(1, -12) or (1,4). you need the base to be 8 units.
Answer:
The area is changing by the rate of 44.62 meters per sec.
Step-by-step explanation:
Let x be the side of the square and r be the radius of the circle,
Then, the area outside the circle but inside the square is,
V = Area of square - area of circle,
∵ Area of a square = side² and area of a circle =
(radius)²,
Thus,
![V=x^2-\pi(r)^2](https://tex.z-dn.net/?f=V%3Dx%5E2-%5Cpi%28r%29%5E2)
Differentiating with respect to t ( time )
![\frac{dV}{dt}=2x\frac{dx}{dt} -2\pi r\frac{dr}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D2x%5Cfrac%7Bdx%7D%7Bdt%7D%20-2%5Cpi%20r%5Cfrac%7Bdr%7D%7Bdt%7D)
We have,
x = 20 meters, r = 3 meters,
![\frac{dr}{dt}=4\text{ meters per sec}](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%3D4%5Ctext%7B%20meters%20per%20sec%7D)
![\implies \frac{dV}{dt}=2(20)(3)-2\pi(3)(4)](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7BdV%7D%7Bdt%7D%3D2%2820%29%283%29-2%5Cpi%283%29%284%29)
![=120-24\pi](https://tex.z-dn.net/?f=%3D120-24%5Cpi)
![=44.6017763138](https://tex.z-dn.net/?f=%3D44.6017763138)
![\approx 44.62\text{ meter per sec}](https://tex.z-dn.net/?f=%5Capprox%2044.62%5Ctext%7B%20meter%20per%20sec%7D)
Answer:
C
Step-by-step explanation:
Well I think that for this problem we should multiply 3x1/3 which is 1 whole. Sorry if I'm incorrect.
In each case, for a) f has local maximum at (1,1) and for b) f has saddle point at (1,1).
a) f_{xx}f_{yy}-(f_{xy})2
=(-4)(-2)-(1)2
=8-1
=7>0
f_{xx}=-4<0
Therefore, f has local maximum at (1,1)
b) f_{xx}f_{yy}-(f_{xy})2
=(-4)(-2)-(3)2
=8-9
=-1<0
Therefore, f has saddle point at (1,1)
A factor at which a feature of variables has partial derivatives identical to 0 however at which the feature has neither a most nor a minimal value.
To learn more about derivatives check the link below:
brainly.com/question/28376218
#SPJ4
Complete question:
Suppose (1, 1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f?a) f_{xx}f_{yy}-(f_{xy})2 and b) f_{xx}f_{yy}-(f_{xy})2