Answer: 18 units squared
Step-by-step explanation:
To find area of a rectangle use A=lw
we can count the units for both and get...
11x2=18
So 18 units squared
I'd say A. 8000, because you'd get the most answers and the biggest variety in answers for a more accurate sample.
Answer:
Step-by-step explanation:
1,2,3,3,3,3,5,6,7,10,10,10,11,11,12,12,13,13,
14,15
Solve for R by simplifying both sides of the equation, the isolating the variable.
R^2h=-r^2+v
Answer:
The volume is decreasing at the rate of 1.396 cubic inches per minute
Step-by-step explanation:
Given
Shape: Cone
--- rate of the radius
--- rate of the height
![r = 2](https://tex.z-dn.net/?f=r%20%3D%202)
![h = \frac{1}{3}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
Required
Determine the rate of change of the cone volume
The volume of a cone is:
![V = \frac{\pi}{3}r^2h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7Dr%5E2h)
Differentiate with respect to time (t)
![\frac{dV}{dt} = \frac{\pi}{3}(2rh \frac{dr}{dt} + r^2 \frac{dh}{dt})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%282rh%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%2B%20r%5E2%20%5Cfrac%7Bdh%7D%7Bdt%7D%29)
Substitute values for the known variables
![\frac{dV}{dt} = \frac{\pi}{3}(2*2*\frac{1}{3}* \frac{1}{2} - 2^2 *\frac{1}{3})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%282%2A2%2A%5Cfrac%7B1%7D%7B3%7D%2A%20%5Cfrac%7B1%7D%7B2%7D%20-%202%5E2%20%2A%5Cfrac%7B1%7D%7B3%7D%29)
![\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}* \frac{1}{2} - \frac{4}{3})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%28%5Cfrac%7B4%7D%7B3%7D%2A%20%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B4%7D%7B3%7D%29)
![\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}(\frac{1}{2} - 1))](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%28%5Cfrac%7B4%7D%7B3%7D%28%5Cfrac%7B1%7D%7B2%7D%20-%201%29%29)
![\frac{dV}{dt} = \frac{\pi}{3}(\frac{4}{3}*- 1)](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%28%5Cfrac%7B4%7D%7B3%7D%2A-%201%29)
![\frac{dV}{dt} = -\frac{\pi}{3}*\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B3%7D%2A%5Cfrac%7B4%7D%7B3%7D)
![\frac{dV}{dt} = -\frac{22}{7*3}*\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20-%5Cfrac%7B22%7D%7B7%2A3%7D%2A%5Cfrac%7B4%7D%7B3%7D)
![\frac{dV}{dt} = -\frac{22}{21}*\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20-%5Cfrac%7B22%7D%7B21%7D%2A%5Cfrac%7B4%7D%7B3%7D)
![\frac{dV}{dt} = -\frac{88}{63}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20-%5Cfrac%7B88%7D%7B63%7D)
![\frac{dV}{dt} =-1.396in^3/min](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D-1.396in%5E3%2Fmin)
The volume is decreasing at the rate of 1.396 cubic inches per minute