Answer:
Step-by-step explanation:
width is 255/15=17
perimeter = 17*2+15*2=64
EZ
Answer:
0.45 ft/min
Step-by-step explanation:
Given:-
- The flow rate of the gravel, ![\frac{dV}{dt} = 35 \frac{ft^3}{min}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%2035%20%5Cfrac%7Bft%5E3%7D%7Bmin%7D)
- The base diameter ( d ) of cone = x
- The height ( h ) of cone = x
Find:-
How fast is the height of the pile increasing when the pile is 10 ft high?
Solution:-
- The constant flow rate of gravel dumped onto the conveyor belt is given to be 35 ft^3 / min.
- The gravel pile up into a heap of a conical shape such that base diameter ( d ) and the height ( h ) always remain the same. That is these parameter increase at the same rate.
- We develop a function of volume ( V ) of the heap piled up on conveyor belt in a conical shape as follows:
![V = \frac{\pi }{12}*d^2*h\\\\V = \frac{\pi }{12}*x^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B%5Cpi%20%7D%7B12%7D%2Ad%5E2%2Ah%5C%5C%5C%5CV%20%3D%20%5Cfrac%7B%5Cpi%20%7D%7B12%7D%2Ax%5E3)
- Now we know that the volume ( V ) is a function of its base diameter and height ( x ). Where x is an implicit function of time ( t ). We will develop a rate of change expression of the volume of gravel piled as follows Use the chain rule of ordinary derivatives:
![\frac{dV}{dt} = \frac{dV}{dx} * \frac{dx}{dt}\\\\\frac{dV}{dt} = \frac{\pi }{4} x^2 * \frac{dx}{dt}\\\\\frac{dx}{dt} = \frac{\frac{dV}{dt}}{\frac{\pi }{4} x^2}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7BdV%7D%7Bdx%7D%20%20%2A%20%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20x%5E2%20%2A%20%5Cfrac%7Bdx%7D%7Bdt%7D%5C%5C%5C%5C%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cfrac%7BdV%7D%7Bdt%7D%7D%7B%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20x%5E2%7D)
- Determine the rate of change of height ( h ) using the relation developed above when height is 10 ft:
![h = x\\\\\frac{dh}{dt} = \frac{dx}{dt} = \frac{35 \frac{ft^3}{min} }{\frac{\pi }{4}*10^2 ft^2 } \\\\\frac{dh}{dt} = \frac{dx}{dt} = 0.45 \frac{ft}{min}](https://tex.z-dn.net/?f=h%20%3D%20x%5C%5C%5C%5C%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%20%5Cfrac%7B35%20%5Cfrac%7Bft%5E3%7D%7Bmin%7D%20%7D%7B%5Cfrac%7B%5Cpi%20%7D%7B4%7D%2A10%5E2%20ft%5E2%20%7D%20%20%20%5C%5C%5C%5C%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%200.45%20%5Cfrac%7Bft%7D%7Bmin%7D)
Y=9 when x=3 and can i get brainliest
He needs 1/2 cup because 3/4-1/4=2/4 which is simplified to 1/2