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The answer is 9900.

The answer is 30.

The answer is 35.

The possible values of b are 44 and 304.

A number \(x\) satisfies \(x = \dfrac{1}{1 + x}\).  Determine \(x - \dfrac{1}{x}\).

\(\begin{array}{|rcll|} \hline \mathbf{x} &=& \mathbf{\dfrac{1}{1 + x}} \quad &| \quad \times (1 + x)\\\\ x(1 + x) &=& 1 \quad &| \quad : x \\\\ 1 + x &=& \dfrac{1}{x} \quad &| \quad - \dfrac{1}{x} \\\\ 1 + x - \dfrac{1}{x} &=& 0 \quad &| \quad -1 \\\\ \mathbf{ x - \dfrac{1}{x} } &=& \mathbf{ -1 } \\ \hline \end{array}\)

What is the remainder when \(x^3 + x^6 + x^9 + x^{27}\) is divided by \(x^2 - 1\)?

\(= x^{25} + x^{23} + x^{21} + x^{19} + x^{17} + x^{15} + x^{13} + x^{11} + x^9 + 2x^7 + 2x^5 + x^4 + 2x^3 + x^2 + 3x + 1 \text{ remainder } 3x + 1 \) 

I'm pretty sure only x^2 works, so there is only one quadratic.

The answer is 1/15.

Hi Melody!!!!!!!!!!

Thank you, CoolStuffYT!

Thank you, CPhill !

Thank you, Melody !

That is a different question.

See a slight variation to the question here:  https://www.quora.com/A-cube-is-painted-blue-on-all-faces-and-divided-into-125-smaller-cubes-of-equal-size-How-many-cubes-are-not-painted-on-any-face

Volume of 8 steel balls =(4 π r^3)/3≈4.18879  x 8 =33.51032 cubic inches.

33.51032 =(4 π r^3)/3

r^3 =[33.51032 /(4/3*  π)

r^3 = 8

r = 8^(1/3)

r = 2 inches - the radius of big steel ball

a=1;b=1;d=0;c=a+b;d=d+b;e=2#d;printb,e;b++;if(b<300, goto3, 0)

n            Perfect Square
1            1(1)
8            36(6)
49          1,225(35)
288        41,616(204)

Completing the square in x and y, we get (x - 9)^2 + (y + 18)^2 = 361, so the radius of the circle is 19.

That looks very impressive Heureka !

Thanks Tiggsy    

Forget your condescending "Hint"

You are, by choice, a nobody.  

You are addressing acknowledge Mathematicians.

If you believe you know the correct answer then spell out your reasons and give the answer, as you see it, in full.

Or if you are incapable of doing that then state why you believe a different answer is correct.

Like you could day. "The answer that the teacher gave me is .... but i do not know how she got it."

Two circles of radius 1 overlap so that the center of each lies on the circumference of the other. What is the area of their union?

The answer is 12.

The answer is 50*sqrt(3).

The distance is 24*sqrt(3).