hi everyone....i have this question to ask....i dont even know how to start for this question....can anybody help me?
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I would hope that you know that the volume of any such prism, with a base of area, A (here the triangular side), and length, l, has volume V= Al. The rate of change of volume, dV, is given, using the product rule, by dV= l dA+ A dl. Now put the information you are given into that equation.
This is a related rates problem. You are given $\dfrac{dV}{dt} = -27 \, cm^3/sec$ and $\dfrac{db}{dt} = 2 \, cm/sec$. The problem statement gives no info about the length of the prism, $L$, so I'm making the assumption it's not changing (remains a constant).
The problem wants to know if $h$ is increasing or decreasing when $b = 6 \, cm$ and $h = 3 \, cm$
First, let's use some common sense. The volume has a decreasing rate of change while the base length has an increasing rate of change ... what would you say is happening to the height?
Doing the calculation, the volume of the prism is $V = \dfrac{1}{2}bh \cdot L$ where $L$, the prism length, is a constant.
Take the derivative of the above volume formula implicitly w/respect to time and determine the value of $\dfrac{dh}{dt}$ in terms of $L$.
Oh ... next time post calculus problems in the calculus forum.