Answer:
The radius is increasing at a rate 0.18 inches per second.
Step-by-step explanation:
We are given the following in the question:
The volume of cylinder is constant.
![\dfrac{dV}{dt} = 0](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%200)
![\dfrac{dh}{dt} = -0.6\text{ inch per second}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdh%7D%7Bdt%7D%20%3D%20-0.6%5Ctext%7B%20inch%20per%20second%7D)
Instant radius= 3 inches
Instant height = 5 inches
Volume of cylinder =
![V = \pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2%20h)
Rate of change of volume =
![\dfrac{dV}{dt} = \pi(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cpi%282r%5Cdfrac%7Bdr%7D%7Bdt%7Dh%20%2B%20r%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D%29)
Putting all the values, we get,
![0 = \dfrac{22}{7}(2(3)\dfrac{dr}{dt}(5)+(3)^2(-0.6))\\\\30\dfrac{dr}{dt} = 9(0.6)\\\\\dfrac{dr}{dt} = \dfrac{9\times 0.6}{30} = 0.18](https://tex.z-dn.net/?f=0%20%3D%20%5Cdfrac%7B22%7D%7B7%7D%282%283%29%5Cdfrac%7Bdr%7D%7Bdt%7D%285%29%2B%283%29%5E2%28-0.6%29%29%5C%5C%5C%5C30%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%209%280.6%29%5C%5C%5C%5C%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B9%5Ctimes%200.6%7D%7B30%7D%20%3D%200.18)
Thus, the radius is increasing at a rate 0.18 inches per second.
Solutions are the answers. What kind of graphing is it or like do you have to write an equation?
Answer:
B. (-5/13, 12/13)
Step-by-step explanation:
The point at distance x from π in the clockwise direction is the reflection of point T across the y-axis. Hence the coordinates are the same, except that the sign of the x-coordinate is reversed.
The point of interest is (-5/13, 12/13).
Answer:
4:00
Step-by-step explanation:
Answer:
x = 59°
y = 67°
Step-by-step explanation:
x = y - 8
x + y + 54 = 180
(y - 8) + y = 180 - 54
2y - 8 = 126
2y = 134
y = 67°
x = 59°
Step-by-step explanation: