Find an equation of a sphere if one of its diameters has endpoints (7, 9, 9) and (3, 5, 7). tep 1 The center of the sphere will be the midpoint of the diameter segment. Recall that the midpoint of a segment between the points (u, v, w) and (p, q, s) is given by u + p + q w + S tep 2 Therefore, the midpoint of the segment between the given endpoints (7, 9, 9) and (3, 5, 7) is (플루, 오늘트 오늘고)- (3 7 + 3 9 + 5 9 +7 2 2
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.
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 alt="Find an equation of a sphere if one of its diameters has endpoints (7, 9, 9) and (3, 5, 7).
tep 1
The center of the sphere will be the midpoint of the diameter segment.
Recall that the midpoint of a segment between the points (u, v, w) and (p, q, s) is given by
u + p
+ q
w + S
tep 2
Therefore, the midpoint of the segment between the given endpoints (7, 9, 9) and (3, 5, 7) is
(플루, 오늘트 오늘고)- (3
7 + 3 9 + 5 9 +7
2
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