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The frequency of a guitar string varies inversely with its length. A 26” long string has a frequency of 440 vibrations per second.
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The frequency varies inversely with the length. | |
Name the variables. | Let
frequency.
length |
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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The number of hours it takes for ice to melt varies inversely with the air temperature. Suppose a block of ice melts in 2 hours when the temperature is 65 degrees.
ⓐ ⓑ hours
The force needed to break a board varies inversely with its length. Richard uses 24 pounds of pressure to break a 2-foot long board.
ⓐ ⓑ 9.6 pounds
Solve Direct Variation Problems
In the following exercises, solve.
If varies directly as and , find the equation that relates .
If varies directly as and , find the equation that relates .
If varies directly as and , find the equation that relates
If varies directly as and find the equation that relates
If varies directly as and , find the equation that relates
The amount of money Sally earns, P , varies directly with the number, n , of necklaces she sells. When Sally sells 15 necklaces she earns $150.
ⓐ ⓑ
The price, P , that Eric pays for gas varies directly with the number of gallons, g , he buys. It costs him $50 to buy 20 gallons of gas.
Terri needs to make some pies for a fundraiser. The number of apples, a , varies directly with number of pies, p . It takes nine apples to make two pies.
ⓐ ⓑ 27 apples
Joseph is traveling on a road trip. The distance, d , he travels before stopping for lunch varies directly with the speed, v , he travels. He can travel 120 miles at a speed of 60 mph.
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