Question

Let y = safe load in pounds and x = depth in inches for a certain type of rectangular horizontal beam. A constant of proportionality exists such that y = kx^2.

Determine the constant k for a beam with y = 1,000 pounds and x = 5 inches.

What depth should be used to support 16,000 pounds?

A. 40 inches
B. 20 inches
C. 10

Answer 1

• k = 40 lb/in²
• B. 20 inches

Explanation:

Fill in the given numbers and solve for k.

y = kx²

1000 lb = k(5 in)²

(1000 lb)/(25 in²) = k = 40 lb/in² . . . . . . divide by the coefficient of k

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Fill in the given numbers and solve for x.

y = kx²

16000 lb = (40 lb/in²)x²

16000 lb/(40 lb/in²) = x² = 400 in² . . . . . . divide by the coefficient of x²

20 in = x . . . . . . . . . take the square root

The depth to support 16,000 pounds should be 20 inches.