Find all critical points of the given plane autonomous system. (Enter your answers as a comma-separated list.) x′ = x 12 − x − 1 2 y y′ = y(20 − y − x)

Answers

Answer 1

Answer:

the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

Step-by-step explanation:

To consider the autonomous system

[tex]x' =x (12 -x - \dfrac{1}{2})[/tex]

[tex]y' = y( 20 -y - x)[/tex]

The critical points of the above system can be derived by replacing x' = o and y' = 0.

i.e.

[tex]x' =x (12 -x - \dfrac{y}{2}) = 0[/tex]

[tex]\dfrac{x}{2} (24 -2x - y) = 0[/tex]

x = 0 or 24 - 2x - y = 0     ----- (1)

Also

[tex]y' = y( 20-y-x) = 0[/tex]

y( 20 -y - x) = 0

y = 0 or 20 - y - x = 0  -----   (2)

By solving (1) and (2);

we get x = 4 and y = 16

Suppose x = 0 from (2)

y = 20

Also;

if y = 0 from (1)

x = 12

Thus, the critical points are (0,0) , (0, 20), (12, 0) , (4,16)


Related Questions

Explain how exercise can benefit your mental and social health

Answers

Answer:

exercising is good

Step-by-step explanation:

exercising releases hormones in your body that can make you happier, it also keeps your mind in tip top shape. Also even just being outside of a building would also release hormones in your brain that causes you to lighten your mood!

Answer: Exercise can help with mental health because when your angry sometimes working out can help get rid of anger and if your sad it can help get more motivated and positive about some stuff. It also helps with discipline and respect which can help with your social skills by talking respectfully to others.

Name the type of transformation.

Answers

Answer: reflection
hope that helps!

Fine the vertex, the axis of symmetry and the y intercept of the graph

Answers

Answer:

vertex: (-3,2) because the vertex would be the center point of the parabola

axis of symmetry: x=-3, the axis of symmetry is the the center/split in the parabola.

y-intercept: y= -1, because this is the point where the parabola crosses through the y-axis

Consider a system with sampling rate 52,500 samples per second.
(a) Determinethe maximum frequency of the pre-sampled signal if the system utilizes 18% oversampling.
(b) Determine the percentage oversampling if the maximum frequency from part (a) isincreased by 10%.

Answers

Answer:

The answer is "[tex]22,246 \ H_z \ \ and \ \ 7.3\%[/tex]"

Step-by-step explanation:

The sampling rate: [tex](f_s) = 52,500 \ \frac{samples}{sec}[/tex]

In point a:

The sample signal frequency = f  

They recognize that the id [tex]\geq[/tex] 2f sampling frequency could be returned to its original signal unless the aliase effect is detected elsewhere,  Yet under percentage =18%

[tex]\ sampling \ rate = 2 \times 1.18 \times f[/tex]

[tex]\to f = \frac{52,500}{2 \times 1.18}\\\\[/tex]

       [tex]= 22,246 \ h_z[/tex]

In point b:

Maximum 22,242 frequency is increased by [tex]10 \ \%[/tex]

[tex]f_a =22,246 \times 1.1[/tex]

    [tex]= 24,470.6\\\\=24,471[/tex]

[tex]\ sampling \ rate= x \times 2 \times 24,2471 \\[/tex]

                    [tex]x= \frac{52,500}{48,942} \\\\x= 1.073\\\\[/tex]

over sampling percentage [tex]= 7.3 \ \%[/tex]

Can someone please explain this to me?

Answers

the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle.

Suppose a DVD costs $19 and a CD costs $12. Which inequality represents how many CDs (c) you can buy along with one DVD (d) if you have $67 to spend?

A. 12c + 19 ≥ 67

B. 12c + 19 ≤ 67

C. 19c + 12 ≤ 67

D. 12c + 19 > 67

Answers

I think the answer is A hope it helps

find the measures of the sides KPL and classify it by its sides
K(-3,2),P(2,1), L (-2,-3)
find the length of KP round to nearest tenth
find length of PL
Find length of KL​

Answers

Answer:

I am so confused. what do you want me to find

A triangle on a sphere could have
degrees.

