Example 8.89 from Elementary Algebra, 8.9 Use Direct and Inverse Variation

Use Direct and Inverse Variation: example 8.89

The maximum load a beam will support varies directly with the square of the diagonal of the beam’s cross-section. A beam with diagonal 4” will support a maximum load of 75 pounds.

ⓐ Write the equation that relates the maximum load to the cross-section.
ⓑ What is the maximum load that can be supported by a beam with diagonal 8”?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds.

ⓐ Write the equation that relates the distance to the time.
ⓑ How far will an object fall in 4 seconds?

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

The distance an object falls is directly proportional to the square of the time it falls. A ball falls 144 feet in 3 seconds.

ⓐ Write the equation that relates the distance to the time.
ⓑ How far will an object fall in 4 seconds?

	The maximum load varies directly with the square of the diagonal of the cross-section.
Name the variables.	Let $L =$ maximum load. $c =$ the diagonal of the cross-section
Write the formula for direct variation, where $y$ varies directly with the square of $x$ .
We will use $L$ in place of $y$ and $c$ in place of $x$ .
Substitute the given values for the variables.

Solve for the constant of variation.

Write the equation that relates $L$ and $c$ .
Substitute in the constant of variation.

	The maximum load varies directly with the square of the diagonal of the cross-section.
Name the variables.	Let $L =$ maximum load. $c =$ the diagonal of the cross-section
Write the formula for direct variation, where $y$ varies directly with the square of $x$ .
We will use $L$ in place of $y$ and $c$ in place of $x$ .
Substitute the given values for the variables.

Solve for the constant of variation.

Write the equation that relates $L$ and $c$ .
Substitute in the constant of variation.

Use Direct and Inverse Variation: example 8.89

Solution

Your turn

Use Direct and Inverse Variation: example 8.89

Solution

Your turn