Which octant/plane
What is the octant/plane of the point that is 4 units above the xy plane, 3 units behind the yz plane, and 7 units in front of the xz plane
The point is (-3, 7, 4), which would be in octant 2
Find distance between (0, 0, 1) and (0, 0, 100)
99
Find center of the sphere: x^2+y^2+(z-1)^2=100
(0, 0, 1)
Determine whether the points make a straight line (collinear) and show work
a. (1, -2, 3)
b. (4, 4, -3)
c. (6, 8, 7)
Not collinear.
Vector A to B = <3, 6, -6>
Vector A to C = <5, 10, 4>
Since scalar from vector A to B, to vector A to C is not consistent, these points are not collinear
Which octant/plane is the (1, 0, 3)
The xz plane because y=0
What is the midpoint between (1, 1, 1) and (1, 2, 3)
Midpoint= (1, 1.5, 2)
What is the center and radius: (x-100)^2 + (y+99)^2 + (z+0.01)^2 = 2.25
Center: (100, -99, -0.01)
Radius: 1.5
What is the point that is 7 units in front of the yz plane, 2 units to the left of the xz plane, and one unit below the xy plane.
(7, -2, -1)
Which octant/plane does (-1, 5, 2)
octant 2 because x<0, while y and z>0
What is the distance between (-1, 3, 7) and (5, 9, -11)
d = 19.8997
Put the equation into the standard equation for a sphere: x^2 + 4x + y^2 - 8y + z^2 - 2z = 4
(x+2)^2 + (y-4)^2 + (z-1)^2 = 25
Find the volume of the sphere: x^2 + 6x + y^2 - 8y + z^2 - 2z = -22
V=4/3(pi)(r)^3
r = 2
V=(32/3)pi
Which octant/plane does (1, 2, 0) belong in
The x-y plane because z=0
The midpoint between point A and point B is (2, -1, 4). If point A has the coordinates (5, 5, -1), What are the coordinates of point B?
(-1, 3, 7)
Do the two spheres overlap to form a shared volume?
S1 (x-2)^2 + (y-3)^2 + (z+1)^2 = 9
S2 (x-7)^2 + (y+1)^2 + (z-4)^2 = 16
Why or Why not?
No, because d > r1 + r2
Which octant/plane is (-3, -9, -2)
Octant 7 because x,y, and z are all negative.
Which octant/plane (-1, 1, -1) belong in
Octant 6 because y >0, but x and z<0
P1=(-5, -3, -7)
P2=(1, 9, -1)
if you reflect P1 off the y-axis to create P3, what is the midpoint between P3 and P2.
Reflecting off the y-axis: (x, y, z) -> (-x, y, -z)
Therefore, P3 = (5, -3, 7)
M = (3, 3, 3)
The surface of a solid is defined by the equation (x - 3)^2 + (y + 1)^2 + (z - 2)^2 = 100. A horizontal "slice" is taken through the solid at the plane z = 8. What is the area of the circular cross-section created by this slice?
plug z = 8, giving (x-3)^2 + (y+1)^2 = 64. center doesn't matter. r=8, making Area=64pi
The surface of a solid is defined by the equation x^2 + y^2 + z^2 = 100. A vertical "slice" is taken through the solid at the plane y = 8. What is the area of the circular cross-section created by this slice?
plug y=8, leading to x^2 + z^2 = 36. Area from there would be 36(pi)