Answer:
The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere is given by the following equation:
![V = \frac{4\pi r^3}{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D)
In which r is the radius.
Implicit derivatives:
This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So
![\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%204%5Cpi%20r%5E2%20%5Cfrac%7Bdr%7D%7Bdt%7D)
The radius of a sphere is increasing at a rate of 4 mm/s.
This means that ![\frac{dr}{dt} = 4](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%204)
How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm?
This is
when
. So
![\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%204%5Cpi%20r%5E2%20%5Cfrac%7Bdr%7D%7Bdt%7D)
![\frac{dV}{dt} = 4\pi*(30)^2*4](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%204%5Cpi%2A%2830%29%5E2%2A4)
![\frac{dV}{dt} = 1508](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%201508)
The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.
The common endpoint is called the vertex of the angle, and the rays are called the sides of the angle.
hope this helped
Answer:corona
Step-by-step explanation:
Answer:
1. 6x+10
2. 3x+
/5
3. 2.5x-1.1
I'm not sure if I did it in the correct format. :(