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Genrish500 [490]
2 years ago
9

Please help me with this question I would really appreciate it!!!

Mathematics
1 answer:
shepuryov [24]2 years ago
8 0

Answer:

0, 1.32

Step-by-step explanation:

16cos(t)*sin(t)=4sin(t)

cos(t)=1/4 or sin(t)=0

t=1.32 or 0

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A particle moves on the hyperbola xy=18 for time t≥0 seconds. At a certain instant, y=6 and dydt=8. What is x that this instant?
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Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let x\cdot y = 18, we get an additional equation by implicit differentiation:

x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0 (1)

From the first equation we find that:

x = \frac{18}{y} (2)

By applying (2) in (1), we get the resulting expression:

\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0 (3)

y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}

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The value of x at this instant is 3.

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