Taking

and differentiating both sides with respect to

yields
![\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B3x%5E2%2By%5E2%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B7%5Cbigg%5D%5Cimplies%206x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%3D0)
Solving for the first derivative, we have

Differentiating again gives
![\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B6x%2B2y%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5D%3D%5Cdfrac%7B%5Cmathrm%20d%7D%7B%5Cmathrm%20dx%7D%5Cbigg%5B0%5Cbigg%5D%5Cimplies%206%2B2%5Cleft%28%5Cdfrac%7B%5Cmathrm%20dy%7D%7B%5Cmathrm%20dx%7D%5Cright%29%5E2%2B2y%5Cdfrac%7B%5Cmathrm%20d%5E2y%7D%7B%5Cmathrm%20dx%5E2%7D%3D0)
Solving for the second derivative, we have

Now, when

and

, we have
Answer:
Step-by-step explanation:
When talking about reflection, we usually mean reflecting across a line, or axis. Reflecting a shape means looking at the mirror image on the other side of the axis. Consider the point (x,y), if you reflect this point across the y-axis you should multiply the x-coordinate by -1, so you get:

For triangle ABC we have:

Therefore, the reflecting points are:

Both the original triangle and the reflected one are shown below.
Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).
<h3>How many bowls of cereal would kathy have?</h3>
We know that for each bowl, she needs 1/2 cups of milk.
And we also know that she has a total of (3 + 3/5) cups of milk.
To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:
(3 + 3/5)/(1/2)
We can rewrite the total as:
3 + 3/5 = 15/5 + 3/5 = 18/5
Then the quotient becomes:
(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5
So she can make 7 bowls of cereal (and some leftover milk).
If you want to learn more about quotients:
brainly.com/question/629998
#SPJ1
600+700 and that’s the answer
50,000 because when the number next to the main number is below 5 then you round down...if it is 5 or above then you round up