The radius of the sphere decreases at the rate of 6 m/ sec
That is, ![\frac{dr}{dt}=-6](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdr%7D%7Bdt%7D%3D-6%20%20)
Surface Area of the sphere of radius r is given by ![S=4\pi r^2](https://tex.z-dn.net/?f=%20S%3D4%5Cpi%20r%5E2%20)
Differentiating with respect to t,
![\frac{dS}{dt}=4\pi (2r)\frac{dr}{dt}=8\pi r\frac{dr}{dt}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdS%7D%7Bdt%7D%3D4%5Cpi%20%282r%29%5Cfrac%7Bdr%7D%7Bdt%7D%3D8%5Cpi%20r%5Cfrac%7Bdr%7D%7Bdt%7D%20)
![\frac{dS}{dt}=8\pi (20)^2(-6)=-960\pi \: m^2/sec](https://tex.z-dn.net/?f=%20%5Cfrac%7BdS%7D%7Bdt%7D%3D8%5Cpi%20%2820%29%5E2%28-6%29%3D-960%5Cpi%20%5C%3A%20m%5E2%2Fsec%20)
Answer:
1. V = πr²h
2. dv/dt = πr²dh/dt
3. dv/dt = 113.04
Step-by-step explanation:
We have these information
Radius R = 3cm
Height = h
Volume = V
We have been given dh/dt = 4cm
1.
An equation relating V, r, h
Volume of cylinder = πr²h
2.
The related rates equation
dv/dt = πr²dh/dt
dv/dt = π3²dh/dt
3. Continuing from number 2 above, we have
dv/dt = π3²dh/dt
= π9x4
= 3.14x9x4
= 113.04
These are the answers to the questions
![2x^{2}+4x-2 \\ \\ \Delta=b^{2}-4ac \\ \\ \Delta=4^{2}-4*2*(-2)=16+16=32](https://tex.z-dn.net/?f=2x%5E%7B2%7D%2B4x-2%20%5C%5C%20%20%5C%5C%20%5CDelta%3Db%5E%7B2%7D-4ac%20%5C%5C%20%20%5C%5C%20%5CDelta%3D4%5E%7B2%7D-4%2A2%2A%28-2%29%3D16%2B16%3D32)
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Tough sorry wish I could help u can’t too hard but I think it is equivalent to the other triangle so I think it’s 31? I THINK
Answer: So,. The sum of the measures of the angles of a quadrilateral is 360. Let m∠J = m∠K = x. ... CCSS SENSE-MAKING If WXYZ is a kite, find each measure. 24. YZ.
Step-by-step explanation: