Question

3) The angles of a triangle are in a ratio of 1:1:2. Find the ratio of the sides opposite these angles.

a) 1:1:2

b) 1:3‾√:2

c) Cannot be determined.

d) 1:1:2‾√

e) 2‾√:2‾√:1

f) *None of the above*

*4)*

Draw acute △ABC with m∠A=30∘. Draw altitude BD⎯⎯⎯⎯⎯⎯⎯⎯ from B to AC⎯⎯⎯⎯⎯⎯⎯⎯. If BD=2, find AB.

a) 23‾√

b) 23‾√3

c) 43‾√3

d) 22‾√

e) 4

f) *None of the above*

*5)*

Assume that WZ=XY . Which of the following statements are true?
(Assume that W, Z, X, Y, and F are nonzero real numbers, and assume
that all expressions have nonzero denominators.)

Create an answer using the numbers associated with the true
statements. For example, if only 1, 2, and 5 are true, then the
answer is 125; if only 3 and 5 are true, then the answer is 35,
etc.

1. W−Z over Z = X−Y over Y (over = ex.1/2) or
divided by. I don't know how else to put it. sorry.

2. W+X over Z+Y = W over Z

3. W+Z over Z = X+Y over Y

4. W−F over Z = X−F over Y

5. W+F over Z = X+F over Y

6. W+F over Z+F = X+F over Y+F

a) 14

b) 123

c) 13

d) 346

e) 1235

f) 135

g) *None of the above*

Answer #1

Compute the surface
integral of f(x,y,z)=x^2 over z=sqrt(x^2+y^2), 0<=z<=1.
Write answer as simply
as possible. Note that this is 8 points and you have two
attempts.
ex) 5 π 2 write
5sqrt(pi)/2
Don't use any spaces
and put in the conventional order, numbers outside square root
first. Rationalize denominators. Use * for multiplication if
necessary.

Find the measures of the three angles, in radians, of the triangle
with the given vertices: D ( 1 , 1 , 1 ) , E ( 1 , − 2, 2 ) , and F
( − 5 , 2 , 6 ) .

Find the derivative of each of the following functions:
(a) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(b) y =63 (d) w=3u^(-1) (f) w=4u^(1/4)
2. Find the following:
(a) d/dx(-x^(-4)) (c) d/dw 5w^4 (e) d/du au^b
(b) d/dx 9x^(1/3) (d) d/dx cx^2 (f) d/du-au^(-b)
3. Find f? (1) and f? (2) from the following functions: Find the
derivative of each of the following functions:
(c) y=x^12 (c) y=7x^5 (e) w=-4u^(1/2)
(d) y =63 (d)w=3u^(-1) (f) w=4u^(1/4)
4.
(a) y=f(x)=18x (c) f(x)=-5x^(-2)...

The random variable W = X – 3Y + Z + 2 where X, Y and Z are
three independent Normal random variables, with E[X]=E[Y]=E[Z]=2
and Var[X]=9,Var[Y]=1,Var[Z]=3.
The pdf of W is:
Uniform
Poisson
Binomial
Normal
None of the other pdfs.

1- find the divergence of F(x,y,z) = <e^x(y),x^2(z),xyz>
at (1,-1,3).
2- find the curl of F(x,y,z)= <xyz,y^2(z),x^2(y)z^3> at
(0,-2,2)

f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the gradient of f.
∇f(x, y, z) =
< , , >
(b) Evaluate the gradient at the point P.
∇f(1, 0, 3) = < , ,
>
(c) Find the rate of change of f at P in the
direction of the vector u.
Duf(1, 0, 3) =

1.) Let f ( x , y , z ) = x ^3 + y + z + sin ( x + z ) + e^( x
− y). Determine the line integral of f ( x , y , z ) with respect
to arc length over the line segment from (1, 0, 1) to (2, -1,
0)
2.) Letf ( x , y , z ) = x ^3 * y ^2 + y ^3 * z^...

find the integral of f(x,y,z)=x over the region x^2+y^2=1 and
x^2+y^2=9 above the xy plane and below z=x+2

Let F(x, y, z) = z tan−1(y^2)i + z^3 ln(x^2 + 7)j + zk. Find the
flux of F across S, the part of the paraboloid x^2 + y^2 + z = 29
that lies above the plane z = 4 and is oriented upward.

Let F(x,y,z) = ztan-1(y^2) i + (z^3)ln(x^2 + 8) j + z k. Find
the flux of F across the part of the paraboloid x2 + y2 + z = 20
that lies above the plane z = 4 and is oriented upward.

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