Question

Due in 15 minutes somebody please help me ASAP!

Answer 1

a) Length= 8x

Width = 3x+2

Height = 2x+1

b) The volume of Prism = 640

c) Dimensions of prism are:

Length= 16

Width = 8

Height = 5

d) Volume of Prism is 640

Explanation:

Volume of Prism =
`48x^3+56x^2+16x`

a) What are the dimensions of prism.

Dimensions of prism can be found by finding the factors of the given Volume.

Volume of Prism =
`48x^3+56x^2+16x`

Take 8x common

`8x(6x^2+7x+2)`

Now we will factor the term:
`6x^2+7x+2`

`6x^2+3x+4x+2\\=3x(2x+1)+2(2x+1)\\=(3x+2)(2x+1)`

So, factors of term :
`6x^2+7x+2` are
`(3x+2)(2x+1)`

Replace term with their factors

`8x(6x^2+7x+2)\\=8x(3x+2)(2x+1)`

We know that
`Volume\: of\: Prism = Length * Width * Height`

So,
`48x^3+56x^2+16x=8x(3x+2)(2x+1)`

So, Length= 8x

Width = 3x+2

Height = 2x+1

b) if x =2, use the polynomial
`48x^3+56x^2+16x` to find Volume of prism.

Put x =2 and calculate Volume

Volume of Prism =
`48x^3+56x^2+16x`

Volume of Prism =
`48(2)^3+56(2)^2+16(2)\\=48(8)+56(4)+32\\=384+224+32\\=640`

So, The volume of Prism = 640

c) If x =2, Use the factors found in part a) to calculate the dimensions.

The dimensions are:

Length= 8x

Width = 3x+2

Height = 2x+1

Put x =2 and find answers

Length= 8x = 8(2) = 16

Width = 3x+2 = 3(2)+2 = 6+2 =8

Height = 2x+1 = 2(2)+1 = 4+1 = 5

So, Dimensions of prism are:

Length= 16

Width = 8

Height = 5

d) Using the dimensions found in part c, calculate the volume.

We know that
`Volume\: of\: Prism = Length * Width * Height`

And

Length= 16

Width = 8

Height = 5

Finding Volume:

`Volume\: of\: Prism = Length * Width * Height`

`Volume\:of\:Prism=16* 8 * 5\\Volume\:of\:Prism=640`

So, Volume of Prism is 640