Width: 84/3 = 28
Length: 93/3 = 31
There are 28 blocks along the width
There are 31 blocks along the length
![z=x^2+2y^2+6x-4y+22\\ z_x'=2x+6\\ z_y'=4y-4\\\\ 2x+6=0\\ 4y-4=0\\\\ 2x=-6\\ 4y=4\\\\ x=-3\\ y=1\\\\ ](https://tex.z-dn.net/?f=z%3Dx%5E2%2B2y%5E2%2B6x-4y%2B22%5C%5C%0Az_x%27%3D2x%2B6%5C%5C%0Az_y%27%3D4y-4%5C%5C%5C%5C%0A2x%2B6%3D0%5C%5C%0A4y-4%3D0%5C%5C%5C%5C%0A2x%3D-6%5C%5C%0A4y%3D4%5C%5C%5C%5C%0Ax%3D-3%5C%5C%0Ay%3D1%5C%5C%5C%5C%0A%0A)
We have a stationary point
![(-3,1)](https://tex.z-dn.net/?f=%28-3%2C1%29)
![z_{xx}''=2\\ z_{xy}''=z_{yx}=0\\ z_{yy}''=4](https://tex.z-dn.net/?f=z_%7Bxx%7D%27%27%3D2%5C%5C%0Az_%7Bxy%7D%27%27%3Dz_%7Byx%7D%3D0%5C%5C%0Az_%7Byy%7D%27%27%3D4)
![2\cdot4-0^2=8 \ \textgreater \ 0](https://tex.z-dn.net/?f=2%5Ccdot4-0%5E2%3D8%20%5C%20%5Ctextgreater%20%5C%200)
therefore there exist an extremum at this point.
![z_{xx}''\ \textgreater \ 0](https://tex.z-dn.net/?f=z_%7Bxx%7D%27%27%5C%20%5Ctextgreater%20%5C%200)
therefore the extremum indeed is the minimum.
![z(-3,1)=(-3)^2+2\cdot1^2+6\cdot(-3)-4\cdot1+22=9+2-18-4+22\\ z(-3,1)=11](https://tex.z-dn.net/?f=z%28-3%2C1%29%3D%28-3%29%5E2%2B2%5Ccdot1%5E2%2B6%5Ccdot%28-3%29-4%5Ccdot1%2B22%3D9%2B2-18-4%2B22%5C%5C%0Az%28-3%2C1%29%3D11)
So, the minimum is equal to 11.
Answer- 180 degree rotation.
Basically how I remember it is by 90 degree clockwise is switch x,y and change the sign of the x—> y,-x. 90 degree counterclockwise is switch x,y and change the sign of the y —> -y, x. 180 degree is changing both signs with no switch. 360 stays the same.
Answer:
48
Step-by-step explanation:
$6.00 × 4 = 24
he gives of his total tips to the hostess which is 24 . so 24 + 24 = 48
Answer:
$25
Step-by-step explanation:
.5 * 50 = 25
25<27.5<30
The cheapest supplier is the first one.