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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?
ⓐ ⓑ 256 feet
The area of a circle varies directly as the square of the radius. A circular pizza with a radius of 6 inches has an area of 113.04 square inches.
ⓐ ⓑ 254.34 square inches
Many applications involve two variable that vary inversely . As one variable increases, the other decreases. The equation that relates them is .
For any two variables x and y , y varies inversely with x if
The constant k is called the constant of variation.
The word ‘inverse’ in inverse variation refers to the multiplicative inverse. The multiplicative inverse of x is .
We solve inverse variation problems in the same way we solved direct variation problems. Only the general form of the equation has changed. We will copy the procedure box here and just change ‘direct’ to ‘inverse’.
If y varies inversely with and when , find the equation that relates x and y .
| Write the formula for inverse variation. |
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| Substitute the given values for the variables. |
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| Solve for the constant of variation. |
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| Write the equation that relates and . |
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| Substitute in the constant of variation. |
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If varies inversely with and when find the equation that relates and
If varies inversely with and when find the equation that relates and .
The fuel consumption (mpg) of a car varies inversely with its weight. A car that weighs 3100 pounds gets 26 mpg on the highway.
ⓐ
| The fuel consumption varies inversely with the weight. | |
| First we will name the variables. | Let
fuel consumption.
weight |
| Write the formula for inverse variation. |
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| We will use in place of and in place of . |
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| Substitute the given values for the variables. |
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| Solve for the constant of variation. |
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| Write the equation that relates and . |
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| Substitute in the constant of variation. |
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ⓑ
A car’s value varies inversely with its age. Elena bought a two-year-old car for $20,000.
ⓐ Write the equation of variation.
ⓑ What will be the value of Elena’s car when it is 5 years old?
ⓐ ⓑ $8,000
The time required to empty a pool varies inversely as the rate of pumping. It took Lucy 2.5 hours to empty her pool using a pump that was rated at 400 gpm (gallons per minute).
ⓐ ⓑ 2 hours
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