Presentation on theme: "3.8 Direct, Inverse and Joint Variation. Direct Variation y = kx n, n>0 k is the constant of variation The relationship between braking distance and car."— Presentation transcript:
3.8 Direct, Inverse and Joint Variation
Direct Variation y = kx n, 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 Earths 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 = kx n z n 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.