#Calculus math

[kimeoshi]

Corrupted Ratio for Twitter! Reached 2k followers and he won in a prompt game

Timelapse:

[lothmoth]

did you know they say calculus is the language of God. did you know they tried to hold math up to infinity like a candle to the void. did you know statisticians plunged into the vastness of random chance and picked out patterns and equations and eight hundred ways to tell you how big your inevitable errors are and how far off those guesses at errors might be. math haters I can't sit with you anymore. human innovation is cradled in these ancient, methodical, desperate attempts at understanding what we are not designed to understand

[dreams-of-soft-rain]

kirby reads hatcher!

[pimn]

my calc professor just called inflection points nonbinary critical points and I'm like ah yes the 3 genders, local maximum local minimum and inflection point

[miscellaneousmathematics]

[ryuusea]

mornings with a math professor…

inspired by this twt

[lilacandladybugs]

Studying for my calc 3 exam and I had a nightmare that I was trying to solve something weird like x²+ 4x + 9 = e^x² + e and I don't remember what my strategy was but you know natural logs were involved. My professor walks by looks at my paper and goes " oh in this situation e is actually a variable" and I was so mad I woke up

[serenityatnight]

Math tells us the saddest love stories

"Parallel lines were never meant to meet"

"Tangent lines only meet once and grow apart forever"

"Asymptotes get closer and closer but will never be together "

[inbetweencoffees]

calculus :)

managed to work for ~2.5h despite feeling quite tired and having a headache (I need a coffee alternative as I simply can’t stand the taste anymore…)

[midnightfairy1]

Do Borrowers Actually Take Fall Damage? (calculus/physics answer)

hey guys! sorry I haven’t been active lately, but im about to finish up my finals so give me one more week before I start posting religiously. I just wanted to share with you some calculations I discovered during my studying for the Physics C AP Exam, with which I am expecting to interest borrower fanatics.

I am very proud of figuring this out and hope you guys find this as entertaining as I did! (By the way, I suggest scrolling to the bottom for the answer if you don’t want to read through all my math, although the math can also be interesting if you want it to be! 😁)

First, I found myself wondering something: If ants are so light that their is no height they could fall from in which they could injure themselves, and humans gain fairly serious injuries after a 16 ft (5 meter) drop, where do borrowers fall on the scale?

I took to my physics notebook and calculated the result.

I won’t share with you the trivial calculations it took to reach my first conclusion. To break normal human leg bones, an impact force a little over 2,000 newtons is needed. For more serious injuries (more serious than a fracture), once the impact force reaches above 3000 newtons the fall becomes very dangerous. By 4000 newtons, the fall will usually become fatal (this happens around a 15 meter or 50 foot drop). But within the 2000 newton to 4000 newton range, a fall with a weird landing can have serious effects. If it interests you or helps put it into perspective, the impact force (in newtons) is equal to (mass(kg)x(velocity(m/s))^2)/(2(distance leg compresses (m))).

Next, I tried looking into the air resistance factor of a borrower. Depending on how high the air resistance is, the terminal velocity will decide the borrower’s impact force. Terminal velocity is defined as the highest velocity one might reach while falling, because air resistance counteracts your gravitational force once you reach a certain speed.

A 5’8” person who’s weighs 150 lbs scaled down to a height of 4” weighs .0136 kg (equivalent to the weight of a few coins). If you’re wondering if the fact that their bones are weaker will affect the outcome, don’t fret. Even though borrower’s bones are literally weaker, their bones are stronger relative to body mass. This is because bone strength is directly proportional to cross sectional area (length squared), and mass is directly proportional to volume (length cubed). this means that mass diminishes at a faster rate than bone strength. In a falling scenario, bone strength relative to body mass is the only thing that matters.

