The volume of a particular rectangular box is given by the equation V= 50x-2x^3. The hieght and length of the box is shown below. Find the width of the box in terms of x.

Question

length= x+5

hieght = 2x

Answer 1

Volume = height x width x length

V = h•l•w

(50x - 2x³) = (2x)•(x+5)•w

(50x - 2x³) = (2x² + 10x)•w

(50x - 2x³)/(2x² + 10x) = w

2x(25 - x²)/(2x(x + 5)) = w

(25 - x²)/(x + 5) = w

(5 + x)(5 - x)/(x + 5) = w

5 - x = w

Answer 2

V=LHW

W = V/LH = (50x-2x^3)/(2x)((x+5) = (2x)(25-x^2)/(2x)(x+5) = (25-x^2)/(x+5) = (5+x)(5-x)/(x+5) = 5-x

W = 5-x

just factor and cancel, numerator V factored to (2x)(5-x)(5+x)

divide by LH = (2x)(5+x) they cancel and leave only 5-x in the numerator,with 1 as the denominator

(5-x)/1 = 5-x