Answer: 2.50 dollars
Explanation:
Locate 5 on the x axis, which corresponds to buying 5 kgs of apples.
Draw a vertical line through 5 on the x axis until you reach the blue line. Mark this as point P.
From point P, draw a horizontal line until you reach the y axis. You should arrive at y = 2.5
This tells us that buying x = 5 kgs of apples will cost a total of y = 2.50 dollars.
Answer:
The Moon is an average of 238,855 miles (384,400 km) away
Implicit defferentation
remember that dy/dx y= dy/dx
so
take derivitive of both sides
![2x+2y \space\ \frac{dy}{dx}=0](https://tex.z-dn.net/?f=2x%2B2y%20%5Cspace%5C%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D0)
solve for
![\frac{dy}{dx}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D)
minus 2x both sides
![2y \space\ \frac{dy}{dx}=-2x](https://tex.z-dn.net/?f=2y%20%5Cspace%5C%20%5Cfrac%7Bdy%7D%7Bdx%7D%3D-2x)
divide both sides by 2y
![\frac{dy}{dx}=\frac{-2x}{2y}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B-2x%7D%7B2y%7D)
![\frac{dy}{dx}=\frac{-x}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B-x%7D%7By%7D)
when is the slope equal to
![\frac{5}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B12%7D)
solve for
![\frac{dy}{dx}=\frac{5}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B5%7D%7B12%7D)
![\frac{dy}{dx}=\frac{5}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B5%7D%7B12%7D)
![\frac{5}{12}=\frac{-x}{y}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B12%7D%3D%5Cfrac%7B-x%7D%7By%7D)
![5y=-12x](https://tex.z-dn.net/?f=5y%3D-12x)
![y=\frac{-12}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-12%7D%7B5%7Dx)
find where the circle and this line intersects
substitute
![\frac{-12}{5}x](https://tex.z-dn.net/?f=%5Cfrac%7B-12%7D%7B5%7Dx)
for y
![x^2+(\frac{-12}{5}x)^2=676](https://tex.z-dn.net/?f=x%5E2%2B%28%5Cfrac%7B-12%7D%7B5%7Dx%29%5E2%3D676)
![x^2+\frac{144}{25}x^2=676](https://tex.z-dn.net/?f=x%5E2%2B%5Cfrac%7B144%7D%7B25%7Dx%5E2%3D676)
![\frac{25}{25}x^2+\frac{144}{25}x^2=676](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B25%7Dx%5E2%2B%5Cfrac%7B144%7D%7B25%7Dx%5E2%3D676)
![\frac{169}{25}x^2=676](https://tex.z-dn.net/?f=%5Cfrac%7B169%7D%7B25%7Dx%5E2%3D676)
times both sides by
![\frac{25}{169}](https://tex.z-dn.net/?f=%5Cfrac%7B25%7D%7B169%7D)
![x^2=100](https://tex.z-dn.net/?f=x%5E2%3D100)
sqrt both sides, take positive and negative roots
x=+/-10
sub back
![y=\frac{-12}{5}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-12%7D%7B5%7Dx)
![y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)](https://tex.z-dn.net/?f=y%3D%28%5Cfrac%7B-12%7D%7B5%7D%29%2810%29%20%5Cspace%5C%20or%20%5Cspace%5C%20%28%5Cfrac%7B-12%7D%7B5%7D%29%28-10%29%20)
![y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-120%7D%7B5%7D%20%5Cspace%5C%20or%20%5Cspace%5C%20%5Cfrac%7B120%7D%7B5%7D%20)
![y=-24 \space\ or \space\ 24](https://tex.z-dn.net/?f=y%3D-24%20%5Cspace%5C%20or%20%5Cspace%5C%2024%20)
the points are (10,-24) and (-10,24)