Answer:
width = 4inches
Step-by-step explanation:
Volume = l*w*h
240 = 10*w*6
240 = 60w
Divide each side by 60
240/60 = 60w/60
4 = w
Answer:
0.3537 feet per minute.
Step-by-step explanation:
Gravel is being dumped from a conveyor belt at a rate of 10 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}=10$ ft^3/min](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D10%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)
If the Base Diameter = Height of the Cone
The 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}=10](https://tex.z-dn.net/?f=%5Cdfrac%7B3%5Cpi%20h%5E2%7D%7B12%7D%5Cdfrac%7Bdh%7D%7Bdt%7D%3D10)
We want to determine how fast is the height of the pile is increasing when the pile is 6 feet high.
![When h=6$ feet$\\\dfrac{3\pi *6^2}{12}\dfrac{dh}{dt}=10\\9\pi \dfrac{dh}{dt}=10\\ \dfrac{dh}{dt}= \dfrac{10}{9\pi}\\ \dfrac{dh}{dt}=0.3537$ feet per minute](https://tex.z-dn.net/?f=When%20h%3D6%24%20feet%24%5C%5C%5Cdfrac%7B3%5Cpi%20%2A6%5E2%7D%7B12%7D%5Cdfrac%7Bdh%7D%7Bdt%7D%3D10%5C%5C9%5Cpi%20%5Cdfrac%7Bdh%7D%7Bdt%7D%3D10%5C%5C%20%5Cdfrac%7Bdh%7D%7Bdt%7D%3D%20%5Cdfrac%7B10%7D%7B9%5Cpi%7D%5C%5C%20%5Cdfrac%7Bdh%7D%7Bdt%7D%3D0.3537%24%20feet%20per%20minute)
When the pile is 6 feet high, the height of the pile is increasing at a rate of 0.3537 feet per minute.
Answer:
7/3
Step-by-step explanation:
Let the two numbers be x and y which are relatively prime to each other.
a/b = 5/2
So you want the ratio of
(a + b) / (a - b)
- Take out a common factor of b
- numerator: b(a/b + 1)
- denominator: b(a/b - 1)
- Put them together
- The b's cancel out
- (a/b + 1) / (a/b - 1)
- but a/b = 5/2
- (5/2 + 1) / (5/2 - 1)
- Numerator: (5/2 + 2/2) = 7/2
- Denominator: 5/2 - 2/2 = 3/2
- numerator over denominator = 7/2 // 3/2 = 7/2 * 2/3 = 7/3
Answer: 7/3
Nice problem: Thanks for posting.
Answer:
0.42
Step-by-step explanation: