s 5562 find a mathematical model representing tatement In ea

s 55-62, find a mathematical model representing tatement. (In each case, determine the constant of In Exercises proportionality.) 55. A varies directly as r2. (A 9 56. y varies inversely as x. (y = 3 when x = 25) 57. y is inversely proportional to x when r-3.) , . (y = 7 when x = 4.)

Solution

55) A varies directly with r^2

A = kr^2

9pi = k (3)^2

k = pi

56) y varies inverse as x

y = k/x

k = y*x

k = 3* 25

k = 75

57) y = k/x

k = y*x

k = 7*4 = 28

39) A varies directly as square of r

mathematical model can be written as

A = kr^2

40) V varies directly as cube of e

so model becomes

V = ke^3