Variation -- Section 2.5 --

 y varies directly with x: y = kx (k is a constant) y varies inversely with x: (k is a constant) y varies jointly with w and x: y = kwx (k is a constant) Find the constant of proportionality. y is directly proportional to x.  If x = 3, then y = 24.
 Solve Step Check The goal is to find k, the constant. y = 8x y = kx Use the formula for direct variation If x = 3, then y = 24. If x = 3, then y = 24. Given y = 8(3) 24 = k(3) Plug in x and y y = 24 24 = 3k Divide by 3 k = 8 constant of proportionality y = 8x Plug 8 in formula for k Now we have a formula that can be used to find values for y for specific values of x.  Find the constant of proportionality. y is directly proportional to x.  If x = 12, then y = 4. [Solution]  Find the constant of proportionality. L is inversely proportional to the square of d.  If d = 2, then L = 3.
 Solve Step Check The goal is to find k, the constant. Plug in the values If d = 3, then L = 5. Use the formula for inverse variation If d = 3, then L = 5. Given L = 5  Plug in d and L Square 3 and multiply both sides by 9 k = 45 constant of proportionality Plug 45 in formula for k  Find the constant of proportionality. z is inversely proportional to the cube of w.  If w = 2, then z = 3. [Solution]  R varies jointly with  p and q. If  R = 20, when p = 5 and q = 8.   Find R , when p = 3 and q = 16
 Solve Step The goal is to find k, then R. Plug in the values. Find the constant of proportionality. R = kpq Use the formula for joint variation  with  p and q If  R = 20, when p = 5 and q = 8 Given 20 = k(5)(8) = 40k Plug in p, q and R constant of proportionality The formula Plug in 3 and 16 to find R R = 24 Done!!  H varies jointly with the square g and the square root f. If  H = 160, when g = 4 and g = 25.   Find H , when g = 1 and f = 81 [Solution] Tutorials and Applets by
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