Inverse and Combined Variation

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What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

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Presentation transcript:

Inverse and Combined Variation Chapter 4 Section 4 Inverse and Combined Variation

Essential Question When collecting data, you might see a pattern. What types of things are related inversely?

Inverse Variation xy = k or y = k/x Neither x nor y can be zero If x is cut in half then y doubles and if x is doubled then y is cut in half Might be easier to set up a xy = xy then a proportion

Practice Inverse Variation (1-12) If machines take 12 days to complete a job, how long will it take for 8 machines to do the job? A gear with 40 teeth turns 30 rpm on another gear with 120 teeth. At how many rpm does the second gear turn? Two painters working at the same speed can paint 800 square feet of wall space in 6 h. If a third painter paints at the same speed, how long will it take all 3 to paint the same wall space?

Combined Variation Variables may be direct and inverse variations If you see “direct” it is multiplied (numerator) and if you see “inverse” it is divided (denominator) Ex: z varies directly as x and inversely as y means z = kx/y Ex 2: A is directly related to the square of B and inversely related to C and D means A = (kB^2)/(CD)

Practice Combined Variation (31-35) Z varies directly a the square of x and inversely as y. Find z when x = 8, y = 15 and the constant of variation is 12. If x varies directly as y and z and inversely as the square of r, and x = 16 when y = 3, z = 12 and r = 3, find x when y = 5, z = 30 and r =10