66 = 4 + 8v - 2 <== ur equation
66 = 2 + 8v
66 - 2 = 8v
64 = 8v
64/8 = v
8 = v <=== there are 8 bulbs in each value pack
0.08 cm/min
Step-by-step explanation:
Given:
![\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D5%5C%3A%5Ctext%7Bcm%7D%5E3%5Ctext%7B%2Fmin%7D)
Find
when diameter D = 20 cm.
We know that the volume of a sphere is given by
![V = \dfrac{4\pi}{3}r^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B4%5Cpi%7D%7B3%7Dr%5E3)
Taking the time derivative of V, we get
![\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%204%5Cpi%20r%5E2%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%204%5Cpi%5Cleft%28%5Cdfrac%7BD%7D%7B2%7D%5Cright%29%5E2%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%20%5Cpi%20D%5E2%5Cdfrac%7Bdr%7D%7Bdt%7D)
Solving for
, we get
![\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})](https://tex.z-dn.net/?f=%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%20%5Cleft%28%5Cdfrac%7B1%7D%7B%5Cpi%20D%5E2%7D%5Cright%29%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B1%7D%7B%5Cpi%2820%5C%3A%5Ctext%7Bcm%7D%5E2%29%7D%285%5C%3A%5Ctext%7Bcm%7D%5E3%5Ctext%7B%2Fmin%7D%29)
![\:\:\:\:\:\:\:= 0.08\:\text{cm/min}](https://tex.z-dn.net/?f=%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%3D%200.08%5C%3A%5Ctext%7Bcm%2Fmin%7D)
Answer:
HELLO! im confused do u want us to answer all of them:D?
Step-by-step explanation:
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