you whispered- you put the sign outside when we came in, remember? It's just you and me -you said, getting closer to kiss him-

His lips felt soft and warm against yours.

You realized that this was probably his first kiss too, so you guided him to follow your movements, slowly.

He partially separated from you as you continued to kiss him, so the words barely came out from between his lips

-But –kiss- what happens if…? –kiss- What if we get caught? –another kiss- it will be your fault if someone finds out

-No one is going to catch us –you assured him leaving one last kiss on his lips- turn your back to me

-My…? –he asked confused before doing as you asked-

You slowly unbuttoned his jeans, letting them swirl around his legs, before pulling down his underwear as well.

His cock was released from the confines of his pants, fully erect, and ready for you to touch it.

A ragged gasp escaped his lips as you wrapped your hand around the base and began to pump him up and down, pumping him with your hand.

Gasps, moans and grunts left Dave’s lips as he slowly began to thrust his hips against your hand.

-God, that feels so good… -he murmured -I’m moving. Is that okay?

-Yes, Dave -you praised, leaning close to his ear -You’re being a good boy for me

-Please, faster -he begged, and you did. He threw his head back, his gorgeous blue eyes fixed on the ceiling of the room -Don’t stop… don’t stop… -he moaned, matching the movements of your hand with those of his hips-

-You have to lower your voice, remember? –you whispered- we're in a library

-I-it's a b-bit difficult –he complained, you smiled- b-but I'll try, I-I'll be a good boy

-I like it that way –you answered satisfied-

-I think… I-I think I'm going to cum –he said pushing hard against your hand- don't stop please… no…

But you stopped, a gasp escaped from between his lips.

-Why, have you done it? –he complained confused- I-I haven't done anything wrong, right?

-No, you haven't –you affirmed slightly lifting your skirt to get rid of your panties, while he watched you attentively, curiosity and excitement reflected in his eyes- I want you to fuck me, Dave

The poor guy almost choked on his own saliva.

-H-how do I do it? I never… -he murmured before stopping and making a gesture with his index finger for you to come closer- come here, I suppose

You opened your legs and slowly sat on him. A squeal escaped from between his lips, at the same time you put your hand on his mouth to keep him quiet. He nodded and you took it away.

-Are you okay? –you asked, he nodded-

-I didn't know it was going to feel like this –he confessed feeling buried deep inside you- I feel like I'm being split in half

-I know –you said- when you're ready you can start moving

-Move? How? Like this? -he asked moving his hips back and forth slowly- oh, fuck- he growled holding your hips- oh, fuck it feels so good- he said moving repeatedly- I don't think I can hold on much longer

-You will, like the good boy you are- you said matching his movements- because you are, right?

-I am- he stated between gasps- I'm a good boy

He moved his hips up, making the tip brush against your clit making you moan loudly. You grabbed his shoulders and kissed him again, at the same time you tangled the curly locks of his neck between your fingers.

Unable to avoid it any longer, he came, and you with him. When he left you a choppy gasp escaped from between his lips, at the same time he did everything possible to catch his breath.

-We should study together more often- he commented making you smile-

[comicaurora]

Hey Red, I'm trying to build a better understanding of mathematics, because to my mind math has always been a collection of arcane sigils that I had to memorize to pass tests in school. I must know how these sigils came to be and why they mean what they mean. Are there any resources you recommend I use in my pursuit of these secrets? Please and Thank You 🙏

It's good you described math as something you "build," because I think that's the best analogy possible.

Mathematics, in its purest form, involves no memorization. Math is the process of taking a very small number of established truths and defined operations that preserve truth, and using those operations on your established truths to expand your space of known truths. As long as you start from a point of truth and only use operations that preserve truth, you will derive truths. If you understand the base principles from which a branch of math is constructed, you can rederive it from first principles. Memorization is easier, but you can rederive it.

For instance, we can start with two things, the number "1" and the operation "+". 1 means "a single thing" and + means "put them together." If those two concepts exist, then we also have 2, 3, 4, and every other positive integer, because we can derive them by using + on as many 1s as we want. If we drop a rock on an empty patch of ground, and then drop a rock on that same patch of ground, that patch of ground now has two rocks on it.

