In Exercises 1-4, a harmonic oscillator equation for y(1) is given. (a) Using HPGSystemsolver, sketch the associated direction field. (b) Using the guess-and-test method described in this section, find two nonzero solu- tions that are not multiples of one another. (c) For each solution, plot both its solution curve in the yo-plane and its y(t)- and v(1)-graphs. 1. di? + 10y =0 di2 + 6y = 0 dt dt dy 3. +4 +y = 0 dt? dy dt d'y 4. +6+7y =0 di? dy dt +
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.
question 4
only part (b)
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