A particle moves on the hyperbola xy=15 for time t≥0 seconds. At a certain instant, x=3 and dx/dt=6. Which of the following is t
1 answer:
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To simplify
we need to use the fact that
Why the absolute value? It's because .
We start by rewriting as
Since , we have
, and the above reduces to
Then we pull out any 4th powers under the radical, and simplify everything we can:
where allows us to write
, and this also means that
. So we end up with
making the last option the correct answer.