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# Module 4

### Variation and Problem Solving

Question | Answer |
---|---|

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 |

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