I'll give a medal to who ever tell me a and b

Question

anonymous · Answer

attachment

anonymous · Answer

I know the first part
K=3.125

How do I get part "b"?

whpalmer4 · Answer

The graph of $y = |x|$ is equivalent to $y = x$ over the range $0 \le x \le \infty$ and symmetrical about $x=0$, so we can just do half the region and multiply by 2.

Integrate the height between $y_2 = 0.08x^2+k$ and $y_1 = x$:
$$2\int_0^{6.25}(0.08x^2+k-x)\,dx$$to get your answer.

anonymous · Answer

So K determines "b"? (meaning the 6.25)

anonymous · Answer

This is what I got
$$2\int\limits_{0}^{6.25}(0.08x^2+3.125-x) dx = 13.0208$$

whpalmer4 · Answer

Yes, because k shifts the parabola up or down, which clearly has a big impact on the surface area....

In fact, if you leave $k$ as a variable and do the integral, you end up with \-26.0417+12.5k\]so the answer is very sensitive to the value of $k$

Yes, I got the same result.  I hope it is correct, it's late :-)

whpalmer4 · Answer

as you can see by my failed formatting...

whpalmer4 · Answer

although I guess the limits of integration will also be altered by changing $k$

anonymous · Answer

Webassign didn't take it :(
I didn't think it was going to take it either way because it is asking to round to five decimal places

anonymous · Answer

Thanks but I already used all my tries

whpalmer4 · Answer

I don't see see why you entered 13.0208 if it said round to 5 decimal places...an exact answer is 625/48, which is 13.0208333...

anonymous · Answer

Oh man, I didn't get the rest of the answer on my calculator. Oh well I still got an A, thx though.