If we include within the definition of "+" that there exists an identity value 0, and every value has an inverse that when added to it produces zero, we also get 0 and all the negative integers, producing the group of integers. Every integer can be expressed using nothing but the number 1, the + operation, and its inverse - if we're feeling spicy.

If we decide to add another truth-preserving operation, "*", with identity value 1 and the same kind of inverse property that "+" has, we rederive every rational number. Every number in this field of rational numbers can be described as a combination of 0s and 1s using only + and * and their inverses; truthful objects combined in truth-preserving operations. We started from the truth and we used it as our only building material to create something equally truthful.

We can memorize a multiplication table, but multiplication is just iterated addition. If we forget, we can just do the addition again.

Algebra is a simple rearrangement of a simple beginning math problem by way of other truth-preserving operations. When you're starting out, you might expect to see something like

3 + 5 = ?

Algebra starts when we replace "?" with a placeholder, "x". This is just a change of terminology. It preserves truth.

3 + 5 = x

This isn't what most algebra problems look like, though. Most basic algebra problems look more like

3x + 7 = 31

But these two formulae are the same, because we can turn one into the other through operations that preserve truth.

3x + 7 = 31 -> subtracting the same value from both sides of the equation is an operation that preserves truth. We subtract 7 from both sides, getting

3x = 24 -> dividing both sides of the equation by the same value is also an operation that preserves truth. We divide both sides by 3, getting

x = 8 -> addition is associative, so we can break 8 up however we want if we do

x = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = (1 + 1 + 1) + (1 + 1 + 1 + 1 + 1) = 3 + 5

Solving an algebra problem is the process of breaking down the things that make it complicated using the truth-preserving operations that defeat them. Added values can be subtracted. Multiples can be divided. Exponents can be root'd.

We understand what it means to put a placeholder in a math problem. We realize, by the same token, we can put in more than one placeholder, if we want. This gives us problems that don't have single numerical solutions, but spaces of solutions. Consider

2*x = ?

We do what we did before, replacing that "?" with something that means the same thing. We use a different letter to avoid confusion.

2*x = y

Now we have multivariable algebra. Instead of getting hard numbers for both variables, we have pairs of numbers. If we pick an x, we get a y. If we pick a y, we get an x. The relationship between the values is clearly defined; x will always be y/2. If x is 3, y is 6. If x is -1.8, y is -3.6.

Now for the sake of convenience, we create shorthand - another change of terminology that preserves truth. We come up with a term that describes this relationship between x and y. We decide to call y a "function."

y = f(x) = 2*x

A function is what we're calling one half of an equation; what goes on the other side of the equals sign. It's just a rename, like when we turned ? into x. It preserves truth.

The trick at this stage is that every element of this seeming increasingly complexity is actually an attempt to make the process simpler as we handle more and more things. We don't technically need any numbers other than 0 and 1 if we're just dealing with rational numbers. We could write 378/5 with nothing but 1s and +, -, * and /, but by god we wouldn't want to. We could write [x^3 + 2x + 5] as ?*?*? + ? + ? + 1 + 1 + 1 + 1 + 1 and it would mean the same thing. The shorthand and symbols get dizzying if you lose track of what they mean, but when you remember what they mean, you understand why you need them.

Any piece of mathematical shorthand basically means "for this thing we're talking about, this set of things is known to be true." We can rederive those things if we need to, but the shorthand is there to help us avoid doing it unnecessarily. We call the integers a group because that means it has an associative operation that is invertible and has an identity element that, when used in the operation, leaves the operated-on value unchanged. We don't want to write that out every time we use + or remember what 0 means, but we can if we have to.

