3.8 Direct, Inverse and Joint Variation

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3.8 Direct, Inverse and Joint Variation

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

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

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.

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

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.

Can use proportions to solve inverse variation:

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

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

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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