P,Q,R can't be 0, because their product is nonzero. Either of S and T could be 0, but the third one only works if S is 0.
Answer:
put a picture up
Step-by-step explanation:
<h3>
Answer: 9V</h3>
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Reason:
The volume expression of a cone with radius r and height h is
![\frac{1}{3}\pi*r^2*h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%2Ar%5E2%2Ah)
Let's plug in the given height h = 12 and we'd get
![\frac{1}{3}\pi*r^2*h\\\\\frac{1}{3}\pi*r^2*12\\\\\left(\frac{1}{3}*12\right)\pi*r^2\\\\4\pi*r^2\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%2Ar%5E2%2Ah%5C%5C%5C%5C%5Cfrac%7B1%7D%7B3%7D%5Cpi%2Ar%5E2%2A12%5C%5C%5C%5C%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%2A12%5Cright%29%5Cpi%2Ar%5E2%5C%5C%5C%5C4%5Cpi%2Ar%5E2%5C%5C%5C%5C)
This is the volume of the first cone. We're told the first cone has a volume of V, so we can say ![V = 4\pi r^2](https://tex.z-dn.net/?f=V%20%3D%204%5Cpi%20r%5E2)
We can't find the actual numeric volume because we don't know what value replaces r. So we leave it as is.
The second cone has the same height (h = 12) but the radius is now 3 times in size. Instead of r, we use 3r
Replace every copy of r with 3r. Then simplify
![4\pi*r^2\\\\4\pi*(3r)^2\\\\4\pi*9r^2\\\\9(4\pi r^2)\\\\9V\\\\](https://tex.z-dn.net/?f=4%5Cpi%2Ar%5E2%5C%5C%5C%5C4%5Cpi%2A%283r%29%5E2%5C%5C%5C%5C4%5Cpi%2A9r%5E2%5C%5C%5C%5C9%284%5Cpi%20r%5E2%29%5C%5C%5C%5C9V%5C%5C%5C%5C)
The radius tripled which results in a volume that's 9 times bigger.
Answer:
From the analysis W1=W2.
they are directly related
Step-by-step explanation:
the work-done in stretching a spring can be expressed as
![W=\frac{1}{2}kx^2](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B1%7D%7B2%7Dkx%5E2)
where k= spring constant
x= change on length of spring
Hence for W1
Given data
x= 34-24= 10 cm
solving in terms of k we have
![W=\frac{1}{2}k*10^2\\\W=\frac{1}{2}k*100\\\W=50k](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B1%7D%7B2%7Dk%2A10%5E2%5C%5C%5CW%3D%5Cfrac%7B1%7D%7B2%7Dk%2A100%5C%5C%5CW%3D50k)
Hence for W2
Given data
x= 44-34= 10 cm
solving in terms of k we have
![W=\frac{1}{2}k*10^2\\\ W=\frac{1}{2}k*100\\\ W=50k](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B1%7D%7B2%7Dk%2A10%5E2%5C%5C%5C%20W%3D%5Cfrac%7B1%7D%7B2%7Dk%2A100%5C%5C%5C%20W%3D50k)