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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
If x2 + y2 = 100 and dy / dt = 4, find dx/dt when y = 6.
Solution:
Given, x2 + y2 = 100
dy/dt = 4
We have to find dx/dt.
When y = 6,
x2 + (6)2 = 100
x2 + 36 = 100
x2 = 100 - 36
x2 = 64
Taking square root,
x = ±8
Differentiating with respect to t,
\(2x(\frac{dx}{dt})+2y(\frac{dy}{dt})=0\)
\(x(\frac{dx}{dt})+y(\frac{dy}{dt})=0\)
Put dy/dt = 4 in the above expression,
\((\pm 8)(\frac{dx}{dt})+(6)(4)=0\)
\((\pm 8)(\frac{dx}{dt})+24=0\)
\((\pm 8)(\frac{dx}{dt})= -24\)
\(\frac{dx}{dt}=(\frac{-24}{\pm 8})\)
\(\frac{dx}{dt}=\pm 3\)
Therefore, dx/dt = ±3
If x2 + y2 = 100 and dy / dt = 4, find dx/dt when y = 6.
Summary:
If x2 + y2 = 100 and dy / dt = 4, then dx/dt when y = 6 is ±3.
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