This question is incomplete, the complete question is;
find the critical points and classify them as local maxima, local minima, saddle points, or none of these.
f(x,y) = (x + y)(xy + 1)
Answer:
(x,y) = (-1, 1), (1, -1) area critical points
f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy²)
at (-1, 1)
f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point
at (1, -1)
f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point
Step-by-step explanation:
Given that;
f(x,y) = (x + y)(xy + 1)
f(x,y) =x²y + xy² + x + y
for critical points fx =0 ,fy =0
fx = 2xy + y² + 1 = 0, fy = x² + 2xy + 1 = 0
2xy + y² + 1 = 0, x²+ 2xy + 1 = 0
2xy + y² + 1 - x² - 2xy - 1 = 0
x² = y²
=> x = y, x = -y
2xy + y² + 1 = 0, x = y
2yy + y² + 1 = 0
3y² = -1 , no solution
2xy + y² + 1 = 0, x = -y
-2yy + y² + 1 = 0
=> -y2 + 1 = 0
=> y = -1, y = 1
y = -1 => x = 1, y = 1 => x = -1
(x,y) = (-1, 1), (1, -1) area critical points
f(xx) =2y, fyy =2x,f(xy) =2x + 2y, D = f(xx)fyy - f(xy²)
at (-1, 1)
f(xx) = 2 ,fyy =-2,f(xy) = 0, D = -4 < 0 saddle point
at (1, -1)
f(xx) = -2, fyy =2,f(xy) =0, D = -4 < 0 saddle point
4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.
Complete the two-column proof.
PLEASE HURRYY
Answer:
Step-by-step explanation:
Given: ∠T ≅ ∠V; ST || UV
Prove: TU || VW
4 connected lines are shown. A line from point S goes slightly down and to the left to point T to form S T. A line from point T goes slightly down and to the right to point U to form T U. A line from point U goes slightly down and to the left to point V to form U T. A line goes slightly down and to the right to point W to form point W.
Complete the two-column proof.
♣ =
✔ alternate interior angles theorem
♦ =
✔ transitive property
♠ =
✔ converse alternate interior angles theorem
just did the assignment
Answer:
Because if ∠T ≅ ∠V, and ST || UV,
the line will go down degrees to form TU || VW.
Answer:
20/100 or 20%
Step-by-step explanation:
Let's see how many candies are in total.
5 orange + 6 blue + 3 green + 4 red + 7 yellow = 25 in total
So there are 5/25 orange candies.
5/25 x 4 = 20/100 (I multiplied by 4 to get the denominator 100)
If you need it in percent it is 20%.
I hope this is helpful for you!
How much is left?
Answer:
625 ml
Step-by-step explanation:
1 litre is 1000 milliliters
1000 milliliters minus 375 milliliters is 625 milliliters
you have to subtract because you are looking for what is left
Answer:
Step-by-step explanation:
7630 x .023 = 175.49
175.49 + 28 = $203.49
Step-by-step explanation:
Letthe two numbers be x and y
By the question
x +y =87.....equation (I)
x -y =65......equation (II)
Now adding both equations we get
2x =152
x =152/2
Therefore x =76
Putting x =76in equation i
76+y =87
y =87-76
Therefore y =11
The two numbers are 76and 11.
Hope it helps :)
Answer:
11, 76
Step-by-step explanation:
Let the two numbers be x and y.
According to the given conditions:
x + y = 87.....(1)
x - y = 65....(2)
Adding equations (1) & (2)
x + y = 87
x - y = 65
__________
2x = 152
x = 152/2
x = 76
Plug x = 76 in equation (1)
76 + y = 87
y = 87 - 76
y = 11
Thus the two numbers are 11 and 76.
Answer:
x = 115° , y = 140° , z = 40°
Step-by-step explanation:
40° , x and 25° lie on a straight line and sum to 180° , that is
x + 40° + 25° = 180°
x + 65° = 180° ( subtract 65° from both sides )
x = 115°
z and 40° are vertically opposite angles and are congruent , then
z = 40°
y and z lie on a straight line and sum to 180° , that is
y + 40° = 180° ( subtract 40° from both sides )
y = 140°