Calculus is where most people think math turns into wizardry, but derivatives and integrals are just another pair of inverse functions like + and - or * and /, and the building block of this branch of math is the derivative. Any formula for a derivative can, in a pinch, be rederived by calculating the difference quotient (f[x+h]-f[x])/h as h approaches 0. If f(x)=x^2, we may memorize that its derivative f'(x)=2x, or we may calculate

[f(x+h) - f(x)]/h =

([x+h]^2 - x^2)/h =

(x^2 + 2xh + h^2 - x^2)/h =

(2xh + h^2)/h = 2x + h

And the limit of this as h->0 is 2x.

Everything in math can be broken down to first principles. Everything. Sometimes it's very hard to figure out what tool you need to break it down to its next stage of simplification, but it was built from first principles and it can be broken down the same way. If it isn't making sense, break it down with truth-preserving methods until it does - even if you have to go all the way back to zeroes and ones.

[seriousfic]

It feels a bit weird that there's a spate of heroic female characters, meant to be protagonists, and their canon, intended personality is... they're pretty much a jerk? Like, other heroic characters will interact with them and openly state she's an unpleasant person to spend time with.

And not an entertaining jerk, like House, or a love-to-hate jerk, but just... wholly a douche. And meant to be taken as a sympathetic heroine.

It's not like they get character development to be more empathic or reveal a heart of gold. At most, there's one character they treat nicely, which means they're capable of doing it elsewhere, they just don't want to.

They act in a consistently assholish way, are somewhat acknowledged as assholes, and... that's it. Mission accomplished.

It feels like, I don't know, seeing the slow kid trying to solve a math problem without knowing how exponents work: "No, see, she's the heroine, you have to like her, she's fighting the bad guys."

"But she acts like a twatwaffle all the time and is mean to other characters I like much more."

"Yes, but, she's the heroine, you see, you're supposed to like her."

"But I don't."

"You're supposed to, though."

"I don't."

"YOU'RE WATCHING THE SHOW WRONG!"

[strwbrythoughts]

time's up | dr. veritas ratio

The doctor - also known as your husband - has come to refine your problem-solving skills, particularly in mathematics.

A/N: This man is insufferable but I simp because smart + muscles = hot!!! Also can you see me projecting onto this and wdym i don't like triangles, ngl i accidentally switched to first person pov at the ending 💀 this is why i need to find time to write in my busy busy schedule

Divider by @/osqrie

"You have 15 minutes to solve these questions. You may begin."

The soft click of the digital stopwatch in his right hand sounded louder than ever to your ears. Your eyes went from his soft, smiling face - which in itself, was a rarity - towards the questions printed on the single sheet of white, A4-sized paper on your desk. They were all mathematics equations. Every single one was an integration-related question.

You always thought that you could escape the topics you didn't like after finishing your studies in the undergraduate level. Life had been pretty smooth-sailing after graduation; you opened a cute and cozy bakery, you married a genius, lived in a comfortable home, have and maintain a loving relationship...but this. This was the least of what you would expect. Being tutored and tested on the one subject you refused to take back in university.

Or perhaps it was your mistake when you told him your weak points in the academic aspect of yourself. That was a side effect of marrying a genius, you supposed...or a 'Mundanite' as he would use to refer to himself.

But you couldn't think of that now. You had a test to complete, and you didn't want to receive his punishment for not being able to do so within the given timeframe. His eyes could be felt on you, as if burning into your body and directly gazing at the very essence of your soul. The rise in your heartbeat and downturned gaze highlighted how nervous you felt to answer this paper.

After taking a deep breath to clear your head, you observed the questions carefully. There were 3 questions, and all of them were pretty easy to solve (or at least, that was what the instructions said). The first two questions were fine; only including polynomials and exponents respectively. As you got to the third question though...you couldn't say it was 'fine'.

It included one of your most disliked topics...trigonometry.

Granted, the trigonometry was pretty simple, but you never seemed to be able to wrap your head around how so many formulas could be derived from them. When Veritas explained it to you in one of your tutoring sessions, you asked for more breaks than usual since you had put a barrier in your mind; 'I will never understand this'; which in turn, made the topic seemed harder than it actually was.

