The area of the ellipse 
is given by
To use Green's theorem, which says
(
denotes the boundary of ), we want to find 
and 
such that
and then we would simply compute the line integral. As the hint suggests, we can pick
The line integral is then
We parameterize the boundary by
with 
. Then the integral is
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Notice that 
kind of resembles the equation for a circle with radius 4, 
. We can change coordinates to what you might call "pseudo-polar":
which gives
as needed. Then with , we compute the area via Green's theorem using the same setup as before:
Answer:
8 + 2x = 30
Step-by-step explanation:
Given,
The initial number of push-ups he does in each day = 8,
And, the number of push-ups, he increases per day = 2,
Let x be the number of days after he will reach his target of 30 push-ups,
Since, the number of push-ups she will increase in x days = 2x,
Thus, the number of push-ups she will do after x days = 8 + 2x,
⇒ 8 + 2x = 30, which is the required equation.
Answer:
On the left side, she used commutative property
On the right side, she used distributive property
Step-by-step explanation:
