Answer:
y=1/3x+13//3
(i cant graph it but i gave u the slope intercept form)
Step-by-step explanation:
21 cans of dog food.
She gives 21/3, or 7 cans to her neighbor.
She now has 21 - 7, or 14 cans for her puppy.
Her puppy eats 4/7 cans a day.
![14 \times \frac{4}{7} =2\times 4= \boxed{\bf{8}}](https://tex.z-dn.net/?f=14%20%5Ctimes%20%5Cfrac%7B4%7D%7B7%7D%20%3D2%5Ctimes%204%3D%20%5Cboxed%7B%5Cbf%7B8%7D%7D)
Jasmine has
8 days supply of dog food for her puppy.
Answer:
12
Step-by-step explanation:
There are 2 tangent lines that pass through the point
![y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B%28-1%2B%5Csqrt%7B3%29%5E2%7D%20%7D%20%28x-1%29%2B2)
and
![y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B%28-1-%5Csqrt%7B3%29%5E2%7D%20%7D%20%28x-1%29%2B2)
Explanation:
Given:
![y=\frac{x}{x+1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7Bx%2B1%7D)
The point-slope form of the equation of a line tells us that the form of the tangent lines must be:
![[1]](https://tex.z-dn.net/?f=%5B1%5D)
For the lines to be tangent to the curve, we must substitute the first derivative of the curve for
:
![\frac{dy}{dx} =\frac{d(x)}{dx}(x+1)-x^\frac{d(x+1)}{dx} \\ \\](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cfrac%7Bd%28x%29%7D%7Bdx%7D%28x%2B1%29-x%5E%5Cfrac%7Bd%28x%2B1%29%7D%7Bdx%7D%20%5C%5C%20%5C%5C)
![\frac{dy}{dx} =\frac{x+1-x}{(x+1)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D%5Cfrac%7Bx%2B1-x%7D%7B%28x%2B1%29%5E2%7D)
![\frac{dy}{dx}= \frac{1}{(x+1)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%20%5Cfrac%7B1%7D%7B%28x%2B1%29%5E2%7D)
![[2]](https://tex.z-dn.net/?f=%5B2%5D)
Substitute equation [2] into equation [1]:
![[1.1]](https://tex.z-dn.net/?f=%5B1.1%5D)
Because the line must touch the curve, we may substitute ![y=\frac{x}{x+1}:](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx%7D%7Bx%2B1%7D%3A)
![\frac{x}{x+1}=\frac{x-1}{(x+1)^2}+2](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bx%2B1%7D%3D%5Cfrac%7Bx-1%7D%7B%28x%2B1%29%5E2%7D%2B2)
Solve for x:
![x(x+1)=(x-1)+2(x+1)^2](https://tex.z-dn.net/?f=x%28x%2B1%29%3D%28x-1%29%2B2%28x%2B1%29%5E2)
![x^2+x=x-1+2x^2+4x+2](https://tex.z-dn.net/?f=x%5E2%2Bx%3Dx-1%2B2x%5E2%2B4x%2B2)
![x^2+4x+1](https://tex.z-dn.net/?f=x%5E2%2B4x%2B1)
![x\frac{-4±\sqrt{4^2-4(1)(1)} }{2(1)}](https://tex.z-dn.net/?f=x%5Cfrac%7B-4%C2%B1%5Csqrt%7B4%5E2-4%281%29%281%29%7D%20%7D%7B2%281%29%7D)
± ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
±
<em> </em>
![x=-2-\sqrt{3}](https://tex.z-dn.net/?f=x%3D-2-%5Csqrt%7B3%7D)
There are 2 tangent lines.
![y=\frac{1}{(-1+\sqrt{3)^2} } (x-1)+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B%28-1%2B%5Csqrt%7B3%29%5E2%7D%20%7D%20%28x-1%29%2B2)
and
![y=\frac{1}{(-1-\sqrt{3)^2} } (x-1)+2](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B%28-1-%5Csqrt%7B3%29%5E2%7D%20%7D%20%28x-1%29%2B2)
Answer:
18
Step-by-step explanation:
I did maths I did maths I did maths I did maths I did maths