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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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Section 3.5 Mathematical Modeling Objective(s): To learn direct, inverse and joint variations. To learn how to apply the variation equations to find the.

Section 3.5 Mathematical Modeling Objective(s): To learn direct, inverse and joint variations. To learn how to apply the variation equations to find the.

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