Question

In the following exercises, let y = safe load in pounds and x = depth in inches for a certain type of rectangular horizontal beam. A constant of proportionality k exists such that y = kx2 (y varies directly as x2).
Determine the constant k for a beam with y = 1,000 pounds and x = 5 inches.
K=____
What is a safe load if x = 10 inches?
____Pounds
What depth should be used to support 16,000 pounds?
____inches

Answer 1

y = kx^2

Putting y = 1000, x = 5
1000 = k * 5^2
1000 = 25k
k = 1000 / 25
k = 40 lb / in^2

Putting x = 10 in, k = 40 lb / in^2
y = 40 * 10^2
y = 40 * 100
y = 4000 lb

Putting y = 16000 lb, k = 40 lb / in^2:
16000 = 40x^2
x^2 = 16000 / 40
x^2 = 400
x = 20 in

Answer 2

thanks annas :)

Answer 3

np :) thats what i do...