Aclosed box with a square base is to be built to house an ant colony. the bottom of the box and all four sides are to be made of material costing $1/ft², and the top is to be constructed of glass costing $5/ft². what are the dimensions of the box of greatest volume that can be constructed for $72?

Dimensions of the box will be 6 ft × 6 ft × 54 feet

Step-by-step explanation:

A closed box is to be built having square base.

Let the dimensions of the box are a ft × a ft × b ft.

Material used to build the base and all four sides cost $1 per square ft.

Therefore, cost of base and four sides = 1[(a)² + 4ab]

Top of the box is to be constructed of glass costing $5 per square feet.

Cost of the top = 5a²

Total cost of the box material = (a² + 4ab) + 5a² = $72

6a² + 4ab = 72

b = -----(1)

Now volume of the box V = a×a×b = a²b

From equation (1),

V = a²()

V = a(18 - 1.5a)

For greatest volume ,

18 - 3a = 0

a = 6

Now form equation (1)

b =

b = 54 feet.

Therefore, dimensions of the box will be 6 ft × 6 ft × 54 feet.

can you add an image ?

step-by-step explanation:

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,