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Math Help - Rates and Related Rates!!

  1. #1
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    Rates and Related Rates!!

    A voltage V across a resistance R generates a current C = V/R. Suppose a constant voltage of 9 volts is put across a resistance that is decreasing at a rate of 0.3 ohms per second when the resistance is 4 ohms.

    (a) At what rate is the current changing?
    dC/dt =

    (b) Is the current increasing or decreasing?


    ok so if someone could like do explain how to do this problem that would help alot, i think you have to use the derivative of t somewhere in there...please help thanks

    mathlete
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  2. #2
    Senior Member Peritus's Avatar
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    first of all using the letter C for current is a really bad idea.

    we know that the resistance is time dependent and thus the current will be also time dependent (Ohm's Law)

    <br />
\begin{gathered}<br />
  C(t) = \frac{V}<br />
{{R(t)}} \hfill \\<br />
   \Leftrightarrow R(t)C(t) = V \hfill \\<br />
  C(t)\frac{{dR(t)}}<br />
{{dt}} + R(t)\frac{{dC(t)}}<br />
{{dt}} = 0 \hfill \\ <br />
\end{gathered} <br />

    now all we have to do is use the given info:


    <br />
\begin{gathered}<br />
   - \frac{9}<br />
{4} \cdot 0.3 + 4\frac{{dC}}<br />
{{dt}} = 0 \hfill \\<br />
   \Leftrightarrow \frac{{dC}}<br />
{{dt}} = \frac{{27}}<br />
{{160}} \hfill \\ <br />
\end{gathered} <br />
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