Answer:
There is no point of the form (-1, y) on the curve where the tangent is horizontal
Step-by-step explanation:
Notice that when x = - 1. then dy/dx becomes:
dy/dx= (y+2) / (2y+1)
therefore, to request that the tangent is horizontal we ask for the y values that make dy/dx equal to ZERO:
0 = ( y + 2) / (2 y + 1)
And we obtain y = -2 as the answer.
But if we try the point (-1, -2) in the original equation, we find that it DOESN'T belong to the curve because it doesn't satisfy the equation as shown below:
(-1)^2 + (-2)^2 - (-1)*(-2) - 5 = 1 + 4 + 2 - 5 = 2 (instead of zero)
Then, we conclude that there is no horizontal tangent to the curve for x = -1.
Answer:
I have no clue j need more free answer
Step-by-step explanation:
3x+2y+z=16 4x-y=-5 y+x=11
37 1/2 +10 1/2 = 48 inches
48 inches is your answer ;)
9514 1404 393
Answer:
![\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%26-2%5C%5C0%26-3%265%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The rotation matrix for 90° CCW is ...
![\left[\begin{array}{cc}0&-1\\1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%26-1%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D)
Then the rotated coordinates are ...
![\left[\begin{array}{ccc}0&-1\\1&0\end{array}\right]\cdot\left[\begin{array}{ccc}0&-3&5\\0&1&2\end{array}\right]=\left[\begin{array}{ccc}0&-1&-2\\0&-3&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%5C%5C1%260%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-3%265%5C%5C0%261%262%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%26-2%5C%5C0%26-3%265%5Cend%7Barray%7D%5Cright%5D)
_____
The transformation of each ordered pair is ...
(x, y) ⇒ (-y, x)
450
10*12= 120 the bottom of the box
10*7.5= 75 one side
75*2= 150 two sides
12*7.5= 90 another side
90*2= 180 two other sides
120+150+180 = 450
Hope this helped :)
