Question

Suppose P varies directly with n and the square of​ m, and P=41.4 when n=4 and m=1.5. a. Find the equation that relates​ P, n, and m. b. Find P when n=3.5 and m=2.

Answer 1

a. The equation that relates P, n, and m is P = 4.6 * n * m^2. b. P when n=3.5 and m=2 is 64.4.

Step-by-step explanation:

a. To find the equation that relates P, n, and m, we can use the formula for direct variation: P=k * n * m^2. Since P=41.4 when n=4 and m=1.5, we can substitute these values into the equation to solve for k. Plug in the values: 41.4 = k * 4 * 1.5^2. Simplify: 41.4 = k * 4 * 2.25. Divide both sides by 9 to isolate k: k = 41.4 / 9 = 4.6. The equation that relates P, n, and m is P = 4.6 * n * m^2.

b. To find P when n=3.5 and m=2, we can substitute these values into the equation: P = 4.6 * 3.5 * 2^2. Simplify: P = 4.6 * 3.5 * 4 = 64.4