The critical points of the system are at (0,0) and (0,r). The point (0,0) is unstable, while the point (0,r) is stable.
The system can be written as:
T' = J - Y
Y' = r - T
To find the critical points, we set T' and Y' equal to zero and solve for T and Y. From T' = J - Y = 0, we have Y = J, and from Y' = r - T = 0, we have T = r. Therefore, the critical point is at (r,J).
To determine the stability of the critical points, we need to find the eigenvalues of the Jacobian matrix evaluated at each critical point. The Jacobian matrix is:
Jacobian = [ -1 1 ; -1 0 ]
At (0,0), the Jacobian matrix evaluated at this point is:
Jacobian(0,0) = [ -1 1 ; -1 0 ]
The eigenvalues of this matrix are λ1 = -0.5 + i√(3)/2 and λ2 = -0.5 - i√(3)/2, which have a negative real part and a non-zero imaginary part. Therefore, this critical point is unstable.
At (0,r), the Jacobian matrix evaluated at this point is:
Jacobian(0,r) = [ -1 1 ; -1 0 ]
The eigenvalues of this matrix are λ1 = -1 and λ2 = 0, which have negative and zero real parts, respectively. Therefore, this critical point is stable.
To plot the phase portrait for the system, we can use the direction field method. We first plot the critical points at (0,0) and (0,r). Then, we draw arrows in the direction of increasing T and Y in each quadrant of the T-Y plane, using the values of T' and Y' evaluated at a few representative points in each quadrant.
The resulting phase portrait shows the trajectories of the system in the T-Y plane, and confirms the stability of the critical points.
For more questions like Matrix click the link below:
https://brainly.com/question/28180105
#SPJ11
Function E is a linear function with an initial value of $2$ , and a rate of change of $\frac{1}{3}$
.
Function F is a linear function. The graph of function F includes the points $\left(2,\ 8\right)$ and $\left(0,\ 2\right)$ .
Which statement is true?
A The two functions have the same initial value.
B The two functions have the same rate of change.
C The initial value in function F is greater than the initial value in function E.
D The rate of change in function E is greater than the rate of change in function F.
Answer:
d
Step-by-step explanation:
The true statement: A The two functions have the same initial value.
What is a linear function?A linear function has a straight line as its graph.
A linear function has the form shown below.
a + bx = y = f (x).
A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.
We know that function E is a linear function with an initial value of 2 and a rate of change of 1/3. Therefore, the equation for function E can be written as:
E(x) = (1/3)x + 2
We also know that function F is a linear function that includes the points (2, 8) and (0, 2).
We can use the two points to find the slope of the line and then use the point-slope form to write the equation for function F.
The slope of F = (8 - 2) / (2 - 0) = 6/2 = 3
Using point-slope form with the point (2, 8), we get:
F(x) - 8 = 3(x - 2)
F(x) = 3x + 2
Now we can compare the two functions.
A. The initial value of function E is 2, while the initial value of function F is 2 + 3(0) = 2. Therefore, statement A is true.
B. The rate of change of function E is 1/3, while the rate of change of function F is 3. Therefore, statement B is false.
C. The initial value of function F is 2, which is the same as the initial value of function E. Therefore, statement C is false.
D. The rate of change of function E is 1/3, which is less than the rate of change of function F, which is 3. Therefore, statement D is false.
Therefore, the only true statement is A. The two functions have the same initial value.
To learn more about the linear function;
brainly.com/question/20286983
#SPJ3
Solve: 3c-c when c=9
Answer:
18
Step-by-step explanation:
give brainlyest???????
Answer:
18
Step-by-step explanation:
3*9-9
3*9=27
27-9=18
Hope this helpsss :)
the area if a rectangle is 7 ¼ with leangth 2⁵/⁷ calculate its breadth
Answer:
Can u explain it one more time their is alot of spelling errors
an internet company charges 20$ a month for service they also charge an initial installation fee if your bill for the first 3 months is 92$ how much was the installation fee? write an equation to solve this problem
Solving Distributive Property Equations,
1. 2(x + 5) = 16 2. 3(t + 1) = 18
3. 3(x + 7) = 15 4. 2(3y – 5) = 14
5. 2(3x + 1) = 8 6. 4(3y – 2) = 88
7. 6(3k + 5) = 39 8. 9(3x – 5) = 9 8. 9(3x – 5) = 9
PLEASE HELP ASAP
What is (-105 + (-35) X(-3 + 5)?