The soft 'ding!' of the bell on my desk reminded you that you had five minutes left for this last question. You gulped, hoping your nervousness would be swallowed away as well. His eyes were glued to the back of your head; not that you dared to look behind my shoulder at the moment.

Every second counts after all, even if you had no clue what steps you should take to solve the problem on the paper.

Your brain seemed to malfunction and your memorisation skills failed you right this moment. You didn't remember the basic formulas, and you didn't know how to derive them from the triangles either. With no viable options left, you decided to unleash your expertise; cooking up your own theories.

'Ah, he's definitely punishing me for this...' was the only thought floating in your brain. Autopilot mode was switched on, and your hand glided across the paper, writing down whatever nonsense that seemed to be related to trigonometry, regardless whether they were correct or not.

The digital stopwatch in Veritas' hand had reached its last minute; the fifteenth minute. "Time's up," his voice bounced off the white walls right into your ears. "Put down your pen and stop writing."

Although reluctant, you did not wish for a heavier punishment. His words were followed by the sound of the pen being put onto the wooden desk. Within seconds, he was stood right next to your desk, using his index finger and thumb to pick up the piece of paper.

His eyes scanned my answers, going from left to right as he inspected each line of working. There was a faint smile on his lips...until it was gone.

Gulp.

He had definitely seen the absolute mess you made on the last question.

A slam onto the wooden desk; you swore you heard the wood crack a little bit. "Did I not teach you this last question?" You could barely reply. His tone was dripping with condescension, but you didn't take offence from it. Both you and him knew he had the right intentions, but his ways wouldn't be able to satisfy everyone.

"You did! I...I just didn't like it."

Veritas let out a 'tsk' thrice, seeming almost animated as he did so. "You do know what you have to do now, right? So come on, what are you waiting for? Is time not ticking?" He took a seat on his chair, eyes looking straight into mine.

You sighed, preparing your facial muscles...as you climbed into his lap. Ah yes, the 'one hundred kisses or you're not leaving this room' punishment. A classic, really. Your lips peppered his face, landing on each part like the first snow of winter; gentle and heartwarming.

"Lunchtime is nearing, so you better carry out your responsibility quickly and dutifully, dear. You'd hate to have lunch at 4 PM again, hm?"

Ah, crap! He was right! Better get to work now!

Thank you for reading!

[yandere-wishes]

⋆ Anomaly ⋆

❤Summary: Reader is an anomaly. A noblewoman of foreign descent. She doesn't belong here. But oh how she wishes to burn the world down just like William.

❤Author's note: A little something for Ana (@yandere-romanticaa) I hope you enjoy it!!

❤Warnings: Reader is traumatized, Yandere behavior, killing and blood, cryptic. I swear I know how math works…I've just been slaking this summer.

There are equations written over your skin. Complex formulas he's yet to solve. Exponents and variables freckle your body, scattered shards that try to tell him something, whispering the world's secrets every time he kisses your hand. You are an anomaly he thinks. Face full of cracks where the stars seep through. You're a mistake in the universe. A perfect doll misplaced. You are something, William is almost sure of it.

At heart, William is and always will be a mathematician. It just so happens that crime and math follow the same principles. Both require diligence and practice. Carefully throughout plans of how one must approach such a conundrum. One may call it a formula or a modus operandi or anything else as jejune. But in the end, a rose by any other name would still smell as sweet.

And yet to Moriarty, you are an equation that refuses to be solved. An enigma he's desperately sought to unravel since your first meeting.

William notices something odd as you stroll down an exquisite exemplar of the golden ratio. Something the lord of crime can't fully place. You're akin to a puzzle missing far too many pieces to properly depict its picture. Maybe it's the setting he ponders as he watches you take careful steps in heeled shoes. Maybe it's the music from the ballroom or the meaningless prattle of the aristocrats that robs your form of all logic. Something is amiss with you and he's frantic to find out what it is.

