Question

Given x^{2}/16 + z^{2}/36 - y^{2}/100 =1
find:

a. The xy, xz, and yz traces

b.Where it intercepts the coordinate axe

Answer #1

The tangent plane at (1,1,1) on the surface x2+y2+z2+xy+xz=5 is
given by
x+ y+ z=
(all values should be positive whole numbers with no common
factors)

1. a) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the tangent plane at (1, 1, 1).
b) For the surface f(x, y, z) = xy + yz + xz = 3, find the
equation of the normal line to the surface at (1, 1, 1).

you are given two vectors:
v=[x2 +y2+ z2, 2xyz,
x+y+2z]
u=[xy+z , xy2 z2 , x+3z]
Calculate the following expressions:
a) curl v
b) grad vz

Suppose that X, Y, and Z are independent, with E[X]=E[Y]=E[Z]=2,
and E[X2]=E[Y2]=E[Z2]=5.
Find cov(XY,XZ).
(Enter a numerical answer.)
cov(XY,XZ)=
Let X be a standard normal random variable. Another random
variable is determined as follows. We flip a fair coin (independent
from X). In case of Heads, we let Y=X. In case of Tails, we let
Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not...

Evaluate ∫∫Sf(x,y,z)dS , where f(x,y,z)=0.4sqrt(x2+y2+z2)) and S
is the hemisphere x2+y2+z2=36,z≥0

Calculate ∫ ∫S f(x,y,z)dS for the given surface and function.
x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.

Find the surface area of the cone x2 + y2
= z2 that lies inside the sphere x2 +
y2 + z2 = 6z by taking integrals.

Find the area of the surface.
The portion of the sphere
x2 + y2 + z2 = 400
inside the cylinder
x2 + y2 = 256
*its not 320pi or 1280pi

Find the area of the part of the cylinder
x2+y2=2ax that lies inside the sphere
x2+y2+z2=4a2 by a
surface integral.
Please step by step solution

Use the Lagrange Multipliers method to find the maximum and
minimum values of f(x,y) = xy + xz subject to the constraint x2 +y2
+ z2 = 4.

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