Question

HELP...The volume of a rectangular prism is 36x^6y^8. The length of the prism is 4x^3y^5, and the width of the prism is 3xy^2. What is the height of the prism? Write a justification of your result. v=lwh​

Answer 1

Answer:

$H = 3x^2y$

Step-by-step explanation:

Given

$V = 36x&^6y^8$

$L = 4x^3y^5$

$W = 3xy^2$

Required

Find the height of the prism

Volume (V) is calculated as:

$V =LWH$

Substitute values for V, L and W

$36x^6y^8 =4x^3y^5 * 3xy^2 * H$

Make H the subject

$H = \frac{36x^6y^8}{4x^3y^5 * 3xy^2}$

$H = \frac{36x^6y^8}{4*3x^3*x*y^5y^2}$

$H = \frac{36x^6y^8}{12x^4*y^7}$

Divide:

$H = 3x^{6-4}y^{8-7}$

$H = 3x^2y$

The height of the prism is: $3x^2y$