Answer:
number2
Step-by-step explanation:
because space pie said so
Answer:
The equation of the tangent at x=-6 is ![y=-\frac{3}{4}x-\frac{15}{2}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B15%7D%7B2%7D)
Step-by-step explanation:
The equation of a circle with center (h,k) with radius r units is given by:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
The given circle has center (-3,1) and radius 5 units.
We substitute the center and the radius into the equation to get;
![(x--3)^2+(y-1)^2=5^2](https://tex.z-dn.net/?f=%28x--3%29%5E2%2B%28y-1%29%5E2%3D5%5E2)
![(x+3)^2+(y-1)^2=25](https://tex.z-dn.net/?f=%28x%2B3%29%5E2%2B%28y-1%29%5E2%3D25)
To find the slope, we differentiate implicitly to get:
![2(x+3)+2(y-1)\fra{dy}{dx}=0](https://tex.z-dn.net/?f=2%28x%2B3%29%2B2%28y-1%29%5Cfra%7Bdy%7D%7Bdx%7D%3D0)
![2(y-1)\frac{dy}{dx}=-2(x+3)](https://tex.z-dn.net/?f=2%28y-1%29%5Cfrac%7Bdy%7D%7Bdx%7D%3D-2%28x%2B3%29)
![\frac{dy}{dx}=-\frac{x+3}{y-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7Bx%2B3%7D%7By-1%7D)
When x=-6;we have ![(-6+3)^2+(y-1)^2=25](https://tex.z-dn.net/?f=%28-6%2B3%29%5E2%2B%28y-1%29%5E2%3D25)
![\implies 9+(y-1)^2=25](https://tex.z-dn.net/?f=%5Cimplies%209%2B%28y-1%29%5E2%3D25)
![\implies (y-1)^2=25-9](https://tex.z-dn.net/?f=%5Cimplies%20%28y-1%29%5E2%3D25-9)
![\implies (y-1)^2=16](https://tex.z-dn.net/?f=%5Cimplies%20%28y-1%29%5E2%3D16)
![\implies y-1=\pm \sqrt{16}](https://tex.z-dn.net/?f=%5Cimplies%20y-1%3D%5Cpm%20%5Csqrt%7B16%7D)
![\implies y-1=\pm4](https://tex.z-dn.net/?f=%5Cimplies%20y-1%3D%5Cpm4)
![\implies y=1\pm4](https://tex.z-dn.net/?f=%5Cimplies%20y%3D1%5Cpm4)
or ![y=5](https://tex.z-dn.net/?f=y%3D5)
From the graph the reuired point is (-6,-3).
We substitute this point to find the slope;
![\frac{dy}{dx}=-\frac{-6+3}{-3-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B-6%2B3%7D%7B-3-1%7D)
![\frac{dy}{dx}=-\frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D-%5Cfrac%7B3%7D%7B4%7D)
The equation is given by
.
We plug in the slope and the point to get:
![y--3=-\frac{3}{4}(x--6)](https://tex.z-dn.net/?f=y--3%3D-%5Cfrac%7B3%7D%7B4%7D%28x--6%29)
![y=-\frac{3}{4}(x+6)-3](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7D%28x%2B6%29-3)
![y=-\frac{3}{4}x-\frac{9}{2}-3](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B9%7D%7B2%7D-3)
![y=-\frac{3}{4}x-\frac{15}{2}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B15%7D%7B2%7D)
That would be (125 * 12.8) / 100
= (5 * 12.8) / 4
= 64/4
= 16 answer
Answer: 1
Step-by-step explanation: