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:
The answer would be (3,-2)
Step-by-step explanation:
At the location of (3,-2), if you went upwards 6 units, you would be at the Marigolds. If you went to the left 5 units, you would be at the Lavender. Therefore, (3,-2) is the correct answer.
Answer:
no because it isnt oxygen it is hydrogen becaus Au + H isnt considered gold it is the bounty chocolate from msrs therefore i like the milkywy
Step-by-step explanation:
Answer:
11 1/5 minutes
Step-by-step explanation:
Luke listens to the three most popular songs on the radio this week. The length of each song is shown. #1 song: 3 1/2 minutes #2 song: 2 57 /60 minutes #3 song: 4 3/4 minutes. What is the length of the three songs all together?
song 1: 3 1/2 minutes
song 2: 2 57 /60 minutes
song 3: 4 3/4 minutes
Total length of the three songs = song 1 + song 2 + song 3
= (3 1/2 + 2 57/60 + 4 3/4) minutes
= 7/2 + 177/60 + 19/4
= (210+177+285) / 60
= 672/60
= 56/5
= 11 1/5 minutes
Total length of the three songs = 11 1/5 minutes
Answer:
21
Plz mark me brainliest
Step-by-step explanation: