Question

PLEASE SOLVE THIS FOR ME ITS DUE TOMORROW

Find an expression for the missing dimension.

Answer 1

The missing length is 2x+5

Explanation:

Given equation of volume of cuboid is V=
`2x^(3) +17x^(2) +46x+40`

Figure show that

Length of cuboid is ?

Width of cuboid is (x+4)

Height of cuboid is (x+2)

The volume of cuboid is given by

V=Length x Width x Height

Let Length be (bx+a)

The volume of cuboid will be

`V=(bx+a)(x+4)(x+2)`

`V=(bx+a)[x^(2)+4x+2x+8 ]`

`V=bx[x^(2)+6x+8]+a[x^(2)+6x+8]`

`V=[bx^(3)+6bx^(2)+8bx]+[ax^(2)+6ax+8a]`

`V=[bx^(3)+(6b+a)x^(2)+(8b+6a)x+8a]`

On comparing coefficient with given equation of volume

We get,

b=2 and 8a=40

Therefore, the value of a is 5 and b is 2

Thus, The missing length is bx+a=2x+5