Answer:
=>12-2
=> 10
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<h2>
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Answer:
The volume of cone is increasing at a rate 1808.64 cubic cm per second.
Step-by-step explanation:
We are given the following in the question:
![\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdr%7D%7Bdt%7D%20%3D%2012%5Ctext%7B%20cm%20per%20sec%7D%5C%5C%5C%5C%5Cdfrac%7Bdh%7D%7Bdt%7D%20%3D%2012%5Ctext%7B%20cm%20per%20sec%7D)
Volume of cone =
![V = \dfrac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h)
where r is the radius and h is the height of the cone.
Instant height = 9 cm
Instant radius = 6 cm
Rate of change of volume =
![\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7Bd%7D%7Bdt%7D%28%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%29%5C%5C%5C%5C%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B%5Cpi%7D%7B3%7D%282r%5Cdfrac%7Bdr%7D%7Bdt%7Dh%20%2B%20r%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D%29)
Putting values, we get,
![\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cdfrac%7B%5Cpi%7D%7B3%7D%282%286%29%2812%29%289%29%20%2B%20%286%29%5E2%2812%29%29%5C%5C%5C%5C%5Cdfrac%7BdV%7D%7Bdt%7D%20%3D1808.64%5Ctext%7B%20cubic%20cm%20per%20second%7D)
Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.
Answer:
-3x - 7
Step-by-step explanation:
-3x - 6 - 1 = -3x - 7
Answer:
the last one is true
Step-by-step explanation:
sin R=PQ/PR=TS/TR
Answer:
x = -1 and y = 18
Step-by-step explanation:
Given the system of equations
y + 8x = 10... 1
2y - 4x = 40 ... 2
From 1; y = 10-8x
Substitute into 2;
2(10-8x) - 4x = 40
20 - 16x - 4x = 40
20 - 20x = 40
-20x = 40 - 20
-20x = 20
x = -1
Recall that y = 10-8x
y = 10 - 8(-1)
y = 10 + 8
y = 18
therefore your answer is x = -1 and y = 18