William introduces himself when you reach the bottom of the staircase. He's never been one to show primary interest in the ladies. Rather he waits in the faint glow of the moonlight until someone approces him. Maybe it's the need to distinguish himself from the other aristocrats, maybe it's the repulsion for their customs and manners that refrains him from ever commencing idle chatter. Yet with you, a girl he's never met before, he finds it fitting to say hello first. To talk, about nothing and everything in the same breath. He mentions his admiration for the staircase in passing. Never expecting you to latch on to the words and morph them into the divine proportion. "My father was a mathematical enthusiast, he's passed that on to me as well." Your words slip into his veins like a narcotic, like the melody of an ancient tune lost to time.

William smiles, easy and bright like the melting rays of the desert sun. "Quite the coincidence, I'm a mathematics professor at Durham University". There's a giggle that bleeds from your rose-tainted lips. Reverberating in the chambers of his heart. "A toast then" you propose "to the lethal magnificence of calculation"

You click your champagne glass against his, as something feral festers within the young nobleman.

It's only days later when he's replaying that night in his head as he sips his afternoon tea. That he realizes your champagne glass was empty that whole time. How strange he pondered, wondering if he'd even seen you touch a single intoxicant all evening.

Four days and three sleepless nights later William finds himself tracing the letters of your name with tender adoration. As if he's engraving prayers upon his bones. He needs to see you again as desperately as he needs to breathe. The letter he writes is aloof, meticulous. Prying on your curiosity, hoping you'll take the bait. One miserable day later Louis delivers a letter bathed in your fragrance. Informing the lord Moriarty of your acceptance of his invitation for tea. William folds the letter with the leniency of a biologist regulating their slides. Tucking it away within his breast pocket.

You wear red when you oblige his invitation. An odd red, one that breaks his perception of the color. It's too vibrant yet too opaque. He's beginning to wonder if everything about you is an irregularity. When he ushers the conversation to your garment you merely laugh and brush it off as having belonged to your mother. There's something wrong with that reply as if the universe weeps at your every word. William watches astonished as if he's been told a secret lost to time.

It becomes a habit, an obsession, an addiction really. Tea thrice a week with the woman who plagues his dreams. He lets his cover slip between sips of tea. Permitting you glances into his dark affairs. There's a moment that breaks the norm. A bizarre instance when you ask him to spare no detail in recounting how a poor tormented man murdered the marquess that raped his wife. William stops the proclean cup mere millimeters from his lips. His voice dies in his throat as his mind races to find an appropriate way to tell a lady such a bloody tale. For a second reality slips away.

Reality has a tendency to slip away unnoticed when he's with you.

You weave William tales of foreign lands that sound like they belong in children's fairytales. You tell him about heroes who've done the impossible and kings whose hearts are as pure as the summer skies.

Something about you reverberates in his subconscious. Oh, how he wishes to engulf you, to pick apart your flesh revealing all those dainty secrets you keep in your pretty little chest.

He asks how you know of such utopic lands. You smile. "Because I once lived there"

One day, as Louis serves black tea with rose petals, you bring up a rather peculiar request. "Permit me to assist you in your quest for equality lord Moriarty." William's beginning to believe he's going mad when he hears you. Albit it may as well be expected. Any sane noble lady would have run away many times over. Yet you remain. Forever poised in your adorned seat. Now more than ever William wishes he knew what you truly are. "I want to help you", you plead. "Allow me to aid you in burning this world down and starting anew". He shouldn't have accepted, he shouldn't have nobbed. He shouldn't have left his seat to trace the side of your face with more love than he knew he possessed.

Sometimes, William wonders if something is haunting you, an apparition nesting within the depths of your heart. He ponders what could drive a brilliant mind such as yours to crave the blood of the rich. You once told him about a heritage disrespected. A legacy buried under sand and water lilies. He's yet to find the true meaning behind those words. Does that make you a threat or an ally? Can either be exalted to a lover?

Moriarty promises you the world. Promise you revenge. He's not sure if he too will burn away in your vendetta. Yet he's willing to take the risk if he can hold you close after every murder case.

