Width of a flower border A landscape architect has included

Width of a flower border A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed, how wide can the border be? Volume of a Box A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded , what upward to form an open box. If the volume of the box is 832 in.^3, what were the It original dimensions of the piece of metal. Volume of a Box In Exercise 23, suppose that the piece of metal has length twice \' the width, and 4-in. squares are cut from the corners. If the volume of the box is 1536 in^3, what were the original dimensions of the piece of metal ? Manufacturing to Specifications A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8pi ft^2. What should the radius of the circular top and bottom of the container be?

Solution

24) let the width of peice of metal w = x

length is twice the width

so length of peice of metal L =2x

4in squares are cut from sides

length of box =2x-4-4

length of box = 2x -8

width of box =x -4-4

width of box =x -8

height of box = 4 in

volume of box =(2x -8)(x -8)(4)= 1536in³

(2x -8)(x -8)(4)= 1536

(x -4)(x -8)= 96

x²-12x+32 =96

x²-12x -64 =0

x²-16x+4x -64 =0

x(x-16)+4(x-16)=0

(x+4)(x-16)=0

x =-4 , x=16

x cannot be negative so x =16

so length of peice of metal L =2*16 =32 in

width of peice of metal w = 16 in