combined variation

-combined variation is just the combination of direct and inverse variation.

combined variation

-if a variable has a combined proportionality with two other variables, then it has a direct proportion with one and an inverse proportion with the other.

-combined variation also called combined proportionality.

Combined variation

The statement, "Z varies directly as x and inversely as y" means Z=kx/y, or K=zy/x, where k is the constant of variation.

statement to mathematical equations

1. P varies directly as the square of x and inversely as s. 2. The electrical resistance R of a wire varies directly as its length l and inversely as the square of its diameter d 3. The acceleration A of a moving object varies directly as the distance d it travels and inversely as the square of the time t it travels. 4. Z varies directly as x and inversely as y

find the k

If Z varies directly as x and inversely as y, and z=9 when x=6 and y=2, find z when x=8 and y=12. solution: equation of variation Z=kx/y Z=3x/y 9=k6/2 solving for z, (9) (2)=6k z=3(8)/12 18=6k z=2 k=18/6 k=3

if x varies directky as y and inversely as z, and x= 10 when y=5 and z=3, for what value of z will x=3 and y=4 x=ky/z 10=k5/3 (10) (3)=5k 30=5k k=30/5 k=6 to find z, when x=3 and y=4 3=6 4/z 3z=24 z=8

real life situation

The time it takes you to complete a puzzle is directly proportional to the number of pieces and inversely proportional to how many people are working on it. you and your three friends can complete a 1,000 pieces puzzle in 2 hours. how long would it take you to complete a 2,500 pieces puzzle by yourself t-time n-number of people p- pieces T=kp/n t=1/125 2=k1000/4 t=2500/125 2=250k t=20 k=1/125

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