The answer to your equation would be: 150x0.200%=0.3
We need to find the percentage of the extra feet that she measured, so first we have to find out how much that is. We can do this by simply subtracting:
4.27 - 4 = 0.27
Now we can set up a proportion to find the percentage.

Solve for x
0.27 x 100 = 27
27/4 = 6.75
The answer is
6.75% :)
Hopefully this helps! If you have any more questions or don't understand, feel free to DM me, and I'll get back to you ASAP! :)
We first have to find the first derivative before we can find the second. First derivative with respect to x is

so

and

. That's the first derivative. Now for the second it's probably easiest to use the quotient rule, even though it's usually long and drawn out. That looks like this:
![\frac{dy}{dx}= \frac{4y^2(-6x)-[-3x^2(8y \frac{dy}{dx})] }{(4y^2)^2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B4y%5E2%28-6x%29-%5B-3x%5E2%288y%20%5Cfrac%7Bdy%7D%7Bdx%7D%29%5D%20%7D%7B%284y%5E2%29%5E2%7D%20%20)
which simplifies a bit to

. We will multiply both sides by that denominator to get rid of it which leaves us with

. Get both dy/dx terms on the same side, and then factor it out.

. Divide to isolate the dy/dx:

. There's no simplifying you could do after that that would make any significant difference.