4.4.notebook
December 09, 2014
4.4 Variation
Direct Variation
Inverse Variation y varies directly with x y varies inversely with x
Joint Variation y varies jointly with w and z
Dec 6­2:16 PM
Translate each expression into a  mathematical model:
The circumference of a circle varies directly with the radius.
At a constant temperature, the volume of a gas varies inversely with  the pressure.
The length of time of a meeting is directly proportional to the square  of the number of people present.
The time  t  it takes to drive a particular distance is inversely  proportional to the speed  s .
The amount of your paycheck  P  varies directly with the number of  hours  h  that you work.
***Make up your own...
Dec 6­2:34 PM
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4.4.notebook
December 09, 2014
Translate each expression into a mathematical  model:
The gravitational force of attraction between two planets varies  jointly with the product of their masses and inversely with the  square of the distance between them.
x  varies directly with the square root of  y  and inversely with  z .
Dec 6­2:38 PM
The variable z varies directly with w.
When w is 16, z is 56. Find the value of z when w is 84
The variable q varies directly with the square of v. When v is 2, q is 40. Find q when v = 7.
Dec 6­2:40 PM
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4.4.notebook
December 09, 2014
The speed of a racing canoe in still water varies directly with the square root of the length of the canoe.
If a 16-ft. canoe can travel 6.2 mph in still water, find a variation model that relates the speed of a canoe to its length.
Find the speed of a 25-ft. canoe.
Dec 6­2:42 PM
The loudness of sound measured in decibels (dB) varies inversely with the square of the distance between the listener and the source of the sound. If the loudness of sound is 17.92 dB at a distance of 10 ft from a stereo speaker, what is the decibel level 20 ft from the speaker?
Dec 6­2:44 PM
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4.4.notebook
December 09, 2014
The amount of simple interest earned in an account varies jointly with the interest rate and time of the investment.
An account earns $40 in 2 years at 4% interest. How much interest would be earned in 3 years at a rate of 5%?
Dec 6­2:46 PM
Problems to try:
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Dec 6­2:48 PM
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