Q7.
Evaluate ∫∫ G(r)dA where G(x, y, z) = arctan(y/x) and S is given by
z...
Q7.
Evaluate ∫∫ G(r)dA where G(x, y, z) = arctan(y/x) and S is given by
z = x2 + y2, with1≤z≤9,x≥0, y≥0.
Let s = f(x; y; z) and x = x(u; v; w); y = y(u; v;...
Let s = f(x; y; z) and x = x(u; v; w); y = y(u; v; w); z = z(u;
v; w). To calculate ∂s ∂u (u = 1, v = 2, w = 3), which of the
following pieces of information do you not need?
I. f(1, 2, 3) = 5
II. f(7, 8, 9) = 6
III. x(1, 2, 3) = 7
IV. y(1, 2, 3) = 8
V. z(1, 2, 3) = 9
VI. fx(1, 2, 3)...
Consider F and C below.
F(x, y, z) = yz i + xz j + (xy...
Consider F and C below.
F(x, y, z) = yz i + xz j + (xy + 12z) k
C is the line segment from (2, 0, −3) to (4, 6, 3)
(a) Find a function f such that F =
∇f.
f(x, y, z) =
(b) Use part (a) to evaluate
C
∇f · dr along the given curve C.
Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV ∬ S F ⋅ d S = ∭ D ∇ ⋅...
Use the Divergence Theorem ∬SF⋅dS=∭D∇⋅FdV ∬ S F ⋅ d S = ∭ D ∇ ⋅
F d V to find ∬SF⋅dS ∬ S F ⋅ d S where F(x,y,z)=3x2i+2y2j+2z2k F (
x , y , z ) = 3 x^2 i + 2 y^2 j + 2 z^2 k and S is the surface of
the rectangular solid bounded by − 6 ≤ x ≤ 2 , − 6 ≤ y ≤ 3 , and −
4 ≤ z...
Suppose the joint probability distribution of X and Y is given
by the following table.
Y=>3...
Suppose the joint probability distribution of X and Y is given
by the following table.
Y=>3 6 9 X
1 0.2 0.2 0
2 0.2 0 0.2
3 0 0.1 0.1
The table entries represent the probabilities. Hence the
outcome [X=1,Y=6] has probability
0.2.
a) Compute E(X), E(X2), E(Y), and E(XY). (For all answers show
your work.) b) Compute E[Y | X = 1], E[Y | X = 2], and E[Y | X =
3].
c) In this case, E[Y...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of
the following elements:
A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x
∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J =
R.
Consider the relation ∼ on S given...
Given that A to Z are mapped to integers 0-25 as follows.
A:0, B:1, C:2, D:3,...
Given that A to Z are mapped to integers 0-25 as follows.
A:0, B:1, C:2, D:3, E:4, F:5, G:6, H:7, I: 8, J: 9, K:10, L:11,
M:12, N:13, O:14, P:15, Q:16, R:17, S:18, T:19, U:20, V:21, W:22,
X:23, Y:24, Z:25.
Encrypt the following message using Vigenere Cipher with key:
CIPHER
THISQUIZISEASY
What is the ciphertext? Show your work.
PLEASE HELP
Four particles are in a 2-D plane with masses, x- and y-
positions, and x- and...
Four particles are in a 2-D plane with masses, x- and y-
positions, and x- and y- velocities as given in the table
below:
m
x
y
vx
vy
1
8.9 kg
-2.4 m
-4.7 m
3.1 m/s
-4 m/s
2
7.8 kg
-3.6 m
3.5 m
-5.2 m/s
5.1 m/s
3
8.7 kg
4.4 m
-5.7 m
-6 m/s
1.9 m/s
4
7.6 kg
5.6 m
2.5 m
4.2 m/s
-3.1 m/s
1) What is the x position of...
Four particles are in a 2-D plane with masses, x- and y-
positions, and x- and...
Four particles are in a 2-D plane with masses, x- and y-
positions, and x- and y- velocities as given in the table
below:
m
x
y
vx
vy
1
9.4 kg
-2.6 m
-4.5 m
3.1 m/s
-4 m/s
2
9.2 kg
-3.6 m
3.4 m
-5.1 m/s
4.9 m/s
3
9 kg
4.5 m
-5.4 m
-6 m/s
1.9 m/s
4
8.9 kg
5.5 m
2.4 m
4 m/s
-2.9 m/s
1)
What is the x position of...