Answers

Answer:
True

Explanation:

A store owner offered a 25% discount off the regular price of a pair of shoes. The amount of the discount is $4.
What is the regular price of the shoes?
A $8
B $12
C $20
D $16

Answers

Answer:

D

Step-by-step explanation:

25% of 16 is 1/4x16=4, which leaves D as as your answer

Answer:

d

Step-by-step explanation:

instead of taking away 4 add it until you have 100%

help please i really dont need to fail

Answers

Answer:

C.) 96 sq cm

Step-by-step explanation:

I split the polygon into 2 rectangles and 1 triangle.

To find the area of a rectangle do base*height

To find the area of a right triangle do base*height/2

The full explanation is in the picture below

Hope this helps ya!!!

2. Which expression is equivalent to 3(4x + 10 = 2+3)?

Answers

Answer: ask ggle it gives you the answer

Step-by-step explanation:

Select the correct answer. Which expression is equivalent to ^3 square root of 200k^15, if k ≠ 0

Please help I’m in the middle of a test

Answers

It is B bc it is in the radical form of ^3sqrt root of 200k^15

The equivalent algebraic expression to [tex]\sqrt[3]{200k^{15}}[/tex] is [tex]2~k^5~\sqrt[3]{25}[/tex]

The correct answer is an option (B)

What is algebraic expression?

"It is a mathematical statement which consists of numbers variables and some algebraic operations."

What are exponents?

"It refers to the number of times a number is multiplied by itself."

For given question,

We have been given an algebraic expression [tex]\sqrt[3]{200k^{15}}[/tex]

We need to find an equivalent algebraic expression to given expression.

We know that the properties of exponents,

for positive integers a, b, n

[tex]\sqrt[n]{a}=a^{(\frac{1}{n} )}\\\\\sqrt[n]{ab}=a^{(\frac{1}{n} )}b^{(\frac{1}{n} )}[/tex]

We can write algebraic expression [tex]\sqrt[3]{200k^{15}}[/tex] as,

[tex]\sqrt[3]{200k^{15}}\\\\=\sqrt[3]{25\times 8\times k^{15}}\\\\=(25)^{\frac{1}{3} }\times (8)^{\frac{1}{3} }\times (k^{15})^{\frac{1}{3} }\\\\=\sqrt[3]{25}\times 2\times (k)^{\frac{15}{3} }\\\\ =2\sqrt[3]{25} \times k^5\\\\=2~k^5~\sqrt[3]{25}[/tex]

Therefore, the equivalent algebraic expression to [tex]\sqrt[3]{200k^{15}}[/tex] is [tex]2~k^5~\sqrt[3]{25}[/tex]

The correct answer is an option (B)

Learn more about the algebraic expression here:

https://brainly.com/question/27911936

#SPJ2

Find the coefficient of x^2 y^3 in the expansion of (-4x+y)^5. Give your answer as an integer.

Answers

Coefficients are the numbers in front of the variables therefore The coefficient of x^2 y^3 would be (-4)x and 1(y). Anytime there isn’t a coefficient shown in front of a variable the coefficient will always be 1. I hope this helped :)

The entrance fee to a carnival is $8, and it costs $0.50 for each ride. If Sanjay rides 6 rides, how much will he spend in total?

A. $28 dollars

B. $14dollars

C. $11dollars

D. $10 dollars

Answers

Answer:

$11

Step-by-step explanation:

0.50 × 6 = 3

3 + 8 = 11

Answer - $11

Hope this helps

The answer is $11 dollars

Determine the slope of the line represented by the equation y + 7 = -9/4(x – 4) . Represent the slope in decimal form.

Answers

Answer:

m=-9/4

Step-by-step explanation:

Use the slope-intercept form  y = mx+b to find the slope m

which of the following rations will form a proportion with 2:3

Answers

Answer:

12/18

Step-by-step explanation:

12/18 good luck hopefully it’s correct

Question Help The mean finish time for a yearly amateur auto race was 185.64 minutes with a standard deviation of 0.314 minute. The winning​ car, driven by Sam​, finished in 185.29 minutes. The previous​ year's race had a mean finishing time of 110.3 with a standard deviation of 0.129 minute. The winning car that​ year, driven by Rita​, finished in 110.02 minutes. Find their respective​ z-scores. Who had the more convincing​ victory?

