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

`H = 3x^2y`

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 = (36x^6y^8)/(4x^3y^5 * 3xy^2)`

`H = (36x^6y^8)/(4*3x^3*x*y^5y^2)`

`H = (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`