struggling with start of calc 1

[pine quail]

forming functions from word problems

[spice crane]

For question 10, it seems like you have to use a formula for radiation decay -something to do with negative exponentials- and that should be given by the question or looked elsewhere. For question 11, a good idea is to start by giving names to the things you care about. Let's call the volume of the reservoir V=11.000, and the radius r. V is a fixed quantity, and r is not, it's the variable we want our cost function to be dependent of.

Okay, so think of it this way: if I set a value for the radius, because the volume I want to make is fixed at 11.000 cubic feet, there is one and only one height the reservoir should be for it to account for that volume. If the radius is huge, the height should be small (a wide, short reservoir), and if the radius is small, the height should be large (a narrow, tall reservoir). So, first off, let's find that height according to the radius:

Remember the formula for the volume of a cylinder with radius $r$ and height $h$: $V=\pi r^2 h$. Bare in mind we know $V=11.000$. So, I substitute $V$ and by manipulating the equation, we wirte $h$ in terms of $r$ as: $h=\frac{11.000}{\pi r^2}$.

[lean thicket]

Notyal_Lewiswestler

[spice crane]

Now, the next step is to actually write the cost of the material. So, again, with formulas for the area of different parts of a cylinder (they are basically the formulas for the area of circles and rectangles), we have that:

$\begin{itemize}
\item Area of the bottom part: $\pi r^2$
\item Area of the top part: $\pi r^2$
\item Area of the side part: $2\pi r h$
\end{itemize}$

[lean thicket]

Notyal_Lewiswestler
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[spice crane]

See that h pop up? That's why we needed it in terms of r, because our cost can only depend on the radius! Now it's a matter to multiply each area by its cost per squared foot and add it all up. I'll leave it up to you, hope you can manage!

[pine quail]

Sorry I just saw this

[urban lynx]

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