Find an autonomous differential equation with all of the following properties:
equilibrium solutions at y=0 and y=3,
y' > 0 for 0 y' < 0 for -inf < y < 0 and 3 < y < inf
dy/dx =

Answers

Answer 1

Answer:

dy/dt = y ( 3 - y )

Step-by-step explanation:

Given data:

Determine an autonomous differential equation with the following properties

y = 0 and Y = 3

y' > 0 for  0 < y < 3

y' < 0 for  -∞ < y < 0  and  3 < y < ∞

considering an autonomous differential equation

dy/dt = y ( 3 - y )

y = 0 and 3 represents equilibrium solutions

if 0 < y < 3  then y ( 3 - y ) > 0  for   0 < y < 3

hence : dy / dt = y' > 0  for 0 < y < 3

y ( 3 - y ) <  0  for -∞ < y < 0 and  3 < y < ∞

hence : dy / dt = y' < 0  for  -∞ < y < 0  and  3 < y < ∞

this shows that the autonomous differential equation satisfies every condition hence the autonomous differential equation is :

dy/dt = y ( 3 - y )


Related Questions

There are 12 more apples than oranges in the basket of 36 apples and oranges. How
many apples are there in the basket?​

Answers

Step-by-step explanation:

Required Answer:-Total number of fruits=36

Let

the number of oranges =x

The number of apples=x+12

ATQ

[tex]{:}\leadsto [/tex][tex]\sf x+x+12=36 [/tex]

[tex]{:}\leadsto [/tex][tex]\sf 2x+12=36 [/tex]

[tex]{:}\leadsto [/tex][tex]\sf 2x=36-12 [/tex]

[tex]{:}\leadsto [/tex][tex]\sf 2x=24 [/tex]

[tex]{:}\leadsto [/tex][tex]\sf x={\dfrac {24}{2}}[/tex]

[tex]{:}\leadsto [/tex][tex]\sf x=12 [/tex]

Number of Apples =12+12=24

Answer:

24 apples

Step-by-step explanation:

apples = x

oranges = y

y+12 = x

x+y = 36

y+y+12 = 36

2y = 24

y = 12

x = 24

PLS GIVE BRAINLIEST

Consider these three squares with known area 25, 144,169

Answers

Answer:

Step-by-step explanation:

three squares with known area 25, 144,169...

1) area of the square =25

Side ×side=25

Side^2=25

Side=√25

Side =5.

Answer is 5.

2) area of the square =144

Side ×side=144

Side^2=144

Side=√144

Side =12

Answer is 12.

3)area of the square =169

Side ×side=169

Side^2=169

Side=√169

Side =13

Answer is 13.

There are 240 students going on a field trip each school bus can hold 48 students complete the equation to show which operation to use and how many school buses are needed then complete the sentence to explain your reasoning

Answers

if you calculate 240/48, you will get 5 without any remainder, which means if you get 5 buses it can exactly take all students?

which statement about 3/4 multiplied by 16/5 is true?

A. The product is greater than 5
B. The product is less than 3/4
C. The product is between 3/4 and 16/5
D. The product is between 16/5 and 5

Answers

Answer:

Option c

Step-by-step explanation:

3/4 multiplied by 16/5

3/4×16/5

12/5

Option c is correct

The product between 3/4 and 16/5

Write the equation of the green line.

Answers

Y=-1/2x+2 is the correct answer in slope intercept form:)

Answer:

y = -1/2x + 2

Step-by-step explanation:

Let the equation of the green line be y = mx + c

From the graph, (-6, 5) and (0, 2) are 2 points on the green line.

m = (2-5)/(0-(-6)) = -1/2 (using gradient/slope formula)

sub (0, 2) and m = -1/2:

2 = -1/2(0) + c

2 = c

therefore,

equation of the line: y = -1/2x + 2

Every 125 pages that Raul reads during his summer reading challenge, he will collect 5 book points to use at his local library. Which graph models a relationship with the same unit rate?

Answers

Answer:

The answer is "[tex]\frac{1}{25}[/tex]"

Step-by-step explanation:

They might claim that perhaps the ratio to Raul would've been:[tex]\frac{y}{x} = \frac{5}{125} = \frac{1}{25}[/tex] per each 125(x) page, which he reviewed throughout a summer competition.

Raul's cost per unit for each paragraph reads is [tex]\frac{1}{25}[/tex] page points, that's why the model a link with the same unit rate. please find the graph in the attached file.

To estimate a proportion of students with a grade point average of 3.7 and higher in a college, a random sample of 200 students was taken and the number of successes counted to be 35. The 95% confidence interval for a population proportion is:

Answers

Answer: [tex](0.1481323,\ 0.2018677)[/tex]

Step-by-step explanation:

The confidence interval for population proportion :

[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex] , where n= sample size, [tex]\hat{p}[/tex] = sample proportion , z*= Critical  z-value.

