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Thank you both; it really helped me.

Thank you Melody! Very well thought out and easy to understand. Thanks again! Hope you can forgive me for my actions before.

Well, given a and b we can write   

It is an AP. Use the AP formula to sum them up:

Sum = 20/2 * [2*100 + 3*(20 - 1) ] =2,570

As follows:

c=0;m=0;p=0;a=listfor(n, 1, 10,listforeach(m, d=reverse(1,2),(c=1/(c + m))
=Sqrt(3) - 1 = 0.7320508076

How do we find the equation of a continuous piecewise function though?

Thank you very much! 

If the curve is continuous then we must have:

At x = 2:   a*2 + 3 = 2 - 5  or 2a = -6   so a = -3

At x = -2:  2*(-2) - b = -2 - 5   or  -4 - b = -7  so  b = 3

Wow! This makes sense, thank you so much! I really understand it now! 

I get the following:

Let \(x = \cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \dotsb}}}}\)

Then x = 1/(x + 1) ==> x^2 + x - 1 = 0 ==> x = (sqrt(5) - 1)/2

(3) 

Suppose f(x) is a cubic polynomial y = ax^3 + bx^2 + cx + d.  Then

d = 47

a + b + c + d = 32

8a + 4b + 2c + d = -13

27a + 9b + 3c + d = 16

==> f(x) = 46/3*x^3 - 57x^2 + 68/3*x + 47.

The sum of the coefficients is 46/3 - 57 + 68/3 = -19.

(4) Matching coefficients, the polynomial is 2x^3 + x^2 - 2x + 3.

The 3 numbers are: 12, 14, 16

If the radius of a larger circle is increased, the ratio of AB to PA  does not change! 

It turns out that there really isn't a good strategy; you should guess whichever card to be the card with the highest number on it, so the best you can do is 1/3.

Reference: https://math.stackexchange.com/questions/3474127/what-is-the-best-betting-strategy-to-maximize-probability-of-winning/

hmm im not really sure that would be correct, the multiple choice options are 4, 4.5, 4.8, 5, and 5.4. could you explain to me how you got 2.4? thank you!

Oh okay thank you, it helped me. For finding area of circumcircles and incircles, then you would just use the circumradius and inradius formulas to the find the radius, and continue on with the circle area formula correct?

2 hrs 24 minutes i think

30 dimes, 29 nickels, and 35 pennies

You must be joking if you think your "solution" has better explanatory power than Alan's solutions. Alan Uses RIGOROUS mathematical solution, using exponents and difference of two squares, to arrive easily and elegantly at the correct answer. Please don't compare the two!.

so it is [biggest number]^5

What's the question?

Guest, if you still don't believe me then here's what i'll say:

some people have the same answers but different explantions

I had a different explanation