Now back to air resistance and terminal velocity. After plugging the borrower’s dimensions as well as other constants to the air resistance (drag force) and terminal velocity equations, I now know that the terminal velocity is equal to 11.4 m/s. This means that, no matter how high the fall is, the borrower will reach a max speed of 11.4 m/s because the drag force at that point will reach a quantity that is able to equally counteract the gravitational force (mass (kg) x gravity (9.81 m/s^2)) acting on the borrower.

Plugging the terminal velocity back into our impact force equation will give us the maximum impact force acting on the borrower. I’m going to do this for all of us, and reveal that the maximum impact force would be roughly 88 newtons. Taking into account a greater drag force (the borrower would most likely be flailing around and wearing clothing while falling), we can assume the maximum impact force would be even lower than this.

We are almost done. The last thing I need to do now is calculate a lethal impact force for a borrower, because it is not the same as a human’s. Impact force corresponds to energy transfer. For the previously mentioned fatal fall of 15 meters for a human, roughly 10000 joules of energy is transferred to the human, cause brain damage or death. any more than this would also lead the fatality (most likely). Scaling this down to borrower size using the same proportions as before, a transfer of roughly 1.94 joules would be fatal to a borrower. This corresponds to an impact force of around 194 newtons, well above the injury threshold calculated earlier. However, it’s good to assume that a fall from a weird angle or onto a hard surface still has the possibility to greatly injure the borrower, even if it is unlikely to be fatal.

One last calculation if you were wondering: the fall height it would take for a borrower to reach their terminal velocity is a height of 6.6 meters (or 21.7 feet) however, this fall would generate a force less than half that of a fatal force.

In conclusion, it is highly unlikely for a borrower to pass away due to fall impact from any height because their maximum impact force is well below the minimum impact force it would take to kill them. However, they can still get injured (and possibly fracture) in unlucky scenarios. This post is in NO WAY encouraging the artists or writers out there reading it to start composing scientifically accurate media, because I love the trope where the human has to chauffeur the borrower around everywhere and keep the borrower safe from high heights 🥰. If there is anything in my math I may have overlooked, please let me know because I would love to learn more! I really appreciate anyone who took the time to read this long, mathy message!

Borrower Speed, Strength, and Durability

[ravings-of-a-mad-scientist]

Math

Geologist: I do more math than you might think

Chemist: I mean, chemical equations are basically mathematical equations. If you think about it (I also do math math)

Physicist: Oh, yeah, it’s all math but we just handwave it

Mathematician: YOU DO WHAT!?

Quantum Physicist: *regularly does math that is literally beyond human comprehension* *now resides in a higher plane of existence*

Engineer: If I don’t do this math correctly PEOPLE WILL DIE

Military Scientist: If I don’t do this math correctly PEOPLE WILL SURVIVE

Topologist: If I don’t do this math correctly PEOPLE WILL BE MOSTLY UNAFFECTED

Philosopher: But what even IS math, really? No seriously, what is it?

Organic Chemist: I kinda forgot how to do math, to be honest

Biologist: I literally only chose this field so I wouldn’t have to do as much math. I love stamp collecting

Biostatistician: wtf

[movietonight]

Shawn lived in Argentina for a year and can tell different Spanish accents apart but can't speak Spanish during the soap opera episode. I love when writers just gave zero fucks about continuity.

[mandomaya]

Ezra doing our maths homework

[incognitopolls]

*This poll is asking what grade levels your school allowed to take calculus, not what grade you learned it. If you were homeschooled, though, you can put the grade in which you learned it.

For those with different grade/level structures, in the US 10th grade is typically age 15–16, 11th grade age 16–17, and 12th grade age 17–18.

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We ask your questions so you don’t have to! Submit your questions to have them posted anonymously as polls.

[smath-or-pass]

Stokes' theorem

[satoblue]

satoru is exceptionally smart and good at math so i can see him helping his kiddos with their homework in his office — sleeves rolled up, pen in hand, barely having to think as he jots down numbers and equations while explaining stuff . . .