An open box is to be made from a rectangular piece of cardboard 30" x 24" by cutting equal squares from the corners and turning up the sides Write a function v(x)

Accepted Solution

Answer:v(x) =x^(3) - 108"x^(2) + 720"xStep-by-step explanation:Dimensions of rectangle,length = 30", breadth=24"Four equal squares are cut, at corners of rectangle.Let the length of square cut be "x".Thus the length of rectangle reduces to = 30"-(2x)2a because the 2 squares are respectively cut from one corresponding length.Similarly, the breadth of rectangle reduces to = 24"-(2x)Thus visualizing the box formed by raising up the sides, height= xlength = 30"-(2x)breadth = 24"-(2x)thus volume as function of dependent variable x is,v(x)=(height)X(lenght)X(breadth)      =(x)X(30"-2x)X(24"-2x)      =(x)X(720"-108"x+x^(2))v(x) =x^(3) - 108"x^(2) + 720"x