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Direct Variation

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Direct Variation

(Y = KX)

- Direct Variation Method
- “Y” varies directly as “X” means y = kx
- Y is a unit and X is another unit.
- Example: If weight varies directly as height and a person who is 73 inches tall weighs 210 lbs. then how tall is a person who weighs 180 lbs.?
- Y = weight, and X = height thus Weight = Height(K)
- 210 = 73k thus k = 210/73
- So 180 = (210/73)X; X = 180/ (210/73) = 430/7 = 62.6 inches

- Proportion Method
- Inches/ lbs = inches / lbs
- 73 / 210 = X / 180
- 73(180) = 210x
- 12960 = 210x
- 12960 / 210 = x
- 430 / 7 = x
- X = 62.6 inches

If the volume of a polyhedron varies directly as the square root

of its surface area, when the volume is 60 cu. ft. with a

surface area 100 sq. ft. what’s the volume for a polyhedron with

a surface area of 400 sq. ft.?

- Volume = K √Surface Area
- 60 = K √100
- 60 = 10K
- 60 / 10 = K; K = 6
- So V = 6√400
- V = 6(20)
- V = 120 cu ft

- Page 565 #’s 2 to 24 evens
- Page 572 #’s 27 to 32
- Page 579 #’s 7 to 10, 23, 24, 27 to 29