"I've tried to kick the habit of strolling around the cemeteries at night. Yet I must admit I rather enjoy this." William smiles at your twisted words as he leads the way. If everything has goes as planned -which is most often the case- then the two of you should be prepared for quite the spectacle. A certain Count - who had shown more interest in you than Moriarty could permit- would be getting knifed by his butler whose life he had ruined. A whole new meaning to the term 'the butler did it'. Quite comedic from William's perspective.

You lean on a withering oak tree, hidden by London's thick fog. William stands by your side, the personification of a grim reaper. You watch the play begin, the cobblestone stage illuminated by the blood-red moon. The confrontation, the knife being thrust into the rich vermin's heart. Again and Again and Again. The butler screams into the bloodstained night. His words quelled by his sobs and screams of agony from his dying tormentor. You only catch half of his reasoning, half of his allegations. And yet that is more than enough to comprehend his motive. You sympathize with the poor man, one whose scars mirror your own.

William's scarlet gaze befalls you, as the performance nears its end.

You pick at your nails in a manner that William finds a little too adorable.

You are an anomaly masquerading as a human. Depression lays heavy over your bones as stardust gathers in the corners of your eyes.

You pray to the creator of the moon, pray for a place long since destroyed.

"I've yet to find someone who truly understands me," you say as the two of you begin the journey back to the Moriarty estate.

"Then we share the same burden, my lady," William says, stopping in his tracks.

He lays a firm hand on your shoulder pulling you backwards into his embrace. Somewhere in the distance, three crows consecrate you with their blessings. Willian's hands rest heavy on your sides. He holds you like a little boy holds his father's arithmatic books. Full of care, full of wonder. "What are you" he whispers into your ear. Leaving a playfully hard bite to the shell. His lips trace yours like one traces a treasure map. Trying to unearth all the riches of the world. "My anomaly" he mutters before he finally commits.

When Moriarty kisses you the whole world melts away.

There's an intriguing lightheadedness that follows. As if the stars themselves have exploded within you. You wonder if basking in his presence will mend your tattered heart.

"My precious little anomaly"

Tag list: @elvyshiarieko @himerurun @latolover @aru-nightmare @guidingstarsstuff @myfancollections

[math-journal2]

Ways to Solve: Logs and Exponents

For the 3rd black box, go to expanding expanding logs to see it solved

Unsolvable Algebraically

pH scale

pH=-log[H^+]

pH > 7 basic

pH < 7 acidic

Small basic - 7 - big acidic

.

Richter scale

*rewrite notes, this is hardest

.

Note: watch for the units of input and output. Sometimes they can be in billions or really small numbers

Note2: don’t be afraid to solve for variables then plug everything in

Note3: substition is a great way to track tricky decimals

[itchybodcrane]

Decided I’m gonna start posting a daily number game I thought of. I have the rules for it and an example below . If people like it I’ll keep doing it.

4 number game (idk a good name for it yet)

You have 4 numbers and you have to split them in to 2 any way you want and make them equal each other. You can use addition, subtraction, multiplication, division and anything under PEMDAS. This includes multiplying by zero or using one or two of the numbers as an exponent to multiply another number by it.

Post your answer in the comments if you’d like

Here is an example

8231

A solution would be 2 to the power of 3 and 1 times 8 making both sides 8. You could also do 3-2 and 1 to the power of 8 to make both sides 1. There are probably more solutions idk.

First Official game below

1273 try and solve this

[study-with-aura]

Wednesday, January 8, 2025

Back to busy days! Eating a quick snack since I just got back from ballet and ate a light dinner five hours ago, and then it's time for a shower and finally bed.

Studying went fast today. There wasn't as much copywork as usual, which gives my hand a break. The copywork is also what always takes so long. I could print everything so I didn't have to copy all of it, but I remember better if I copy it and it allows me to work on handwriting, which I know, strange given the digital age. I would love to work on stylistic handwriting one day, but until then, I will work on my own personal style which is a tad sloppy but legible nonetheless.

