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The above is the graph of

I used Winplot to plot the two functions and find their extreme values. You could also use calculus to do the same , and if requested, I would be happy to show my work.

But where does the equation come from? The equation given is the equation of a circle that has the standard form

I solved this equation for y to get

and then subtracted the expression for y from x to get f(x). By the way, the exact values of the coordinates of the extreme point displayed in the plot are

So the maximum value of x-y is \(\frac{\sqrt{33}}{2}\) or approximately 2.87228.

just a little typo but 20/5 is 4

so the answer is 10

In attempting to list them, I got

8 triangles with smallest side = 1

11 triangles with smallest side = 2

13 triangles with smallest side = 3

10 triangles with smallest side = 4

4 triangles with smallest sides = 5

1/8(x^2 + 8x + 4) and x^2 + 8x + 4 will have the same roots. 

=^._.^=

Sorry, I'm a bit confused. How did the 4x^6 get canceled out?

m + n = 48.

There are 6054 permutations.

q(-1) = -18.

how?

The possible values of y^2 are 8 and 12.

how did you get that? thanks

There are 225 possible polynomials.

The probability is 7/16.

The volume of tetrahedron ABCF is 108.

ABCDEFGH is a rectangular prism with CD = 5, AD = 6, and AE = 8. Find the volume of tetrahedron ABCF.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

CD = 5      AD = 6       AE = 8       

V_(ABCF) = 1/6(CD * AD * AE) 

The area of triangle XYZ is 8*sqrt(2).

The probability is pi/8.

The GCD has at least 3 three digits.

The probability that teaem Beta wins is 17/48.

a) There are 1080 ways.

b) There are 6480 ways.

By Inclusion-Exclusion, there are 7 students who do all 3.

The volume of tetrahedron ABCD is 1/2*5*6*8 = 120.