Answers

Answer:

Sam has the more convincing victory with a greater Zscore value

Step-by-step explanation:

Given that :

Year 1:

Mean finish time (m) = 185.64

Standard deviation (s) = 0.314

Sam's time (x1) = 185.29

Year 2:

Mean finish time (m) = 110.3

Standard deviation (s) = 0.129

Rita's time (x1) = 110.02

Zscore = (x - mean) / standard deviation

Sam's Zscore :

(185.29 - 185.64) / 0.314

= - 0.35 / 0.314

= −1.114649

= - 1.115

Rita's Zscore :

(110.02 - 110.3) / 0.129

= - 0.28 / 0.129

= −2.170542

= - 2.171

Sam has the more convincing victory with a greater Zscore value

M = -2 x= 3 y=14 Use y=mx+b ,what is b=

Answers

Answer:

the b is 20

Step-by-step explanation:

The computation of the b is shown below

Given that

y = mx + b

where

m = -2

x = 3

y = 14

Now placing these values to the above formula to determine the value of b

14 = -2(3) + b

14 = -6 + b

b = 14 + 6

= 20

Hence, the b is 20

We simply applied the above formula so that the correct value could come

And, the same is to be considered

(-52 + x – 5) – (–70² – 7x – 3)

Answers

Answer:

7x+4846

Step-by-step explanation:

the answer is 7x+4846

You can buy an 8-pack of soda for $7.92 or a 12-pack for $11.64. Which is the better buy?

Answers

Answer:

I would assume the 8-pack to be the answer because:

Step-by-step explanation:

8 ÷ 7.92 = 1.01

12 ÷ 11.64 = 1.03

1.01 < 1.03

Answer:

I believe the better buy is the twelve pack.

Step-by-step explanation:

If you look, 7.92 is closer to 8, which almost makes it 1 dollar per soda, where the 11.64 is farther from twelve. :) i hope this helps you!

What is the reverse of subtract 16?

Answers

Answer:

If you mean the opposite.

The opposite of subtraction is addition.

So plus 16. (+16)

Answer:

Adding 16

Step-by-step explanation:

Subtract opposite is addition so adding 16 is the reverse

whats the slope of a perpendicular line that passes through the lines (29,24) and (3,4)

Answers

I believe the answer is 1.3
explanation: to find slope you do x’s over y’s so you would have

29-3
———
24-4

which gets you

26
——
20

and simplified its 1.3. Sorry if it is wrong :/.

Hi! free one hundred points for anyone who answers also whoever answers ill give brainiest!

Answers

Answer:

what is your question?

Step-by-step explanation:

Answer:

Central Pacific

Step-by-step explanation:

built a track from Sacroimento eastward

Can someone help me with this?

Answers

It is B because it’s sounds the smartest
The answer to b is 8 feet away from the wall

BRAINLIEST TO HONEST ANSWER
In common app ,do teachers have to write letter of recommendation only once?? and I can submit it to any colleges I want??​

Answers

i would think so but u may need more

pls answer corectly

ignore the teacher in the backruond

Answers

What’s the question?

Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help me

Answers

Answer:

the answers are B,D and E

Step-by-step explanation:

Please help I need this

Answers

B I think if I’m wrong I’m sorry

Answer:

B

Step-by-step explanation:

false

Sophia went out to eat dinner, and the meal cost $40.00. If Sophia received a 35% discount, what was
total value of the discount?
$12.60
$14.00
$15.20
$16.80
Sub

Answers

Answer:

The total value of the discount is $14

Step-by-step explanation:

40 x 0.35 = 14

A light bulb consumes 9900 watt-hours in 5 days and 12 hours. How many watt-hours does it consume per day?

Answers

5 days and 12 hours = 132 hours

9900 total watts / 132 hours = 75 watts per hour

Since the light bulb consumes 75 watts an hour, we need to multiply 75 watts by 24 hours, to figure out how many watts are consumed in a day.

75 watts per hour x 24 hours = 1,800 watt-hours per day
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