A rectangular box is to have a square base and a volume of 50 ft3. The material for the base costs 44¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 26¢/ft2. Letting x denote the length of one side of the base, find a function in the variable x giving the cost (in dollars) of constructing the box.
which one is the answer?
The question asked for the cost.
Damon the answer is wrong.
To find the cost of constructing the box, we need to determine the cost of each component (base, sides, and top) and then add them up.
Let's start with the base. The base is a square, so each side has a length of x ft. The area of the base is x * x = x^2 ft^2. The cost of the base material is 44¢/ft^2, so the cost of the base is 44 * x^2 cents.
Next, let's consider the sides. The box has four sides, each with a length of x ft. Since the box has a square base, the height of the box will also be x ft. The area of each side is x * x = x^2 ft^2. The cost of the side material is 10¢/ft^2, so the cost of all four sides is 4 * 10 * x^2 = 40 * x^2 cents.
Finally, let's look at the top. The top is also a square, so its side length is x ft. The area of the top is x * x = x^2 ft^2. The cost of the top material is 26¢/ft^2, so the cost of the top is 26 * x^2 cents.
To determine the total cost, we need to convert the cost from cents to dollars by dividing by 100 cents/dollar.
The function to calculate the cost, C(x), in dollars is:
C(x) = (44 * x^2 + 40 * x^2 + 26 * x^2) / 100
= (110 * x^2) / 100
= 1.1 * x^2
Therefore, the cost of constructing the box can be expressed as a function of the side length x, given by C(x) = 1.1 * x^2 dollars.
let each side of base be x
let the height be y
x^2y = 50
y = 50/x^2
cost = 44x^2 + 4(10)(xy) + 26x^2 , where cost is in cents
=70x^2 = 40x(50/x^2)
= 70x^2 + 2000/x