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SSSSS [86.1K]
3 years ago
11

Imagine a clock with a circular face and two hands (hours and minutes) that is set at 12:00 noon. Describe the transformation of

each hand on the clock over the next hour.
Mathematics
1 answer:
cricket20 [7]3 years ago
5 0
The minute hand would go all around the clock so it rotates 360 degrees ending up in the same place as where it started.
the hour hand would move from 12 to 1, so it rotates 30 degrees.
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The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m^2 and then divide it in half with a fence dow
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If you notice the picture below, the amount of fencing, or perimeter, that will be used will be 3w + 2l

now    \bf \begin{cases}
A=l\cdot w\\\\\
A=3000000\\
----------\\
3000000=l\cdot w\\\\
\frac{3000000}{w}=l
\end{cases}\qquad thus
\\\\\\
P=3w+2l\implies P=3w+2\left( \cfrac{3000000}{w} \right)\implies P=3w+\cfrac{6000000}{w}
\\\\\\
P=3w+6000000w^{-1}\\\\
-----------------------------\\\\
now\qquad \cfrac{dP}{dw}=3-\cfrac{6000000}{w^2}\implies \cfrac{dP}{dw}=\cfrac{3w^2-6000000}{w^2}
\\\\\\
\textit{so the critical points are at }
\begin{cases}
0=w^2\\\\
0=\frac{3w^2-6000000}{w^2}
\end{cases}

solve for "w", to see what critical points you get, and then run a first-derivative test on them, for the minimum

notice the 0=w^2\implies 0=w   so.  you can pretty much skip that one, though is a valid critical point, the width can't clearly be 0

so.. check the critical points on the other

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Answer:

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4 0
4 years ago
Read 2 more answers
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