If a graph is proportional then the line will go through the origin at point (0, 0). If the equation is proportional then it will be in the form of y=kx with no other operations after. The constant of proportionality is another way to say the slope and in your specific equation the slope would be 1/5.
It looks like the integral is
where <em>C</em> is the circle of radius 2 centered at the origin.
You can compute the line integral directly by parameterizing <em>C</em>. Let <em>x</em> = 2 cos(<em>t</em> ) and <em>y</em> = 2 sin(<em>t</em> ), with 0 ≤ <em>t</em> ≤ 2<em>π</em>. Then
Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on <em>C</em> nor in the region bounded by <em>C</em>, so
where <em>D</em> is the interior of <em>C</em>, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: 
.
<h3>
Answer: Choice A</h3>
What we do is simply replace every n with k+1. So (3n)^2 turns into (3(k+1))^2
We see that only choice A has the correct term mentioned on the left hand side, so this must be the answer.
The right hand side is treated the same way. We plug in n = k+1. Your teacher did a bit of algebraic manipulation to get what is shown for choice A.
First, find the percentage of the price after the sale occures
percent = 100% - 20%
percent = 80%
We need to find the price for the pairs with the percentage above
new price = percentage of new price/percentage of old price × old price
new price = 80%/100% × 55
new price = 4/5 × 55
new price = 44
The new price is $44
Now we estimate how much the tax
tax = 6% × 44
tax = 6/100 × 44
tax = 2.64
Calculate how much Josie will pay
pay = new price + tax
pay = 44 + 2.64
pay = 46.64
Josie will pay $46.64
Shoe=10
Girl=5
Belt=8
1 shoe+girl+belt=23
