How do we find the area inside both cardioidsr =1+sin(0) and r = 1+cos(0)? %3D
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Parts B and C
![1.
Sketch the region of integration for each. Then set up the double integral
used to solve the problem.
(a) How do we find the volume of the solid below the hyperboloid z = 5-/1+x² + y²
and above the region R = {(x, y) |1< x² + y² < 4in quadrants II and III}?
(b) How do we find the area inside both cardioids r = 1+sin(0) and r = 1+cos(0)?
1
Ue V16 – 2 – y
: {(x, y) | x² + y² < 16, x > 0, and y > 0}?
(c) How can we evaluate
dA over the region
R =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F371e94ac-4ad2-4489-8b5d-9778522c52be%2Fb89f85c3-0bed-40df-9b40-90b22e3612f7%2Fzdcmsrm_processed.png&w=3840&q=75)
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