Answer:
The volume of cone is increasing at a rate 2512 cubic inches per second.
Step-by-step explanation:
We are given the following in the question:
![\dfrac{dr}{dt} = 3\text{ inches per second}\\\\\dfrac{dh}{dt} = -3\text{ inches per second}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%203%5Ctext%7B%20%20inches%20per%20second%7D%5C%5C%5C%5C%5Cdfrac%7Bdh%7D%7Bdt%7D%20%3D%20-3%5Ctext%7B%20%20inches%20per%20second%7D)
Radius = 40 inches
Height = 30 inches
The volume of cone is given by:
![V = \dfrac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h)
Rate of change of volume is given by:
![\dfrac{dV}{dt} = \dfrac{1}{3}\pi (2r\dfrac{dr}{dt}h+\dfrac{dh}{dt}r^2)](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20%282r%5Cdfrac%7Bdr%7D%7Bdt%7Dh%2B%5Cdfrac%7Bdh%7D%7Bdt%7Dr%5E2%29)
Putting the values, we get,
![\dfrac{dV}{dt} = \dfrac{1}{3}(3.14) \big(2(40)(3)(30)+(-3)(40)^2\big)\\\\\dfrac{dV}{dt} = \dfrac{1}{3}(3.14)(2400)\\\\\dfrac{dV}{dt} = 2512](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%283.14%29%20%5Cbig%282%2840%29%283%29%2830%29%2B%28-3%29%2840%29%5E2%5Cbig%29%5C%5C%5C%5C%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%283.14%29%282400%29%5C%5C%5C%5C%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%202512)
Thus, the volume of cone is increasing at a rate 2512 cubic inches per second.
The quotient of a number and -2 = n/-2 or = -n/2
Hope that helps.
Answer:
3 pounds per month
Step-by-step explanation:
22-4 = 18
18/6=3