Answer:
Restate the question please?
Step-by-step explanation:
<span>The cost of a service or item is an expense
</span>
Answer:
4%
Step-by-step explanation:
After losing 4.17, it came down to 100.08, so the opening price was:
100.08 + 4.17 = 104.25
To find percentage decline, we find the ratio of the "change" (which is 4.17) divided by the opening (original) price, which is 104.25. Then we multiply that fraction by 100 to get our percentage decline.
So,
![\frac{4.17}{104.25}*100=4](https://tex.z-dn.net/?f=%5Cfrac%7B4.17%7D%7B104.25%7D%2A100%3D4)
Thus, the
percentage decline = 4%
Answer:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Step-by-step explanation:
The area of a sphere is given by the following formula:
![A = 4\pi r^{2}](https://tex.z-dn.net/?f=A%20%3D%204%5Cpi%20r%5E%7B2%7D)
In which A is the area, measured in cm², and r is the radius, measured in cm.
Assume that the radius r of a sphere is expanding at a rate of 40 cm/min.
This means that ![\frac{dr}{dt} = 40](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%2040)
Determine the rate of change in surface area when r = 20 cm.
This is
when
. So
![A = 4\pi r^{2}](https://tex.z-dn.net/?f=A%20%3D%204%5Cpi%20r%5E%7B2%7D)
Applying implicit differentiation.
We have two variables, A and r, so:
![\frac{dA}{dt} = 8r\pi \frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%208r%5Cpi%20%5Cfrac%7Bdr%7D%7Bdt%7D)
![\frac{dA}{dt} = 8*20\pi*40](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%208%2A20%5Cpi%2A40)
![\frac{dA}{dt} = 20106.19](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%2020106.19)
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.