Notes: 1



1.10 Direct and Inverse Variation

Direct Variation: The following are all equivalent:

✓ Y varies directly as x.

✓ Y is directly proportional to x.

✓ [pic] for some nonzero constant k where k is the constant of variation or the constant of proportionality.

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Ex.1 The simple interest on an investment is directly proportional to the amount of the investment. By

investing $2500 in a certain bond issue, you obtained an interest payment of $187.50 at the end of the

first year. Find a mathematical model that gives the interest for this bond issue at the end of the first

year in terms of the amount invested P.

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Direct Variation as an nth power: The following are all equivalent:

✓ Y varies directly as the nth power of x.

✓ Y is directly proportional to the nth power of x.

✓ [pic] for some nonzero constant k.

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Ex. 2 Neglecting air resistance, the distance S an object falls varies directly as the square of the duration t

of the fall. An object falls a distance of 144 feet in 3 seconds

(a) Write an equation relating distance S and duration t.

(b) How far will the object fall in 6 seconds?

TURN->>>

Inverse Variation : The following are all equivalent:

✓ Y varies inversely as x.

✓ Y is inversely proportional to x.

✓ [pic] for some constant k.

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Ex. 3 A company has found that the demand for its product varies inversely as the price of the product.

When the price is $2.75, the demand is 600 units.

(a) Write an equation relating demand d and price p .

(b) Approximate the demand when price is $3.25.

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Joint Variation : The following are all equivalent:

✓ Z varies jointly as x and y.

✓ Z is jointly proportional to x and y.

✓ [pic] for some constant k.

Ex. 4 The volume of a right circular cylinder varies jointly as its height and the square of its radius.

(a) Write an equation relating volume to height and radius where the volume is 2000 [pic] when the

radius is 5 inches and the height is 10 inches.

(b) Find the radius of the right circular cylinder when the volume is 8000[pic] and the height is 10 inches.

|Homework: P. 112: 39 – 62 all |

|P. 99: 16, 24 (algebraic only on 16 and 24), 40, 42, 44, 54 (just find [pic]on 54) |

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