Question

Using V = lwh, what is an expression for the volume of the following prism? The dimensions of a prism are shown. The height is StartFraction 2 d minus 6 Over 2 d minus 4 EndFraction. The width is StartFraction 4 Over d minus 4 EndFraction. The length is StartFraction d minus 2 Over 3 d minus 9 EndFraction.

Answer 1

its c on E2020

Step-by-step explanation:

Answer 2

Step-by-step explanation:

We know that the volume of a prism is defined by:

`V=lwh \\ \\ \\ Where: \\ \\ l:length \\ \\ w:width \\ \\ h:height \\ \\ \\ l=(d-2)/(3d-9) \\ \\ w=(4)/(d-4) \\ \\ h=(2d-6)/(2d-4)`

Substituting values:

`V=\left((d-2)/(3d-9)\right)\left((4)/(d-4)\right)\left((2d-6)/(2d-4)\right) \\ \\ \\ Simplifying: \\ \\ V=(d-2)/(3d-9)\cdot (4)/(d-4)\cdot (d-3)/(d-2) \\ \\ V=(\left(d-2\right)\cdot \:4\left(d-3\right))/(\left(3d-9\right)\left(d-4\right)\left(d-2\right)) \\ \\ V=(4\left(d-3\right))/(\left(3d-9\right)\left(d-4\right)) \\ \\ V=(4\left(d-3\right))/(3\left(d-3\right)\left(d-4\right))`

`Finally: \\ \\ \boxed{V=(4)/(3\left(d-4\right))}`