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.
Answer:
A
Step-by-step explanation:
f(-2)=3(4)+1
=13
Answer:
<h2>the LCM of 6 and 7 is 42<u><em>
i hope the worked! </em></u></h2>
Step-by-step explanation:
Answer:
The answer is Y.
Step-by-step explanation:
Answer: The average rate of change is ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Step-by-step explanation:
The points (1, 2); (2, 2.5); (3, 3); (4, 3.5) and (5, 4) belong to the line shown in the graph attached.
The average rate of change for the sequence is the slope and you can calculate it with the formula:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Then, choose two points of the line and substitute them into
:
Let's choose the point (1,2) and the point (2,2.5). Then:
![m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m=\frac{2.5-2}{2-1}\\\\m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B2.5-2%7D%7B2-1%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B1%7D%7B2%7D)