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**A3 3.7 Direct and Indirect Variation**

Homework: p odd

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Direct Variation K= constant of variation, the same for an entire data set Graph: Words: y varies directly with x y is directly proportional to x

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**Direct Variation Example**

The volume of blood, B, in a person’s body varies directly as body weight, W. A person who weighs 160 pounds has approximately 5 quarts of blood. Estimate the number of quarts of blood on a person who weighs 200 lbs.

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**another direct variation…with a twist!**

The distance, S, that a body falls from rest varies directly as the square of time, t, of the fall. If skydivers fall 64 feet in 2 seconds, how far will they fall in 4.5 seconds?

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Inverse Variation K = constant of variation, still the same for the entire data set! Graph: Words: y varies inversely as x y is inversely proportional to x

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**Inverse Variation Example**

The length of a violin string varies inversely as the frequency of its vibrations. A violin string 8 inches long vibrates at a frequency of 640 cycles per second. What is the frequency of a 10-inch string?

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**another variation example with a new twist!**

The force of gravitation, F, between two bodies varies jointly as the product of their masses, and inversely as the square of the distance between them. G is the gravitational constant.

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**Last cool example of variation…**

The volume of a cone, V, varies jointly as its height, h, and the square of its radius. A cone with a radius measuring 6 feet and a height measuring 10 feet has a volume of cubic feet. Find the volume of a cone having a radius of 12 feet and a height if 2 feet.

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**White board equation writing!**

Write all equations, then solve for y! X varies jointly as Y and the square of Z X varies directly as the cube root of Z and inversely as Y X varies jointly as Z and the difference between Y and W.

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200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Ratio and Proportions Percents Direct and Inverse Variation.

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