eeeeeeeEEEEee I got a captainclara mathanon

so excite :D :D

What exactly is Pi? 

Pi is the ratio of the circumference of a circle divided by its diameter.

π = C/d

It just so happens that this ratio is infinite and none repetitive, which makes it an irrational number.

π=3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609...

oooooor 

I hope your semester/trimester/quarter/work or whatever applies is going well. Personally mine is just starting which is why I'm still not posting daily updates. I'll start posting soon. Posts may include GRE prep work. 

For the first picture: 

The first derivative lets you know if the slope increases (positive) or decreases (negative). If the first derivative is 0 The second derivative lets you know if the curve is concave up (u: positive) or concave down (n: negative). If the second derivative is 0: the point can be a maximum or a minimum. Example:

Knowing this give the problem a try if you still can't do it feel free to come back :) 

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As for the second picture: 

The equation can be rewritten as: 

(3-x^3)^(-1/3) using the chain rule: (derivative of the outside time the derivative of the inside)

-1/3 * (3-x^3)^(-4/3) * -3x^2

x^2 * (3-x^3)^(4/3)

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An easier way to say this is: Solve for z

Solving for z will give you a complex number that makes your equation true.

Here’s how we do it: 

1) multiply both sides by the denumerator and simplify. you should end up with the following

z = (1+i) (1+z)

2) expand the right side then simplify

z = 1 + i +z + zi

0 = 1 + i +zi

3) solve for z

-zi= 1 +i 

- z = -i + 1

z = -1 + i

And there you go! You now have a complex number z that when plugged in to your equation will give you 1 + i.

to solve functions you create an x/y table or in your cases x/g & t/h tables. What you do is you give the x or t a value and then you substitute the value until you have a final number.

Ex.

g(x)=2x-3

if x = 0

g(0) = -3

if x = 1

g(1) = 2(1)-3 = -1

and so on. Once you have at least 7 values (from -3 to 3) you can have a trustworthy plot. 

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To solve function compositions I’ll explain with an example:

g(h(t)) is the g(x) function except the x is your h(t) function. In other words substitute your x for the function on the inside. 

Hello!

I'm not that good with stats 'cause I've never taken a stat class (yet), but if I had to guess:

you have 10/26 = (roughly) 38%

3/26 =(roughly) 12%

the probability of one of them being a sophomore is 12% of a 38% or a 4% so a 96% chance they're not?