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**3.8 Direct, Inverse and Joint Variation**

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**Direct Variation y = kxn, n>0 k is the constant of variation**

The relationship between braking distance and car speed. As the speed of the car increases, the braking distance also increases at a constant rate

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**Ex 1 suppose y varies directly as x and y = 45 when x = 5/2**

Find the constant of variation and write an equation Use the equation to find the value of y when x = 4

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Ex 2 When an object such as a car is accelerating, twice the distance d it travels varies directly with the square of the time t elapsed. One car accelerating for 4 minutes travels 1440 ft. Write an equation. Find the distance traveled in 8 minutes.

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Ex 3 If y varies directly as the square of x and y = 30 and x = 4, find x when y = 270.

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**Inverse Variation (Inversely proportional)**

As one value increases the other decreases. When you travel to a higher elevation above Earth’s surface, the air temperature decreases.

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**Can use proportions to solve inverse variation:**

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**Ex 4 If y varies inversely as x and y = 14 when x =3, find x when y = 30.**

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**Joint Variation – when one quantity varies directly as the product of two or more other quantities.**

y = kxnzn where x and z cannot = 0 and n > 0

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Ex 5 In Physics, the work W done in charging a capacitor varies jointly as the charge q and the voltage V. Find the equation of joint variation if a capacitor with a charge of coulomb and a voltage of 100 volts performs 0.20 joule of work.

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Direct Variation We say that two positive quantities x and y vary directly if an increase in one causes a proportional increase in the other. In this case,

Direct Variation We say that two positive quantities x and y vary directly if an increase in one causes a proportional increase in the other. In this case,

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