Answer:
-175 I believe
Step-by-step explanation:
Answer:
-280
Step-by-step explanation:
-105+-35= -140
-3+5= 2
-140*2= -280
Hope this helps others
In a factory, eggs are packaged in groups of six per box how many full boxes of eggs can the factory make with 937 eggs
Answer:
156 boxes
Step-by-step explanation:
Simply divide the total amount of eggs (937) by the amounts which are packaged in the boxes (6)
937 / 6 = 156 [tex]\frac{1}{6}[/tex]
So there are 156 full boxes and 1 egg left
Since you can't pack one egg, the answer is 156 boxes
Answer:
156
Step-by-step explanation:
937 ➗ 6 which 156.16667 near to 156
what is the hcm of 18 and 45
Answer:
90
Step-by-step explanation:
90 Or, we can say that it is a method of breaking down the given integer into its prime factors. Therefore, the HCF of 18 and 45 is 9. Therefore, the HCF of 18 and 45 is 90.
What is the answer for x?
-7=3.5+5x
Answer:
x=-2.1
Step-by-step explanation:
Use the Distributive Property to simplify the expression. 8(s−1) =
Answer:
the answer would be 8s -8
Step-by-step explanation:
I learned this a long time ago
Answer:
anong grade Yan tol??g7 g7 g8 g9 g10 g11 g12?
What is the answer I have no clue
Helppppp, I don’t knowwww
Answer:
1 and 4 and 2
Step-by-step explanation:
What is the sum of i° + k°?
Answer
1 + 32 + 243 + 1024 + .. + n5
Step-by-step explanation:
The segment AB has the endpoints A(1,5) and B(3,2). The segment is translated 2 units down and 2 units right. What are the endpoints of the translated segment A'B'?
The endpoints of the translated segment A'B' after undergoing the given translation is; A'(3, 3) and B'(5, 0)
How to carry out translation transformation?In transformation in mathematics, there are different types such as dilation, reflection, rotation, translation e.t.c
Now, in this case what we are dealing with is translation which simply means moving an object or figure from one point to the other without changing the shape or dimensions.
To translate the point AB(x, y) , 2 units down and 2 units right, we will use the translation rule;
A'B'(x + 2, y − 2) .
We are given the coordinates of AB as A(1,5) and B(3,2)
Thus;
A'(1 + 2, 5 - 2) = A'(3, 3)
B'(3 + 2, 2 - 2) = B'(5, 0)
Read more about Translation at; https://brainly.com/question/4289712
#SPJ1
What is the domain of the function represented by this graph?
prove that...
sin A = Cos (90°- A)
Step-by-step explanation:
assuming A=90 degree and B =A
cos90=0 and sin90=1
please help me with this
Answer: D. 3[tex]\sqrt[3]{20}[/tex]
Step-by-step explanation:
Answer:
think A or B
Step-by-step explanation:
i am not sure
What is the missing value in the image above? *
Answer:
8
Step-by-step explanation:
because there is nothing to subtract 8 from
PLS PLS PLS I NEED HELP WITH MATH!!!! GAVE OFF ALL MY POINTS FOR THIS PLEASE GIVE A GOOD ANSWER!!!!!
1. a closed figure made up of line segments
2. any face that is not a base
3. three-dimensional figure with a polygon base and triangles for all other faces
4. three-dimensional figure with two parallel, congruent, polygonal faces and parallelograms for all other faces
5. the perpendicular width of a plane figure
6. a two-dimensional representation of a three-dimensional shape when unfolded
7. a plane figure that is one side of a solid figure
8. a prism with a rectangular base and right angles between the base and sides
9. geometric figure with three dimensions
10. a prism with a triangular base and right angles between the base and sides
hi! im chimken and i have your answers!!!
1. polygon: is a closed figure where the sides are all line segments.
2. lateral face: a side of three-dimensional figure that is not a base.
3. pyramid: a solid figure that has a polygon for a base and triangles for sides. it is named for the shape of its base.
4. polyhedron: formed by two parallel, congruent, polygonal bases connected by lateral faces that are parallelograms.
5. i don't know this one :(
6. a net: a two dimensional representation of a three-dimensional figure that is unfolded along it's edges so that each face of the figure is shown in two dimensions.
7. face: is a plane figure that serves as one side of a solid figure.
8. i don't know this one :(
9. there are 4 possible answers. rectangular prism, sphere, cone, cylinder: 3D geometric shapes with the basic three-dimensional shapes.
10. triangular prism: with a known base and height of its face.
i hope this helped!!!
braise bingus!
properties of a cube
Answer:
Step-by-step explanation:
Analyze the graph and identify some factors that may contribute to the rotifer population leveling off in the absence of water fleas. Explain your answer in 1–2 sentences
25 POINTS!
Answer:
Step-by-step explanation:
Firstly, we should begin to know what leveling off is.
Leveling off- to stay the same after a period of increase
Nearing the end of the graph you can see there is no continuous increase for the rotifers. That can be explained by carrying capacity. The flask has limited space.
There is no continuous increase for the rotifers.
We have given that the scatter diagram
And we have to determine, the graph and identify some factors that may contribute to the rotifer population leveling off in the absence of water fleas
What is the leveling off?Leveling off- to stay the same after a period of increase
Nearing the end of the graph you can see there is no continuous increase for the rotifers.
