Jack cuts four squares with side length X inches from corners by a 5" x 7" cardboard rectangle. He folds the remaining cardboard to make a tray that is x inches high. Write and simplify a function for the volume V of the tray in terms of X.

Step-by-step explanation:

Given:

Dimensions of rectangle cardboard:

Length, l = 7 inches

Width, b = 5 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, therefore:

Length of the tray = length of cardboard - 2 (side of the square )

= 7 - (2 × x)

= 7 - 2x inches

Width of the tray = width of cardboard - 2(side of square)

= 5 - (2 × x)

= 5 - 2x inches

height of tray = cut sides of square

= x inches

volume of tray = Length × width × height

= (7 - 2x) × (5 - 2x) × x

Volume of tray = 35x - 10x^2 - 14x^2 + 4x^3

Simplifying further,

= (35x - 24x^2 + 4x^3) cubic inches

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