<span>Sphere: (x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100
Intersection in xy-plane: (x - 4)^2 + (y + 12)^2 = 36
Intersection in xz-plane: DNE
Intersection in yz-plane: (y + 12)^2 + (z - 8)^2 = 84
The desired equation is quite simple. Let's first create an equation for the sphere centered at the origin:
x^2 + y^2 + z^2 = 10^2
Now let's translate that sphere to the desired center (4, -12, 8). To do that, just subtract the center coordinate from the x, y, and z variables. So
(x - 4)^2 + (y - -12)^2 + (z - 8)^2 = 10^2
(x - 4)^2 + (y - -12)^2 + (z - 8)^2 = 100
Might as well deal with that double negative for y, so
(x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100
And we have the desired equation.
Now for dealing with the coordinate planes. Basically, for each coordinate plane, simply set the coordinate value to 0 for the axis that's not in the desired plane. So for the xy-plane, set the z value to 0 and simplify. So let's do that for each plane:
xy-plane:
(x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100
(x - 4)^2 + (y + 12)^2 + (0 - 8)^2 = 100
(x - 4)^2 + (y + 12)^2 + (-8)^2 = 100
(x - 4)^2 + (y + 12)^2 + 64 = 100
(x - 4)^2 + (y + 12)^2 = 36
xz-plane:
(x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100
(x - 4)^2 + (0 + 12)^2 + (z - 8)^2 = 100
(x - 4)^2 + 12^2 + (z - 8)^2 = 100
(x - 4)^2 + 144 + (z - 8)^2 = 100
(x - 4)^2 + (z - 8)^2 = -44
And since there's no possible way to ever get a sum of 2 squares to be equal to a negative number, the answer to this intersection is DNE. This shouldn't be a surprise since the center point is 12 units from this plane and the sphere has a radius of only 10 units.
yz-plane:
(x - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100
(0 - 4)^2 + (y + 12)^2 + (z - 8)^2 = 100
(-4)^2 + (y + 12)^2 + (z - 8)^2 = 100
16 + (y + 12)^2 + (z - 8)^2 = 100
(y + 12)^2 + (z - 8)^2 = 84</span>
Answer:
$0.33
Step-by-step explanation:
Unit rate=1
if 3 equal to $0.99, then
1 will equal $0.33.
0.99/3=$0.33
Answer: It is linear. When a line is linear it just means it makes a straight line when you graph it. When it isn’t it will be curved or in some weird shape.
Step-by-step explanation:
9514 1404 393
Answer:
- 126 children
- 63 adults
- 60 students
Step-by-step explanation:
Let a represent the number of adults that attended. Then 2a is the number of children, and (249 -a -2a) is the number of students. The total revenue is ...
5(2a) +7(249 -3a) +12a = 1806
a +1743 = 1806 . . . . simplify; next, subtract 1743
a = 63 . . . . . . . . adults
2a = 126 . . . . . . children
249 -3a = 60 . . students
126 children, 63 adults, and 60 students attended.
Answer: For the cirlces since I already answered the triangles
1. Area:660.519855417
Circumference:91.1061869541
2. Area: 572.555261117
Circumference:84.8230016469
3. Area:283.528736986
Circumference:59.6902604182
4. Area:1017.87601976
Circumference:113.097335529
5. Area: 63.6172512352
Circumference: 28.2743338823
6. Area:380.132711084
Circumference:69.115038379
Step-by-step explanation:
The formula for the area of a circle is π*r^2, r being the radius or the half line in the circle, and the formula for the circumference is π*r*2, or π*d, or the diameter which is the line that goes all the way through like number 5. The radius is half the diameter.
