Question

Lucy cuts 4 square with side length x in. From the corners of a 6 in by 9 in cardboard rectangle. She folds the remaining cardboard to make a tray that is x in high. Write and simplify a polynomial fiction for volume V of the tray in terms of x

A and B

Answer 1

`V=4x^3-30x^2+54x`

Explanation:

From the question we are told that

Breath of cardboard h=6

Length of cardboard l=9

Let x be the height when fold

Generally the new rectangle is mathematically given as

Breath
`h'=(6-2x)`

Length
`l'=(9-2x)`

Generally the Volume of tray is mathematically given as

`V=L*B*H`

`V=(9-2x)*6-2x*x`

`V=x(4x^2-30x+54)`

`V=4x^3-30x^2+54x`