Answer:
hmmmmmmm
Step-by-step explanation:
nah I am good thx for the free points
<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:
(-5,7) (-5,8) (-5,3)
Step-by-step explanation:
Dont know if this will help but here you go
Answer:
960
Step-by-step explanation:
<u>Given:</u>
- Stan's cookie recipe makes 24 cookies.
- It needs exactly 384 sprinkles.
<u>To Find:</u>
- Number of sprinkles needed for 60 cookies
<h2><u>Solution:</u></h2>
<u>Find the number of sprinkles needed for 1 cookie:</u>
- 24 cookies = 384 sprinkles
- 1 cookie = 384 ÷ 24
- 1 cookie = 16 sprinkles
<u>Find the number of sprinkles needed for 60 cookies:</u>
- 1 cookie = 16 sprinkles
- 60 cookies = 16 x 60
- 60 cookies = 960 sprinkles
Answer: Stan will need 960 sprinkles for 60 cookies.
Answer:
<u>The approximate total weight of the grapefruits, using the clustering estimation technique is B. 35 ounces.</u>
Step-by-step explanation:
We notice that the weights of the grapefruits given are slightly down or above 7, then we will use <em>7 as our cluster</em> for the estimation, as follows:
Weights
7.47 ⇒ 7
7.23 ⇒ 7
6.46 ⇒ 7
7.48 ⇒ 7
6.81 ⇒ 7
<u>Now we can add up 7 + 7 + 7 + 7 + 7 for the weights of the grapefruits and the approximate total weight is B. 35 ounces.</u>
