Section 2.8 Modeling Using Variation. Direct Variation.

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Presentation transcript:

Section 2.8 Modeling Using Variation

Direct Variation

Example The volume of a sphere varies directly as the cube of the radius. If the volume of a sphere is cubic inches when the radius is 5 inches, what is the radius when the volume is 33.5 cubic inches. r

Inverse Variation

Example The pressure, P, of a gas in a spray container varies inversely as the volume, V, of the container. If the pressure is 6 pounds per square inch when the volume is 4 cubic inches, what is the volume when the pressure is down to 3 pounds per square inch?

Combined Variation

Example The TIXY calculator leasing company has determined that leases L, vary directly as its advertising budget and inversely as the price/month of the calculator rentals. When the TIXY company spent $500 on advertising on the internet and charge $30/month for the rentals, their monthly rental income was $4000. Write an equation of variation that describes this situation. Determine the monthly leases if the amount of advertising is increased to $2000.

Joint Variation

d m1m1 m2m2

Example The volume of a model square based pyramid, V, various jointly as its height, h, and the square of its side, s,of the square base. A model pyramid that has a side of the square base that is 6 inches, and the height is 10 inches, has a volume of 120 cubic inches. Find the volume of a pyramid with a height of 9 inches and a square base of 5 inches.

(a) (b) (c) (d) r

(a) (b) (c) (d)