CPhill

The distance is given by

√[(-4-8)^2 + (4-4)^2] = √[(12)^2 + 0^2] = √(12)^2  = √144 = 12

I assume this is

C(x) = x^3 -15x + 14

So.... the cost to make 900 units is given by

(900)^3 - 15(900) + 14

And I'l let you finish this one....

The volume of the cube is given by

s^3  = 4913  take the cube root of both sides

s = 17cm

And the diagonal is given by s√3 = 17√3cm

If the area of the base of one cube is twice that of the other, the ratio of their sides is s√2 to s

So, the ratio of their volumes is  (s√2)^3 / s^3  = (√2)^3  = 2√2

We have that  2s^2 = d^2      where s is the side and d is the diagonal......so we have

2s^2  = (9√3)^2

2s^2 = 243   divide by 2 on both sides

s^2 = 243/2   take the square root of both sides

So  s = √(243/2)

And the diagonal of a cube is given by

√(3s^2)  =  √[3(243/2)] = √(243*1.5) = about 19.09  units

A dm  = .1m   ... so 3dm  = .3m

The lateral area (area of the sides) is given by  4*s*.3    where s is = the side of the base

So

4*s*.3m = 110m^2

1.2s = 110    divide by 1.2

s = 275/3 = about 91.667m

Let x be one dimension....then the other dimensions are 1.5x  and 2.5x

Therefore  (x)(1.5x)(2.5x) = 2432

So

3.75x^3  = 2432     divide both sides by 3.5

x^3  = 2432/3.75    take the cube root of both sides

x = ³√(2432/3.75 ) = about 8.656cm

And 1.5x = about 12.984cm

And 2.5x = 21.64cm

Proof  8.656 * 12.984 * 21.64 = about 2432.....

The surface area is given by S_a = 6s^2

So.....6s^2  = 96     divide by 6 on both sides

s^2  = 16    take the square root of both sides

s = 4

And the volume of a cube is just s^3  =  4^3  = 64cm^3