Homework 6 section 3.5 (Homework)

Question

The area of a projected picture on a movie screen varies directly as the square of the distance from the projector to the screen. If a distance of 80 feet produces a picture with an area of 64 square feet, what distance (in ft) produces a picture with an area of 100 square feet?

Answer 1

Hi Riley, you can think of this problem in terms of the following equation:

Area = distance^2 * k, where distance is how far the projector is from the screen and k is a constant that will be multiplied to the distance squared. We will need to solve for k to get the answer. Using the first example, if a distance of 80 provides an area of 64, we can plug these numbers back into our equation. So 64 = 80^2 * k

64 = 6400K, k = .01. Using our value of k we can solve the problem.

.01 * (D^2) = 100

Solving for D, 100/.01 = 10000=D^2,

sqrt(10000) = 100. The distance is 100.