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Chapter 3.1

Chapter 3.1. Variation. Other Type of Direct Variation. General equation, y = f(x) = kx n. y = kx 2 K> 0. = kx K> 0. y= kx 3 K > 0. Inverse Variation. y = n where k is positive constant and n> 0 y is inversely proportional to x n. Inverse Variation.

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Chapter 3.1

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  1. Chapter 3.1 Variation

  2. Other Type of Direct Variation • General equation, y = f(x) = kxn y = kx2 K> 0 = kx K> 0 y= kx3 K > 0 Inverse Variation y = n where k is positive constant and n> 0 y is inversely proportional to xn

  3. Inverse Variation y varies inversely with x if y = , x = 0 where k is a positive constant 40 30 20 10 f(R) = 200 400

  4. No 4, Ex 3.1 ( pg 247)The force of gravity( F ) on a 1-kg mass is inversely proportional to the square of the object’s distance (D) from the center of the earth F F= • Fd2 = k = 9.8(1)2 K = 9.8 b) F= substitute k 2 Distance Earth Radii Force (Newtons) 8 6 4 2 Graph Force 1 2 3 4 5 Distance d

  5. Pg 249, No 13The weight of an object on the moon varies directly with its weight on earth d) a)m w where m = weight of object, on moon and w= wt . Of object on earth m = kw m = 24.75 pounds, w = 150 pounds K = 24.75/150 = 0.165 m = 0.165w , substitute k b)m = 0.165( 120) = 19.8 pounds c) w= = 30/0.165 = 181.8 pound Wt. on earth (W) Wt. on moon (m)

  6. No 21 No 26 y varies directly with xy varies inversely with the square of x y = kx y = y = 1.25 when x = 4, so y = 1.5, when x = 5 So 1.5 = k(5) 1.25 = and k = 1.25(4) 2 k = 1.5/5 = 0.3

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