Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2...
Let D be the solid region defined by D = {(x, y, z) ∈ R3; y^2 +
z^2 + x^2 <= 1},
and V be the vector field in R3 defined by: V(x, y, z) = (y^2z +
2z^2y)i + (x^3 − 5^z)j + (z^3 + z) k.
1. Find I = (Triple integral) (3z^2 + 1)dxdydz.
2. Calculate double integral V · ndS, where n is pointing
outward the border surface of V .
Consider the surface defined by z = f(x,y) = x+y^2+1.
a)Sketch axes that cover the region...
Consider the surface defined by z = f(x,y) = x+y^2+1.
a)Sketch axes that cover the region -2<=x<=2 and
-2<=y<=2.On the axes , draw and clearly label the contours
for the eights z=0 ,z=1,and z=2.
b)evaluate the gradients of f(x,y) at the point (x,y) = (0.-1),
and draw the gradient vector on the contour diagrqam .
c)compute the directional derivative at(x,y) = (0,-1) in the
direction V =<2,1>.
Question 2
D is the region in the first octant bounded by: z = 1 −...
Question 2
D is the region in the first octant bounded by: z = 1 −
x2 and z = ( y − 1 )2
Sketch the domain D.
Then, integrate f (x, y, z) over the domain in 6 ways: orderings of
dx, dy, dz.
A space curve C is parametrically parametrically defined by
x(t)=e^t^(2) −10,
y(t)=2t^(3/2) +10,
z(t)=−π,
t∈[0,+∞).
(a)...
A space curve C is parametrically parametrically defined by
x(t)=e^t^(2) −10,
y(t)=2t^(3/2) +10,
z(t)=−π,
t∈[0,+∞).
(a) What is the vector representation r⃗(t) for C ?
(b) Is C a smooth curve? Justify your answer.
(c) Find a unit tangent vector to C .
(d) Let the vector-valued function v⃗ be defined by
v⃗(t)=dr⃗(t)/dt
Evaluate the following indefinite integral
∫(v⃗(t)×i^)dt. (cross product)
Variable Z is distributed standard normal: Z ~ N(0; 1), so using
the statistical table of...
Variable Z is distributed standard normal: Z ~ N(0; 1), so using
the statistical table of the Standard Normal Distribution provided,
find the values of the following probabilities:
(A) P[Z ≤ 1.27] =
(B) P[Z ≥ 0.41] =
(C) P[Z ≤ 1:96] =
(D) P[-1 ≤ Z ≤ 2] =
(E) P(Z ≤ 1.87)
(F) P(Z ≥ - 0.53). Hint: P(Z ≤ - a)=P(Z ≥ a), where a ∈ ?, and
a≥0.
(G) P(Z ≤ - 0.06)
(H) P(1.12 ≤...
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
Find an absolute max for the function f(x,y)=xy defined on the
region D={(x,y)/ x^2/16+y^2<=1}.
Do this...
Find an absolute max for the function f(x,y)=xy defined on the
region D={(x,y)/ x^2/16+y^2<=1}.
Do this problem two ways:
first by finding the critical point(s) and parametrizing
boundary
and then, by using Lagrange multipliers.
State what you learned about the Lagrange method from having
these two sets of solutions.
Let X ∼ Beta(α, β).
(a) Show that EX 2 = (α + 1)α (α +...
Let X ∼ Beta(α, β).
(a) Show that EX 2 = (α + 1)α (α + β + 1)(α + β) .
(b) Use the fact that EX = α/(α + β) and your answer to the
previous part to show that Var X = αβ (α + β) 2 (α + β + 1).
(c) Suppose X is the proportion of free-throws made over the
lifetime of a randomly sampled kid, and assume that X ∼ Beta(2,
8)
....