Question

Let
`(dy)/(dx) -√(xy)=0` and y=0 when x=1. If y=73, what is the best approximation for x?

Answer 1

E

Explanation:

dy/dx - sqrt(x/y) = 0

dy/dx = sqrt(x) ÷ sqrt(y)

y^½ .dy = x^½ .dx

Add 1 to the power and divide by the new power

(⅔)y^(3/2) = (⅔)x^(3/2) + c

x = 1, y = 0

0 = ⅔ + c

c = ⅔

(⅔)y^(3/2) = (⅔)x^(3/2) + ⅔

y^(3/2) = x^(3/2) + 1

At y = 73

73^(3/2) = x^(3/2) + 1

622.7122734 = x^(3/2)

x = 622.7122734^⅔

x = 72.9219527

Approximately 73