Answer:
---- critical point
local minima
Step-by-step explanation:
Given
![f(x,y) = x^2 + y^2 + 2xy](https://tex.z-dn.net/?f=f%28x%2Cy%29%20%3D%20x%5E2%20%2B%20y%5E2%20%2B%202xy)
Required
Determine the critical point
Differentiate w.r.t x
![f_x =2x + 2y](https://tex.z-dn.net/?f=f_x%20%3D2x%20%2B%202y)
Differentiate w.r.t y
![f_y =2y + 2x](https://tex.z-dn.net/?f=f_y%20%3D2y%20%2B%202x)
Equate both to 0
![2x + 2y =0](https://tex.z-dn.net/?f=2x%20%2B%202y%20%3D0)
![2y =0-2x](https://tex.z-dn.net/?f=2y%20%3D0-2x)
![2y =-2x](https://tex.z-dn.net/?f=2y%20%3D-2x)
Divide by 2
----- in both equations
Hence:
The critical point is: ![y =-x](https://tex.z-dn.net/?f=y%20%3D-x)
Solving (b):
We have:
![f_x =2x + 2y](https://tex.z-dn.net/?f=f_x%20%3D2x%20%2B%202y)
![f_y =2y + 2x](https://tex.z-dn.net/?f=f_y%20%3D2y%20%2B%202x)
This is represented as:
![D = \left[\begin{array}{cc}2&2\\2&2\end{array}\right]](https://tex.z-dn.net/?f=D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%262%5C%5C2%262%5Cend%7Barray%7D%5Cright%5D)
Calculate the determinant
![|D| =2 * 2 -2 * 2](https://tex.z-dn.net/?f=%7CD%7C%20%3D2%20%2A%202%20-2%20%2A%202)
![|D| = 4-4](https://tex.z-dn.net/?f=%7CD%7C%20%3D%204-4)
![|D| = 0](https://tex.z-dn.net/?f=%7CD%7C%20%3D%200)
The critical point is at local minima
9,200 contains 92 hundreds.
Explanation:
One hundred can go into 9200 92 times
(9,200 % 100)
Answer:
A
Step-by-step explanation:
Given
3![(1.5)^{t}](https://tex.z-dn.net/?f=%281.5%29%5E%7Bt%7D)
When the culture was created t = 0, thus
3
= 3 × 1 = 3
That is there were initially 3 bacteria in the culture → A
Answer:
23 stsstxtxychuvuvuvcy is the answe
Substitution
x+3=-2+12
X+3=10
X=7