2) The formula for the area of a circle is: A =
![\pi r x^{2}](https://tex.z-dn.net/?f=%20%5Cpi%20r%20x%5E%7B2%7D%20)
Differentiate both sides to get:
![\frac{dA}{dt} = 2 \pi r \frac{dr}{dt}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20%202%20%5Cpi%20r%20%5Cfrac%7Bdr%7D%7Bdt%7D%20)
where dA/dt is the rate of change of the area of the circle with respect to time, and dr/dt is the rate of change of the radius of the circle with respect to time.
We want to know dA/dt when r = 3 and dr/dt = 2, so plug those into the equation to get:
![\frac{dA}{dt} =2 \pi (3)(2) = 12 \pi feet per second.](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%20%3D2%20%5Cpi%20%283%29%282%29%20%3D%2012%20%5Cpi%20feet%20per%20second.%20)
3) The amount of revenue gained in a week is equal to the price per good times the number of goods sold, or R = x*p. Thus, R = x(150-.002x) = 150x - .002x^2. Differentiate both sides to get:
![\frac{dR}{dt} = 150 \frac{dx}{dt} - .004x \frac{dx}{dt}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdR%7D%7Bdt%7D%20%3D%20150%20%5Cfrac%7Bdx%7D%7Bdt%7D%20-%20.004x%20%5Cfrac%7Bdx%7D%7Bdt%7D%20)
, where dR/dt is the rate of change of revenue and dx/dt is the rate of change of production.
We want dR/dt when dx/dt = 200 and x = 2000, so plug those in to get:
Answer:
22
Step-by-step explanation:
Perimeter is every side added together soo...
6 + 5+ 6+ 5 =22
Answer:
<u> 800 20 1 </u>
50<u>| | | |</u>
4 <u>| | | |</u>
pretty much a rectangle with 800 20 1 at the top
50 4 on the side
and split the numbers in the box - i tried to recreate it as much as possible
oh then in each little box you have to multiply the numbers so
50 x 800 = 40,000 in the box
50 x 20 = 1,000 in the next box
50 x 1 = 50 in the next box
4 x 800 = 3,200
4 x 20 = 80
4 x 1 = 4
then you add all of them which would be 44,334
Answer:
5
Step-by-step explanation: