dz a) Find dz and dx where xz- cos(yz) + ; 4хуz. ду
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.
Answer all parts
![dz
and
dx
dz
a) Find
where xz- cos(yz)+
= 4xyz.
ду
b) Traveling waves (for example, water waves or electromagnetic waves) exhibit periodic motion
in both time and space. In one space dimension, some types of wave motion are governed by
the one-dimensional wave equation
dt?
dx² '
where u(x,t) is the height or displacement of the wave surface at position x and time t, and
c > 0 is the constant speed of the wave.
Show that the function u(x,t) = 5 cos(2(x+ct))+3 sin(x– ct) is a solution of the wave
(!
equation.
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