Math Fun! (Answers)

[Ellie Williams]

Here are the answers to Math Fun. Please do the problems/attempt to do the problems (or just look at them briefly) before looking at the solutions.

Spoiler: Solutions

Spoiler: #1: Arithmetic

Spoiler: #2: Arithmetic

Spoiler: #3: Arithmetic

Spoiler: #4: Arithmetic

Note: this problems asks for the remainder, not the quotient. Therefore, the correct answer is 6 (the quotient would be approx. 7.85).

Spoiler: #5: Algebra

Spoiler: #6: Algebra

Let x be multiple choice and y be fill-in-the-blanks.

Spoiler: #7: Geometry

The perimeter would be increased by 2m. (If the tile was removed from the corner, the perimeter would stay the same.)

Spoiler: #8: Statistics

Spoiler: #9: Statistics

 

[Ellie Williams]

Spoiler: Solutions continued (can't post more than 20 images in one post)

Spoiler: #10: Statistics

Spoiler: #11: Calculus

Spoiler: #12: Calculus

Spoiler: #13: Calculus

This one's complicated. Let me walk you through this.
Step 1: Solve for x using the Pythagorean Theorem.

Step 2: Implicitly differentiate the Pythagorean Theorem with respect to t.

Step 3: Plug in your known values and solve for dx/dt.

Spoiler: #14: Calculus

Here's the indefinite integral:

Spoiler: #15: Calculus

Here's the indefinite integral:

 

[Ellie Williams]

Spoiler

Spoiler: Bonus #1: Algebra

A neat little formula discovered by Carl Friedrich Gauss that easily lets you add up all numbers from 1 to x quickly:

Spoiler: Bonus #2: Calculus

Here's a graph so you can better visualize it:

Spoiler: Bonus #3: Precalculus

Spoiler: Bonus #4: Calculus

False, because the result is missing the constant of integration ("+ C").

Spoiler: Bonus #5

i eight sum pi
(I ate some pie.)

 

[Ellie Williams]

Spoiler: Solution to Trigonometry Problem

Last edited by Leonhard Euler, April 15, 1707​

 

[Thaus]

Ya know about 99.99999999% of the people hate math ya know?

 

[Ellie Williams]

Ya know about 99.99999999% of the people hate math ya know?

Do you mean 99.9 repeating %?

If so, it means that 100% of people hate math, which is false, because I like math ;).

Here are some proofs.

 

[Thaus]

Do you mean 99.9 repeating %?

If so, it means that 100% of people hate math, which is false, because I like math ;).

Here are some proofs.

No im just exaggerating but you know what I mean. I also proved myself wrong cuz I like math too. Don't think too literal plz.

 

[iDontPlayMinecraft.exe]

Wow, ur the smartest person I've ever met, this insane how you do these problems

 

[maxminoS]

In my defense, I haven't learnt integrals, I've just started on differentiation/calculus

 

[Ellie Williams]

Anyone want me to go through a detailed explanation of the harder problems?

For the limit problem, use l'Hôpital's rule.

 

[Ellie Williams]

What do you guys think is harder: Statistics or Calculus?

 

[Thaus]

I would rather just do addition.....
Hey but you are really good at math! Keep at it!

 

[CARDAN18]

Math is very challenging for me, no idea how it is possible to do a lot of it.

 

[Ellie Williams]

#15 was also very difficult.

Spoiler: Walkthrough

1. Factor the denominator:

2. Split the fraction into partial fractions, and substitute the numerators with constant variables:

3. Multiply both sides by the left denominator, and simplify:

4. Solve for B and C:

Spoiler: B

Spoiler: C

5. Substitute back the constants, expand, then factor:

6. Solve for A:

Spoiler: 3 = -2A + 1

7. Substitute the constants back into the partial fraction:

8. The rest is straightforward:

Spoiler: Your final answer

Note: for the indefinite integral, you're on your own. But just substitute the antiderivative with x=128, then subtract the antiderivative with x=32. Ignore the constant of integration

 

[Rainbowaffelz]

Just looking at the answers makes my head hurt

 

[Ellie Williams]

Just looking at the answers makes my head hurt

Math is very challenging for me, no idea how it is possible to do a lot of it.

In my defense, I haven't learnt integrals, I've just started on differentiation/calculus

Can you guys at least memorize your trigonometric identities?

 

[Jeff_Bllkth]

I love Math xD But not when there are many problems

 

[CARDAN18]

Can you guys at least memorize your trigonometric identities?

No I can't, I forgot what that even is.

 

[QuikMiner]

*Face palm* I thought knowing linear algebra was something to brag about... my man you know a lot.

 

[packta]

Those were cool! Enjoyed solving them :) Can you make some more please? I missed the first post when you made it @CattyCat