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Calc 3 10.1

 

<== Calculus 3
Number Question Answer
See the work

1.

What are the projections of the point (-5, 6, 1) on the coordinate planes?


The xy-plane:

The yz-plane:

The xz-plane:

 On the xy-plane: (-5, 6, 0)
 On the yz-plane: (0, 6, 1) 
 On the xz-plane: (-5, 0,1)
The work

Point Cost: 0

2.

 

 

Determine whether the three points P= (9, 3, -9), Q = (11, 7, -3), 
R=(13, 13, 3) are colinear by computing the distances between pairs
of points.

 

Distance from P to Q: 7.48331477354788

Distance from Q to R: 8.71779788708135

Distance from P to R: 16.1245154965971

Are the three points colinear (y/n)? N

The work

Point Cost: 2

3.

 

 

What is the distance from the point (1, 5, 8) 
to the xz-plane? Distance

 

5

The work

Point Cost: 0

4.

 

 

 

 

 

What do the following equations represent in R3? 
Match the two sets of letters: 

a. a vertical plane
b. a horizontal plane
c. a plane which is neither vertical nor horizontal

A. 7x+2y= -3
B. x = -3
C. y = -10
D. z = 8

A. a 

B. a 

C. a

D. b

The work

5.

 

 

 

Find the equation of the sphere centered at (0,9,10) 
with radius 7. 
______________= 0. 

Give an equation which describes the intersection
of this sphere with the plane z = 11. 
______________= 0.

 

(x)^2+(y-9)^2+(z-1)^2-(7)^2=0


(x)^2 + (y-9)^2 + 1 -(7)^2=0

The work

Point Cost: 1
6.

 

Find the equation of the sphere if one of its
diameters has endpoints (10, -2, -9) and (11, 0, -6).
______________= 0.

(x-9.5)^2 + (y+3)^2 + (z-10.5)^2 -1.8708287=0
The work

Point Cost: 2

7.

 

Find an equation of the sphere that passes through the origin
and whose center is (5, -6, 6).
________________= 0
xˆ2 + yˆ2 + zˆ2 + (-4*x - 12*y - 6*z)
The work

Point Cost: 2
8.

 

Find an equation of the largest sphere with
center (4, 8 , 6) that is contained completely in the first octant.
__________=0

xˆ2 + yˆ2 + zˆ2 - 2*(3*x + 6*y + 9*z) - 3ˆ2 + (3ˆ2 + 6ˆ2 +
9ˆ2)
The work

Point Cost: 3

9.

 

 

Find the center and radius of the sphere
x^2  + 12x + y^2 - 18y + z^2  + 16z = -145
Center: ( _, _, _)
Radius:_________

Center: ( -6, 9, -8)

Radius: 6

The work

Point Cost: 3

10.

 

 

 

Write down an (in)equality which describes the
solid ball of radius 5 centered at (6, 3, -3).


It should have a form like x^2+y^2+(z-2)^2-4 >= 0 where you use one of the following symbols ≤, <, =, ≥, >.<br /> The first blank is for the algebraic expression; <br /> the drop-down list gives the (in)equatilty. <br /> ____________________? 0..

(x + 6)^2 + (y + 6)^2 + (z - 9)^2 - 7^2 ≤ 0

The work

Point Cost: 1

11.

 

 

Find the distance from (-3,6,-11) to each of the following:

1. The xy-plane:

2. The yz-plane:

3. The xz-plane:

4. The x-axis:

5. The y-axis:

6. The z-axis:


1. The xy-plane: abs(-11)

2. The yz-plane: abs(-3)

3. The xz-plane: abs(6)

4. The x-axis: See Work

5. The y-axis: See Work

6. The z-axis: See Work

The work

Point Cost: 3