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This seems trickier  than it really is

Look  at the following figure  :

Note  that   since the sides of the  square = 18....then DB = sqrt 2*18 = AC

E is the  center of the  square so  BE  = CE  =  sqrt (2)*10

And angle CEB = 90°

And the circle has a radius of 18

So....if we take  the area of 1/2 of this  circle  and  subtract  the  area of triangle CEB we will have the same area  as  the shaded region

Area of half-circle  with radius of 12  =  pi (6/2)^2  / 2 =  18*pi

Area of triangle CEB  =  area of an isosceles triangle  with equal sides of sqrt (2)/2  and an included angle of 90° =

(1/2) [ sqrt (2) / 2 ] ^2 *sin 90° =  12

So....the shaded area =   16*pi - 4

Midpoint of AB  = (27/2,11/2)

Slope = (7 - 4)/(24 - 3) = 3/21 = 1/7

y - 11/2 = 1/7*(x - 27/2), y - 4 = 7(x - 3)

(x,y) = (13/2,5/2)

2x - 4y = 3

(a^3 + b^3) = (a + b)(a^2 - ab + b^2)

==> 1/(cbrt(3) - cbrt(2)) = (4^(1/3) + 12^(1/3) + 36^(1/3))/3, so A + B + C + D = 55.

OC = 42        CB = 56

AB = 2(OC + CB) = 176             AO = AB/2 = 88

AK = 1/2(AB - CB) = 60

Radii are:    28, 60, and 88

please read the question. It says less than 15

ab - 3a +5b = 137

a = (137 - 4 5)/(b - 3), or:
b = (3 a + 137)/(a + 5)
For positive solutions, I see only 2 as follows:
a =56 and b=112
a=143 and b=89
From the 3 above, the one with smallest absolute difference is:
abs[112 - 56] = 27

Here's the same problem, except it says two times it's edge length.  You'd solve it the same way though. 

                                         https://web2.0calc.com/questions/a-cube-of-edge-length-s 

_.

https://web2.0calc.com/questions/find-the-equations-of-the-median-from-vertex-a-to_1

A large sphere has a volume of 288*pi cubic units. A smaller sphere has a volume which is 64% of the volume of the larger sphere. What is the ratio of the radius of the smaller sphere to the radius of the larger sphere? Express your answer as a common fraction.

V_s = 0.64*V_l = 0.64*288*pi

4pi*r^3 = 144*pi ==> r = 12

4pi*s^3 = 28*pi ==>  s = 8

r/s = 8/12 = 2/3

The shaded region shown consists of 11 unit squares and rests along the x-axis and the y-axis. The shaded region is rotated about the y-axis to form a solid. In cubic units, what is the volume of the resulting solid? Express your answer in simplest form in terms of pi.

V = 3*pi + 2*pi*4 = 11*pi

Given: ΔАВС, m∠ACB = 90° 
CD ⊥ AB, m∠ACD=60°,BC = 6 cm

 Find CD, Area of ΔABC 

CD = sin(60º) * 6

AC = tan(60º) * 6

[ABC] = (AC * AB) / 2

angle A = 30 degrees

The smallest x = 36

[36 x 400] mod 576 ==0

Star pentagon theorem: Sum of all angles in star pentagon is 180

==> Angle A = 180 - 100 - 70 + 40 = 50

The area of triangle DMN is 5*sqrt(3).

Wrong 

(a^3 + b^3) = (a + b)(a^2 - ab + b^2)

==> 1/(cbrt(3) - cbrt(2)) = (6^(1/3) + 8^(1/3) + 9^(1/3))/2, so A + B + C + D = 25

Quadratic formula: x = (-b +/- sqrt(b^2 - 4ac))/2a

optimal value of x = -b/2a

==> largest value of t is 78 dollars

Wow I din't think of this that way

fifteen

eighty one     so the binomial square becomes   ( x + 9)²

(t-6)(2t-1) = (2t-8)(t-3)

2t^2 -13t + 6 = 2t^2 -14t+24

t = 18

Jack =90  x  1.06  x  0.8 =76.32 - his total

Jill =90  x  0.8   x  1.06 =76.32 - her total

76.32  -  76.32 ==0 difference.