Answer:
0.25 feet per minute
Step-by-step explanation:
Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.
![\dfrac{dV}{dt}=20$ ft^3/min](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D20%24%20ft%5E3%2Fmin)
![\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20a%20cone%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h)
Since base diameter = Height of the Cone
Radius of the Cone = h/2
Therefore,
![\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20the%20cone%7D%3D%5Cdfrac%7B%5Cpi%20h%7D%7B3%7D%20%28%5Cdfrac%7Bh%7D%7B2%7D%29%20%5E2%20%5C%5CV%3D%5Cdfrac%7B%5Cpi%20h%5E3%7D%7B12%7D)
![\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}](https://tex.z-dn.net/?f=%5Ctext%7BRate%20of%20Change%20of%20the%20Volume%7D%2C%20%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B3%5Cpi%20h%5E2%7D%7B12%7D%5Cdfrac%7Bdh%7D%7Bdt%7D)
Therefore: ![\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20](https://tex.z-dn.net/?f=%5Cdfrac%7B3%5Cpi%20h%5E2%7D%7B12%7D%5Cdfrac%7Bdh%7D%7Bdt%7D%3D20)
We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.
![h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)](https://tex.z-dn.net/?f=h%3D10%24%20feet%24%5C%5C%5C%5C%5Cdfrac%7B3%5Cpi%20%2A10%5E2%7D%7B12%7D%5Cdfrac%7Bdh%7D%7Bdt%7D%3D20%5C%5C25%5Cpi%20%5Cdfrac%7Bdh%7D%7Bdt%7D%3D20%5C%5C%20%5Cdfrac%7Bdh%7D%7Bdt%7D%3D%20%5Cdfrac%7B20%7D%7B25%5Cpi%7D%5C%5C%20%5Cdfrac%7Bdh%7D%7Bdt%7D%3D0.25%24%20feet%20per%20minute%20%28to%20two%20decimal%20places.%29)
When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute
Answer:
1488 sandwiches in thirty minutes
Step-by-step explanation:
Answer:
I'm not sure for my answer 'cuz I just learned this but i think its A because even though the size changes, the corresponding angle measure are the same and the corresponding sides are proportional.
(Tell me if I'm wrong.)
Answer:
w = ![\frac{p -2l}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bp%20-2l%7D%7B2%7D)
Step-by-step explanation:
p = 2l + 2w Subtract 2l from both sides of the equation
p - 2l = 2p Divide both sides by 2
= w