That can be explained by carrying capacity.
The flask has limited space.
Therefore, there is no continuous increase for the rotifers.
To learn more about the scatter graph visit:
https://brainly.com/question/6592115
what value of x makes the equation 0.75(x+20)=2+0.5(x−2) true?
Answer:
x= -56..................
can you please help me solve this equation using substitution? I’ve been trying to solve it for so long and can’t do it.
2x-y=5 and 3x+y=-9
Answer:
x=-4/5 y= -33/5
Step-by-step explanation:
y=-3x-9
2x+3x+9=5
5x=-4
x=-4/5
Then plug it in into an equation.....2(-4/5)-y=5
-8/5-y=25/5
-y=33/5
y=-33/5
You can check if you want
Answer:
x = -4/5, y = -6 3/5
Step-by-step explanation:
The way to use substitution to solve is to isolate (Put it on one side without anything else on that side of the equation) a variable. We can use the first equation to isolate y. We can add y on both sides to get that 2x = y + 5 and then subtract by 5 on both sides to get that y = 2x - 5. Next, we can substitute 2x - 5 in for y in the second equation because y = 2x - 5. We would get that 3x + 2x - 5 = -9, so 5x - 5 = -9, and if you add by 5 on both sides, you get 5x = -4. Finally, we can divide by 5 on both sides to get that x = -4/5. If you want to find y, we can find it by substituting x into the equation 2x - 5 = y. 2 * -4/5 - 5 is equal to y, so -8/5 - 5 = y, and lastly, y = -6 3/5
What is the center of the circle shown below?
ma
A. SI
B. MN
C. N. D. 2
The requreid, in the given diagram, we can see a circle, and it is indicated that the center of the circle is L.
What is a circle?The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by
(x - h)² + (y - k)² = r²
Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.
Here,
In the given diagram, we can see a circle, and it is indicated that the center of the circle is L. The center of a circle is a point that is equidistant from all points on the circumference of the circle. This means that if we draw a line segment from the center to any point on the circumference of the circle, the length of that line segment will be the same as the length of the line segment from the center to any other point on the circumference.
Thus, the requreid, in the given diagram, we can see a circle, and it is indicated that the center of the circle is L.
Learn more about Circle here:
brainly.com/question/11833983
#SPJ5
I need help I have been waiting for 2 hours
other person alr did #1, and #2 is 0.175
5% of 3 and one half is 0.175 as a decimal
Answer:
$139.24
Step-by-step explanation:
$98+$20=$118
(1.18)($118)=$139.24
the 1.00 in 1.18 is the cost without tax, the 0.18 is the tax, so if you want the cost of the room with tax you would multiply the cost of the room before tax with 1.18
The tax for every room is the same(.18). Tax is taken from the initial cost so you would do 98+20= 118. $118 is the cost of the double room without tax, $139.24 is with tax.
Meena cuts a 287-in. long ribbon into 2 pieces in the ratio 3 : 4. What is the length of the longer piece of ribbon? (ASAP)
Answer:
164 inches
Step-by-step explanation:
First, add 3 and 4
3+4= 7
Then divide 287 by 7
287/7= 41
Then, multiply 4 (from the ratio) by 41
4*41= 164
To get the length of the shorter piece, subtract 164 from 287
287-164= 123
Check your work:
123+164= 287
Hope this helps!
I need help with this question. I need to find the perimeter of the hexagon RSTUVW.
9514 1404 393
Answer:
47.71
Step-by-step explanation:
Two "special" triangles are involved.
ΔSWR is a 30°-60°-90° right triangle, so will have sides in the ratio 1 : √3 : 2.
ΔUVW is a 45°-45°-90° right triangle so will have sides in the ratio 1 : 1 : √2.
For ΔSWR, the side SW is given as 6, so the other sides are ...
WR = 6√3
RS = 2(6) = 12
For ΔUVW, the side WU is given as 8, so the other sides are ...
UV = VW = 8/√2 = 4√2
Then the perimeter of the figure is ...
P = RS +ST +TU +UV +VW +WR
P = 12 +8 +6 +4√2 +4√2 +6√3 ≈ 47.71
8. Complete the following table. 5x-2y = 6
Answer:
x=2/5y+6/5
Step-by-step explanation
5x-2y=6
5x-2y+2y=6+2y
5x=2y+6
step 2
5x/5=2y+6/5
x=2/5y+6/5
ayda porfavor si quieren mas puntos solo contesten bien
es la respuesta del de abajo pero es 62 no 61 ya que marca 61,5 y se aproxima 62 sí o sí xf
You have 5 cells and they double everyday. How many cells will you have after 8 days
Answer:
40
Step-by-step explanation:
5 cells x 8 days = 40 cells
your welcome.
Answer:
[tex]5^{2} (8)[/tex] = 200
Step-by-step explanation:
[tex]5^{2} = 25[/tex] 200In 8 days you will have 200 cells