Let
rt{xy}=0" alt="\frac{dy}{dx} -\sqrt{xy}=0" align="absmiddle" class="latex-formula"> and y=0 when x=1. If y=73, what is the best approximation for x?
1 answer:
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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