Answer:
12.995
Step-by-step explanation:
Answer:
1/2 is more than 2/12
Step-by-step explanation:
Answer:
She is correct.
Step-by-step explanation:
Answer:
y = -2
Step-by-step explanation:
To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx
The equation is
![y^2(y^2-4)=x^2(x^2-5)](https://tex.z-dn.net/?f=y%5E2%28y%5E2-4%29%3Dx%5E2%28x%5E2-5%29)
implicit differentiation give us
![\frac{d}{dx}[y^2(y^2-4)=x^2(x^2-5)]\\\\2y\frac{dy}{dx}(y^2-4)+y^2(2y\frac{dy}{dx})=2x(x^2-5)+x^2(2x)\\\\4y^3\frac{dy}{dx}-8y\frac{dy}{dx}=2x^3-10x+2x^3\\\\\frac{dy}{dx}=\frac{4x^3-10x}{4y^3-8y}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5By%5E2%28y%5E2-4%29%3Dx%5E2%28x%5E2-5%29%5D%5C%5C%5C%5C2y%5Cfrac%7Bdy%7D%7Bdx%7D%28y%5E2-4%29%2By%5E2%282y%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D2x%28x%5E2-5%29%2Bx%5E2%282x%29%5C%5C%5C%5C4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D-8y%5Cfrac%7Bdy%7D%7Bdx%7D%3D2x%5E3-10x%2B2x%5E3%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B4x%5E3-10x%7D%7B4y%5E3-8y%7D)
But we know that
![m=\frac{dy}{dx}\\y=mx+b](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bdy%7D%7Bdx%7D%5C%5Cy%3Dmx%2Bb)
Hence, for the point (0,-2) and by replacing for dy/dx
![m=\frac{dy}{dx}_{(0,-2)}=\frac{4(0)+10(0)}{4(-2)^3-8(-2)}=0](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bdy%7D%7Bdx%7D_%7B%280%2C-2%29%7D%3D%5Cfrac%7B4%280%29%2B10%280%29%7D%7B4%28-2%29%5E3-8%28-2%29%7D%3D0)
Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:
y=(0)x+b = -2
HOPE THIS HELPS!!
Explanation:
First, switch sides of an equation.
![m+80=188](https://tex.z-dn.net/?f=m%2B80%3D188)
Then, you subtract by the 80 from both sides of an equation.
![m+80-80=188-80](https://tex.z-dn.net/?f=m%2B80-80%3D188-80)
And finally, simplify and subtract the numbers.
![188-80=108](https://tex.z-dn.net/?f=188-80%3D108)
![\boxed{m=108}](https://tex.z-dn.net/?f=%5Cboxed%7Bm%3D108%7D)
Hope this helps!
Thank you!
Have a great day!