(b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmas) (e) Given k? / ? - (1/1ay°, calculate the ratios of the second partial derivatives below. (Use the following as necessary: e.) Hofo
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
![Perform the following steps to verify by substitution that equations C and D are solutions to Equations A and B, respectively.
a²E
= Eolo
at?
E = E.
cos(kx – wt)
max
Equation A
Equation C
В - В
cos(kx
- wt)
max
ax?
at?
Equation B
Equation D
(a) Calculate the first partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax:)
-kE
тах
sin ( kx – ot)]
Əx
[sin(kx-
ot) ]
дв
-kB
тахL
- OT
ax
JE
wE
max sin(kx – ot)]
at
дв
wB
max sin(kx – wt)]
at
(b) Calculate the second partial derivatives listed below. (Use the following as necessary: k, w, x, t, and either Emax or Bmax)
a²E
-E
ax?
a2B
%3D
ax?
at?
at?
(c) Given k2 / w² = (1 / f 1)², calculate the ratios of the second partial derivatives below. (Use the following as necessary: c.)
a2E
ax2
Hoo
at?
a2B
ax2
Activate Windov
a2B
Go to Settings to activ
at2
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