Type of Variation



Alg 2X – U8 Day 13 – Variation

|Type of Variation |Equation |k is: |

|Direct | | |

|Inverse | | |

k is called the __________________________________________

#1. y varies directly as x, and y = 12 when x = 4. Find an EQUATION that represents the variation.

#2. y varies inversely as x, and y = 12 when x = 4. Find an EQUATION that represents the variation.

#3. y varies directly as x, and y = 20 when x = 5. Find y when x = 10.

#4. y varies inversely as x, and y = 20 when x = 5. Find y when x = 10..

Word Problems. Choose "nice" letters as your variables.

1. The amount of money raised at a charity fundraiser is directly proportional to the number of attendees. The amount of money raised for five attendees was $100. How much money will be raised for 60 attendees?

2. Bob's dentist determined the number of cavities developed in his patient's mouth each year is inversely proportional to the total number of minutes spent brushing during each session. If Bob developed four cavities during the year he spent only 30 seconds brushing his teeth each time, how many annual cavities will Bob develop if he increases his brushing time to two minutes per session?

JOINT Variation: Used to describe a sitation in which there is a

___________ relationship with ____________________________ variables.

3. x varies jointly with y and z. If x=36 when y=3 and z=2, find x when y=5 and z=-7.

4. The volume of a cylinder varies jointly as the height of the cylinder and the square of the radius. When the radius is 3 inches and the height is 2 inches, the volume of the cylinder is [pic]. Find an EQUATION that represents the relationship between volume, radius and height.

5. Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour. What is the intensity at a distance of 2.5 meters?

COMBINED Variation: Used to describe a sitation in which there is a

both a _____________ relationship and an _________________ relationship.

6. y varies directly with x and inversely with z. If y=36 when x=3 and z=2, find y when x=5 and z=-7.

Determine whether the values in each table represent a direct variation, inverse variation or neither.

|x |y |

|2 |6 |

|4 |3 |

|-1 |-12 |

|12/7 |7 |

|x |y |

|27 |3 |

|306 |34 |

|81 |9 |

|18 |2 |

1. 2.

|x |y |

|2 |6 |

|9 |3 |

|12 |4 |

|1 |3 |

|x |y |

|2 |32.5 |

|5 |13 |

|25/7 |91/5 |

|1 |65 |

3 4.

5. Fill in the chart, given that y varies jointly with x and z.

|x |2 |10 |25 | |

|y |120 | |2400 |144 |

|z |5 |15 | |6 |

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