Answer:
The slope of tangent at point (1,-2) is
.
Step-by-step explanation:
The given equation of ellipse is
![2x^2+xy+y^2=4](https://tex.z-dn.net/?f=2x%5E2%2Bxy%2By%5E2%3D4)
Differentiate both sides with respect to x.
![\frac{d}{dx}(2x^2+xy+y^2)=\frac{d}{dx}(4)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%282x%5E2%2Bxy%2By%5E2%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%284%29)
![\frac{d}{dx}(2x^2)\frac{d}{dx}(xy)+\frac{d}{dx}(y^2)=\frac{d}{dx}(4)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%282x%5E2%29%5Cfrac%7Bd%7D%7Bdx%7D%28xy%29%2B%5Cfrac%7Bd%7D%7Bdx%7D%28y%5E2%29%3D%5Cfrac%7Bd%7D%7Bdx%7D%284%29)
![4x+x\frac{dy}{dx}+y+2y\frac{dy}{dx}=0](https://tex.z-dn.net/?f=4x%2Bx%5Cfrac%7Bdy%7D%7Bdx%7D%2By%2B2y%5Cfrac%7Bdy%7D%7Bdx%7D%3D0)
![(4x+y)+(x+2y)\frac{dy}{dx}=0](https://tex.z-dn.net/?f=%284x%2By%29%2B%28x%2B2y%29%5Cfrac%7Bdy%7D%7Bdx%7D%3D0)
![\frac{dy}{dx}=-\frac{4x+y}{x+2y}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B4x%2By%7D%7Bx%2B2y%7D)
Calculate the value of \frac{dy}{dx} at (1,-2).
![\frac{dy}{dx}_{(1,-2)}=-\frac{4(1)+(-2)}{(1)+2(-2)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D_%7B%281%2C-2%29%7D%3D-%5Cfrac%7B4%281%29%2B%28-2%29%7D%7B%281%29%2B2%28-2%29%7D)
![\frac{dy}{dx}_{(1,-2)}=-\frac{2}{-3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D_%7B%281%2C-2%29%7D%3D-%5Cfrac%7B2%7D%7B-3%7D)
![\frac{dy}{dx}_{(1,-2)}=\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D_%7B%281%2C-2%29%7D%3D%5Cfrac%7B2%7D%7B3%7D)
Therefore the slope of tangent at point (1,-2) is
.
Answer:
x=2
Step-by-step explanation:
We know AC = BC since this is an isosceles triangle
6 = 2x+2
Subtract 2 from each side
6-2 =2x+2-2
4 =2x
Divide each side by 2
4/2 =2x/2
2=x
Just multiply all them together for volume, 468 ft ^3
I believe the points should be as follows : X, S, Y, and U.