Tasks Completed:

Algebra 2 - Reviewed exponent rules + learned to solve exponential equations + practice

American Literature - Copied vocabulary terms + read about Ralph Ellison + read about Ellison's novel Invisible Man + read about using rhetorical strategies for persuasion + read through a list of argumentative writing topic ideas and tried to narrow down what I want my topic to be

Spanish 3 - Reviewed clothing vocabulary + browsed a Spanish online clothing store

Bible 2 - Read 2 Chronicles 31-32:1-19

Early American History - Read more about the War of 1812 + went through a timeline presentation of the battles of the War of 1812

Earth Science with Lab - Watched a short documentary about Jupiter and the outer planets

Art Appreciation - Read about imaginative seeing and completed activity

Khan Academy - Completed Algebra 2 Unit 6: Lesson 5.1-5.2

Duolingo - Studied for approximately 15 minutes (Spanish + French + Chinese) + completed daily quests

Piano - Practiced for three hours

Reading - Read pages 38-72 of Threads That Bind by Kika Hatzopoulou

Chores - None today

Activities of the Day:

Personal Bible Study (Luke 12)

Group Bible Study + Devotional (Job 17-20)

Ballet

Variations

Journal/Mindfulness

[coming-up-with-usernames-is-hard]

PhD Blog Week 17

Courses

Solitons: only half a lecture this week due to the storm, solved the Schrodinger equation, could have been back in 2nd year modern physics class, really wish we could get on to something new

Rep theory: moved on to focus on group reps, spent way too long on the simple stuff and rushed the more complicated bits

Hopf algebras: finally defined a Hopf algebra, but that was about it before the lecutrers computer died. I've agreed to give a talk next week (this week now, gonna have to rush planning it) about string diagrams, mostly out of frustration at how awful monoidal categories are without them

Supervisor Meeting

Tried to present the calcuation I did, got talked over, then supervisors spent ages debating a point that was at best tangential to what I was trying to do

Teaching

Just the one first year maths tutorial this week, basic matrices and combinatorics. The matrices are fine, although I had to point out that superscript T is the transpose, not an exponent, several times. Combinatorics is hard to explain, my method for the types of counting problems they have to do has always been to stare at it until I've convinced myself I know the answer, this makes it pretty hard to explain

Talks

Integrable Systems talk on spin chains, a pretty interesting generalisation of things like the Ising model that I've spend far too much time thinking about, but now there's some interesting representation theory happening, still don't know what a Yangian is

Group Project

Officially started this week (delayed due to the storm). Our topic is quantum groups, which is nice because I was planning to learn about them any way. Hopefully I can get a little more guidance on what I should focus on though

[international-baccalaureshit]

just forgot how to solve for a variable when it's in an exponent so i wrote "i forgot how to do this part so i put in n = 7 and it worked" i hope my math teacher understands

[kaiserkisser]

I couldnt even tell you what this is bro… im trying to get put in pre calc because i literally did this last year butttttt its just simplifying exponents,,

no wait this seems pretty familiar (i like to think that im okay at exponents) buuuuut uhm

so i tried solving some random questions from here aaaaand...

soooo im pretty sure you cant directly subtract √a - √a since the first one has a coefficient (unless im wrong???) So unless the value of a is 1, i dont think you can get the answer as 3??? and if the coeff was just 3 instead of 3a then the ans would be 2√a i think (i havent touched exponents since last year soooooo please dont mind me if im wrong 😭😭😭)

riiight so in the a subpart i yk just cancelled out the denominator bc fuck i hate roots lmao and that gave me a totally different answer 😭😭 and in the b one, im pretty sure if you multiply by just u2 then it actually does not go into the cube root and instead gets multiplied to the u outside the root and makes it u3 and the root remains, so you have to multiply it by 3√u2 iirc so that the denominator gets rationalised but the cube root remains in the numerator like in the second step unless yk you wanna go all the way back to exponents again which i dont think you do....

ofc the concepts im using to solve these are ones i learnt in like 9th grade so i wouldn't know if youve learnt something idk abt plus idk the questions 🫠🫠🫠 ill try to solve some more later lol (my moms shouting at me rn) idk how useful itll be but u can ask me if you have doubts ig lmao