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
###
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:
If 19 out of 28 renters keep a pet, there are 
renters who don't keep a pet.
Whenever you have a subset of some set, and you want to know which percentage of the set the subset represents, you simply have to compute
So, in your case, you're wondering what percentage of 28 does 9 represent. So, the formula becomes
<span>Given the
table that shows the hair lengths y (in inches) of your friend and her cousin in different months x.
Month Friends Hair(in) Cousins Hair(in)
3 4 7
8 6.5 9.
To solve for the
cousins hair, recall that the equation of a line is given by
y = mx + c
From the table,
7 = 3m + c . . . (1)
9 = 8m + c . . . (2)
(1) - (2) ⇒ -2 = -5m
Substituting for m into equation (1) gives:
Therefore, the equation representing the growth of the cousin's hair is given by y = 1.2x + 5.8
</span>
<h2>
Answer:</h2>
Ques 1)
Ques 2)
<h2>
Step-by-step explanation:</h2>
Ques 1)
We know that if a graph is stretched by a factor of a then the transformation if given by:
f(x) → a f(x)
Also, we know that the translation of a function k units to the right or to the left is given by:
f(x) → f(x+k)
where if k>0 then the shift is k units to the left
and if k<0 then the shift is k units to the right.
Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
This means that the function g(x) is given by:
Ques 2)
We know that the transformation of the type:
f(x) → f(x)+k
is a shift or translation of the function k units up or down depending on k.
If k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by:
The question is incorrect.
The correct question is:
Three TAs are grading a final exam.
There are a total of 60 exams to grade.
(c) Suppose again that we are counting the ways to distribute exams to TAs and it matters which students' exams go to which TAs. The TAs grade at different rates, so the first TA will grade 25 exams, the second TA will grade 20 exams and the third TA will grade 15 exams. How many ways are there to distribute the exams?
Answer: 60!/(25!20!15!)
Step-by-step explanation:
The number of ways of arranging n unlike objects in a line is n! that is ‘n factorial’
n! = n × (n – 1) × (n – 2) ×…× 3 × 2 × 1
The number of ways of arranging n objects where p of one type are alike, q of a second type are alike, r of a third type are alike is given as:
n!/p! q! r!
Therefore,
The answer is 60!/25!20!15!
