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# Module 4

### Variation and Problem Solving

If y varies directly as x, find the constant variation of k. y=10 when x=5 k=2
If y varies directly as x, find the direct variation equation for the situation. y=20, x=4 y=5x
If y varies directly as x, find the constant variation of k and the direct variation equation for the situation. y=4, x=8 k=1/2
The weight of a synthetic ball varies directly with the square of its radius. A ball with a radius of 4 inches, weighs 3.2 pounds. Find the weight of a ball of the same material with a 2 inch radius. .8 pounds
The amount of waste (W) varies directly with the population (P) of people. City A has a population of 320,000 people and produced 128,000 pounds of waste. If City B has a population of 480,000 people how much waste should be predict City B to produce? 192,000 pounds
If y varies inversely as x find the constant variation of k and the inverse variation equation for the situation. y=81, x=9 k=729, y=729/x
If y varies inversely as x find the constant variation of k and the inverse variation equation for the situation. y=1/8, x=72 k=9, y=9/x
Pairs of markings a set distance apart are Over a fixed distance, the speed R varies inversely with the time T. In one particular pair of markings, R is 60 mph when T is 5 seconds. Find the speed of a car that travels the given distance in 4 seconds. 75mph
If the voltage V in an electric circuit is held constant, the current I is inversely proportional to the resistance R. If the current is 60 amperes when the resistance is 280 ohms, find the current when the resistance is 160 ohms. 105 amperes
The intensity of light (in foot-candles) varies inversely as the square of x, the distance in feet from the light source. Intensity of light 3 feet from the source is 81 foot-candles. How far away is the source if the intensity of light is 9 foot-candles. 9 foot-candles
Write the statement as an equation. a varies jointly as b and c a = kbc
Write the statement as an equation. h varies jointly as i and the cube of j h = kij³
For the statement, find the constant of variation and the variation equation. y varies directly as the square of x; y = 3 when x = 2 k = 3/4 y = 3/4x²
Find the constant of variation and the variation equation. y varies directly as the square root of x; y = 1.5 when x = 9 k = .5 y = .5√x
For the statement, find the constant of variation and the variation equation. y varies jointly as x and the square of z; y = 96 when x = 2 and z = 4 k = 3 y = 3xz²
The max weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length.Find the constant of variation and the equation if a beam 1/2 ft wide, 1/4 ft high, and 16 ft long can support 32 tons, k = 16,384 m = (16,384wh²)/L
The volume of a cone varies jointly as the square of its radius and its height. If the volume of a cone is 60π in³ when the radius is 4 in and the height is 2 inches, find the volume of a cone when the radius is 3 inches and the height is 5 inches. k = 15/8π 84.375π in³
Created by: casablancachic