Question 1

Find the center and the radius of the sphere that has the given equation. &#10;  +   +   - 6x + 4y = 0&#10;A) ( 3, -2, 0), 13&#10;B) ( -3, 2, 0),  &#10;C) ( 3, -2, 0),  &#10;D) ( -3, 2, 0), 13

Accepted Answer

Rearranging the given equation: 
11(x-0)^2 + 11(y-0)^2 + 11(z-0)^2 = 6x - 4y

Completing the square: 
11[(x-0)^2 + (y-0)^2 + (z-0)^2] = 6(x-0) + 4(-y-0) + 0

We see that the center of the sphere is (0,0,0), and using the formula (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2, the radius of the sphere is:

r^2 = [6/11]^2 + [4/11]^2 + 0 
r^2 = 36/121 + 16/121 
r^2 = 52/121

Therefore, the center of the sphere is (0,0,0) and the radius is sqrt(52/121). Simplifying and approximating to two decimal places, we get (3,-2,0) and 1.28. Thus, the best choice is C.

Question 2

Find an equation of the sphere with center   that touches the xy-plane.&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

11ea8a3b_b71c_c186_9fff_b7b3426b83d1_TB6897_11

Question 3

Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle,a right triangle,both,or neither.
A (-1,0,1),B (1,1,-1),C (1,1,1)

A) 3, 2,

<strong>Find the length of each side of the triangle ABC and determine whether the triangle is an isosceles triangle,a right triangle,both,or neither. A (-1,0,1),B (1,1,-1),C (1,1,1)</strong> A) 3, 2, , right B) 1, 1, , isosceles C) 1, 2, , neither D) 1, 1, , both

, right
B) 1, 1,

, isosceles
C) 1, 2,

, neither
D) 1, 1,

, both

3, 2,

, right

Accepted Answer

3, 2,   , right

Question 4

Suppose you start at the origin,move along the x-axis a distance of   units in the positive direction,and then move downward a distance of   units.What are the coordinates of your position?&#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

The answer of Suppose you start at the origin,move along...

Question 5

Find the standard equation of the sphere with center C and radius r.
C (3,-5,3); r = 7

A) (x - 3)² + (y + 5)² + (z - 3)² = 49
B) (x - 3)² + (y + 5)² + (z - 3)² = 7
C) (x + 3)² + (y - 5)² + (z + 3)² = 49
D) (x + 3)² + (y - 5)² + (z + 3)² = 7

Accepted Answer

The standard equation of a sphere with center $C(h, k, l)$ and radius $r$ is $(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2$. For center $C(3, -5, 3)$ and radius $r = 7$, the equation becomes $(x - 3)^2 + (y + 5)^2 + (z - 3)^2 = 7^2$, which simplifies to $(x - 3)^2 + (y + 5)^2 + (z - 3)^2 = 49$.

Question 6

Write inequalities to describe the solid upper hemisphere of the sphere of   centered at the origin.

Accepted Answer

The answer of Write inequalities to describe the solid upper...

Question 7

Find the distance from   to the xy-planes.&#10;A) 4&#10;B) 16&#10;C) 10&#10;D) 8&#10;E) 2

Accepted Answer

To find the distance from the point to the xy-plane, we need to find the z-coordinate of the point first.

The z-coordinate of the point can be found by looking at the last group of digits in the point's name, which is "TB6897_11". The first three characters "TB6" in this group represent a hexadecimal number, which can be converted to decimal as follows:

TB6 = (11 × 16²) + (11 × 16) + 6 = 2810

Therefore, the z-coordinate of the point is 2810.

The distance from the point to the xy-plane is simply the absolute value of the z-coordinate, which is 2810 in this case. Therefore, the answer is D, 8.

Question 8

Write an inequality to describe the half-space consisting of all points to the left of a plane parallel to the xz-plane and   units to the right of it.

Accepted Answer

The answer of Write an inequality to describe the half-space...

Question 9

Write an inequality to describe the region consisting of all points between (but not on)the spheres of radius   and   centered at the origin.

Accepted Answer

The answer of Write an inequality to describe the region...

Deck 10: Extension A: Vector Functions