Use the given volume of a box and its length and width to express the height of the box algebraically. (Simplify your answer completely.)

Question

Use the given volume of a box and its length and width to express the height of the box algebraically. (Simplify your answer completely.)

Volume is 10x³ + 47x² + 16x − 48,  length is 5x − 4,  width is 2x + 3

Answer 1

10x^3 +47x^2 +16x -48 divided by 5x-4

use long or synthetic division

= a quadratic 2x^2 + 11x +12

divide by 2x-3 to get x+4

dimensions are width = 4/5, depth = -4 and Length= -3/2

or graph the cubic and find the x intercepts x= .8 and 2 negative numbers -3/2 and -4

for x= +.8 dimensions are 12, 36 and 13

volume = 36x12x13= 5616 ft^2

10(8^3)+27(8^2) +17(8) -47 = (640+ 216+17)(8) -47= 6897

10(-4)^3 +27(-4)^2 + 17(-4) -47 =- 640 +432-68-47=-323

10(-1.5)^3 +27(1.5)^2 + 17(-1.5) -47 = --33.75 +60.75- 25.5-48= -46.5

go with 12,13 and 36 feet dimensions