calculas 3,solutions

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Hamad Almuhanna math 250 S2014 15553 WeBWorK assignment number Homework 12-1 is due : 02/19/2014 at 09:30am PST. The

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1. (1 pt) What is the distance from the point (3, 9, 4) to the xz-plane?

Distance =

2. (1 pt) 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. −1x + 3y = 9

B. x = 10

C. y = −9

D. z = 1

3. (1 pt) Find an equation of the sphere with center (0, 4, 0) and radius

5. = 0

Note that you must move everything to the left hand side of the equation and that we desire the coefficients of the quadratic terms to be 1.

4. (1 pt) Find the center and radius of the sphere x2 −6x + y2 + 2y + z2 −20z = −29 Center: ( , , ) Radius:

5. (1 pt) Find an equation of the largest sphere with center (6, 7 , 5)

that is contained completely in the first octant. = 0

Note that you must move everything to the left hand side of the equation that we desire the coefficients of the quadratic terms to be 1.

6. (1 pt) On the number line, what is the point (i.e., number) midway

between -5 and -9? Midpoint =

In the plane, what is the midpoint of the line segment joining (0,2) to (-5,7)? Midpoint =

In three-dimensional-space, what is the midpoint of the line segment joining (-3,4,-2) to (-1,6,-5)? Midpoint =

7. (1 pt) Find the equation of a sphere if one of its diameters has end-

points: (-12, -9, -4) and (-8, -5, 0). = 0

Note that you must move everything to the left hand side of the equation and that we desire the coefficients of the quadratic terms to be 1.

8. (1 pt) Two spheres with the same radius r, one centered at (1,2,-4) and the other centered at (4,4,3), touch each other tangentially at a single point. Find the value of the radius r.

r =

9. (1 pt) For each equation or system of equations, what fig- ure is represented in R3? Match the two sets of letters:

a. a line b. a circle c. a plane d. a cylinder

A. 4x−4z = 2

B. (y−6)2 + (z + 10)2 = 7 and x = −7

C. (x + 7)2 + (z−1)2 = 2

D. x = 7 and 4y + 2z = −1