When the diameter is 10 m the volume is <span>523.6 m^3</span>
Answer:
see below
Step-by-step explanation:
![\dfrac{J(t)}{Y(t)}=\dfrac{12-\dfrac{2}{3}t}{3-\dfrac{1}{8}t}=\dfrac{8}{3}\cdot\dfrac{36-2t}{24-t}\\\\=\dfrac{288-16t}{72-3t}](https://tex.z-dn.net/?f=%5Cdfrac%7BJ%28t%29%7D%7BY%28t%29%7D%3D%5Cdfrac%7B12-%5Cdfrac%7B2%7D%7B3%7Dt%7D%7B3-%5Cdfrac%7B1%7D%7B8%7Dt%7D%3D%5Cdfrac%7B8%7D%7B3%7D%5Ccdot%5Cdfrac%7B36-2t%7D%7B24-t%7D%5C%5C%5C%5C%3D%5Cdfrac%7B288-16t%7D%7B72-3t%7D)
Answer:
The slope is 1/8.
Step-by-step explanation:
So basically, when we are trying to find slope, we think of the change of y over the change of x. And so the change of y between those two points would be 4-2 which is 2. And the change of x would be 32-16, which is 16. Because slope is y/x, therefore the slope is 2/16, which is also 1/8 simplified. I hope this helps!
Lily made $75.36 more than Layla did. If Layla raised her price to $1.00, she would still not make more money than Lily.
Use a proportion to find the number of cupcakes Lily makes in 8 hours. She bakes 7 cupcakes in 10 minutes; we want to know how many she makes in 8(60)=480 (since there are 8 hours and each hour is 60 minutes):
7/10 = x/480
Cross multiply:
7*480 = 10*x
3360 = 10x
Divide both sides by 10:
3360/10 = 10x/10
336 = x
Lily bakes 336 cupcakes.
She sells 2/3 of these; 2/3(336) = 2/3(336/1) = 672/3 = 224 cupcakes sold.
Each cupcake is sold for $1.29; 224(1.29) = 288.96
To find the number of cupcakes Layla makes in 8 hours, we set up a different proportion. We know she bakes 8 cupcakes in 12 minutes; we want to know how many she bakes in 8(60) = 480 minutes:
8/12 = x/480
8*480 = 12*x
3840 = 12x
Divide both sides by 12:
3840/12 = 12x/12
320 = x
She bakes 320 cupcakes. She sells 75% of those; 75% = 75/100 = 0.75:
0.75(320) = 240
Each of those 240 cupcakes sells for $0.89:
0.89(240) = 213.60
This means Lily makes 288.96-213.60 = 75.36 more than Layla.
If Layla raised her price to $1.00, she would make 1(240) = $240; this is still less than Lily.
Answer:
![(x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 16](https://tex.z-dn.net/?f=%28x%20-%205%29%5E%7B2%7D%20%2B%20%28y%20-%204%29%5E%7B2%7D%20%2B%20%28z%20-%209%29%5E%7B2%7D%20%3D%2016)
Step-by-step explanation:
The general equation of a sphere is as follows:
![(x - x_{c})^{2} + (y - y_{c})^{2} + (z - z_{c})^{2} = r^{2}](https://tex.z-dn.net/?f=%28x%20-%20x_%7Bc%7D%29%5E%7B2%7D%20%2B%20%28y%20-%20y_%7Bc%7D%29%5E%7B2%7D%20%2B%20%28z%20-%20z_%7Bc%7D%29%5E%7B2%7D%20%3D%20r%5E%7B2%7D)
In which the center is
, and r is the radius.
In this problem, we have that:
![x_{c} = 5, y_{c} = 4, z_{c} = 1](https://tex.z-dn.net/?f=x_%7Bc%7D%20%3D%205%2C%20y_%7Bc%7D%20%3D%204%2C%20z_%7Bc%7D%20%3D%201)
So
![(x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = r^{2}](https://tex.z-dn.net/?f=%28x%20-%205%29%5E%7B2%7D%20%2B%20%28y%20-%204%29%5E%7B2%7D%20%2B%20%28z%20-%209%29%5E%7B2%7D%20%3D%20r%5E%7B2%7D)
Interior contained in the first octant:
The first octant is bounded by:
The xy plane, in which z is 0. The distance from the center of the sphere to the xy plane is 9.
The xz plane, in which y is 0. The distance from the center of the sphere to the xz plane is 4.
The yz plane, in which x is 0. The distance from the center of the sphere to the yz plane is 5.
This means that if the radius is higher than four, the sphere will cross into a different octant.
So the radius for the largest sphere is 4.
The equation is
![(x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 4^{2}](https://tex.z-dn.net/?f=%28x%20-%205%29%5E%7B2%7D%20%2B%20%28y%20-%204%29%5E%7B2%7D%20%2B%20%28z%20-%209%29%5E%7B2%7D%20%3D%204%5E%7B2%7D)
![(x - 5)^{2} + (y - 4)^{2} + (z - 9)^{2} = 16](https://tex.z-dn.net/?f=%28x%20-%205%29%5E%7B2%7D%20%2B%20%28y%20-%204%29%5E%7B2%7D%20%2B%20%28z%20-%209%29%5E%7B2%7D%20%3D%2016)