Using y to represent number of bottles filled in x minutes, y = 250x.
This is rather basic, and I urge you to think about it so that it's very clear to you, and you will be able to do similar problems on your own in the future.
The graph will be a straight line passing through the origin (0,0).
40 feet or 13 yards and 1 foot
using the conversion
1 yard = 3 feet then 1 yard 2 feet = 5 feet ← material for 1 pillow, hence
8 pillows require 8 × 5 = 40 feet
Step-by-step explanation:
Firstly, we'll try to simplify the integrand. By hint 1, we see that:

Simplifying the integrand gives us:

Next, by hint 2, we observe that:

So this tells us to make the substitution: 
Doing so gives us:
, which should be trivial.