Valishati
Valishati Valishati
  • 09-04-2020
  • Mathematics
contestada

Let [tex]\frac{dy}{dx} -\sqrt{xy}=0[/tex] and y=0 when x=1. If y=73, what is the best approximation for x?

Let texfracdydx sqrtxy0tex and y0 when x1 If y73 what is the best approximation for x class=

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amna04352
amna04352 amna04352
  • 09-04-2020

Answer:

E

Step-by-step 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

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