Answer:
The height is increasing at the rate of 0.42 ft/min
Step-by-step explanation:
Given that:
The diameter = height
and
diameter d = 2 r
2 r = h
r = ![\frac{h}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bh%7D%7B2%7D)
The volume of the cone formed = v
v ⇒
= 40 ft³/ min
![v = \frac{1}{3} \pi r^2h](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2h)
![v = \frac{1}{3} \pi (\frac{h}{2})^2 h](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%28%5Cfrac%7Bh%7D%7B2%7D%29%5E2%20h)
![v = \frac{1}{3} \pi \frac{h^3}{4}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%5Cfrac%7Bh%5E3%7D%7B4%7D)
![v = \frac{\pi}{12}h^3](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7B%5Cpi%7D%7B12%7Dh%5E3)
![\frac{dv}{dt}= \frac{\pi}{12}3h^2\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%3D%20%5Cfrac%7B%5Cpi%7D%7B12%7D3h%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dv}{dt}= \frac{\pi}{4}h^2\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7Dh%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}= \frac{4}{\pi h^2}\frac{dv}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%20%5Cfrac%7B4%7D%7B%5Cpi%20h%5E2%7D%5Cfrac%7Bdv%7D%7Bdt%7D)
at h = 11 ft high
![\frac{dh}{dt}= \frac{4}{\pi (11)^2}* (40)](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%20%5Cfrac%7B4%7D%7B%5Cpi%20%2811%29%5E2%7D%2A%20%2840%29)
![\frac{dh}{dt}= 0.42 \ ft/min](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%200.42%20%5C%20ft%2Fmin)
Hence, the height of the pile was increasing at the rate of 0.42 ft/min
Answer:
Mabel would have to draw a new angle that measured 97°.
Step-by-step explanation:
Supplementary angles always add up to 180°.
So, she would have to draw an angle that was
°
°
.
So Mabel would have to draw a new angle that measured 97°.
Answer:
The last set cannot be the angles of a triangle
Step-by-step explanation: 61+61+59= 181. The angles of a triangle must always total 180°
All the other combinations meet that requirement.
Answer:
so d = 43
and the answer to the question is divide
33 minutes because 56 plus 10 equals 66 divided by 2 equals 33