Let p = population proportion of successes.

Given: n= 200 , [tex]\hat{p}=\dfrac{35}{200}=0.175[/tex]

Critical z value for 95% confidence = 1.96

The 95% confidence interval for a population proportion is:

[tex]0.175\pm (1.96)\sqrt{\dfrac{(0.175)(1-0.175)}{200}}\\\\=\ 0.175\pm (1.96)\sqrt{0.000721875}\\\\= 0.175\pm (1.96)(0.0268677)\\\\=(0.175-0.0268677,0.175+0.0268677)\\\\= (0.1481323,\ 0.2018677)[/tex]

Required confidence interval: [tex](0.1481323,\ 0.2018677)[/tex]

What is the solution to x^6 – 6x ^5 + 15x ^4 – 20x ^3 + 15x^ 2 – 6x + 1 ≥ 0? x = 0 x = 1 all real numbers all real numbers except zero

Answers

Answer:

Answer: C all real numbers

Answer: All real numbers

Step-by-step explanation: Edge 2022

AACB = ADCE
ZA = 3x-10, ZC = 45°, ZD = 2x+10

Answers

Step-by-step explanation:

< A = < D

3x_10 = 2X+10

X=20

a rectanguluar parking lot has a length that is 5 yards greater than the width the area of the parking lot is 300 square yards find the length and the width use formula area =length * width the -parking lot width is of yards is? the length is?

Answers

Answer:

Required Answer:-Area=300yards^2

Let

Breadth =x

length=x+5

As we know that in a rectangle

[tex]{\boxed{\sf Area=lb}}[/tex]

Substitute the values

[tex]{:}\longrightarrow[/tex][tex]\sf x (x+5)=300[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x^2+5x=300 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x^2+5x-300=0 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x^2+20x-15x-300=0 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x (x+20)-15 (x+20)=0 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf (x+20)(x-15)=0 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x+20=0\:or\:x-15=0 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf x=-20 (Impossible)\:or \;x=15 [/tex]

Width=15yardsLength=15+5=20yards

5. Juliet has swimming lessons every 5th day and dance lessons every 3rd day. If she
had a swimming lesson and a dance lesson on October 1, when will be the next
date on which she has both swimming and dance lessons?
A. October 5
B. October 10 C. October 15 D. October 18

Answers

Hope this helps!

C. October 15

2. Joanne's car insurance is reduced by 10% for each year that she has not had an
accident.
The normal cost of her insurance is £420 but she has a 3-years' no claims bonus.
How much is her insurance?​

Answers

Answer:

220

Step-by-step explanation:

During the summer months, the prices of nonsmoking rooms with a king-sized bed in hotels in a certain area are roughly Normally distributed with a mean of $131.80 and a standard deviation of $29.12. A travel agent randomly selects prices of nonsmoking rooms with a king-sized bed from 15 hotels in the area. What is the probability that their average cost will be more than $150?
a) 0.0077
b) 0.3678
c) 0.2660
d) 0.1125

Answers

C

If you have a graphing calculator, go to 2nd vars, normalcdf(.

Put 150 for the lower bound and 99999999 for the upper bound. You want to know the probability of all the values over 150. Put 131.8 for the mean and 29.12 for the standard deviation. Click paste.

Your answer will be .266

Evaluate the expression 9x for x= 2.
9x = when x = 2.
(Simplify your answer.)

Answers

Plug in 2 for x so 9x when x=2 is 9(2) nine times two is
18

Cuánto le falta a 3/5para llegar a 9/10

Answers

Answer:

3/10

Step-by-step explanation:

3/5 se puede convertir en 6/10

(3x2)/(5x2).

9/10 - 6/10 = 3/10

le falta 3/10 para llegar a 9/10.

you invest $4500 into an interest earning account that compounds daily at 5%.How much will you have in 6 years.How much interest will you earn​

Answers

Answer:

4500*1.05^(365*6) = 1.1422929e+50

8x + 13x

PLEAsE HLEP ME SLOVE THIS PLEASE SHOW WORK TO? THANK YOU

Answers

Answer & Step-by-step explanation:

Since they are like terms (meaning they are in the same form), you can add:

[tex]8x+13x=21x[/tex]

:Done

I need the answer
I don't need you to make it a whole paragraph

Answers

Answer:

3

Step-by-step explanation:

Answer:

3 cups

Step-by-step explanation:

!!!!!!!!!!!!!!!plz help asap. 50 POINTS!!!!

Answers

Answer:

its c. 1,155.00

Step-by-step explanation:

The answer is B i believe

The two boxes shown are cuboids.
20 cm
4 cm
30 cm
3 cm
50 cm
10 cm
Work out how many of the smaller boxes you would need
to completely fill the larger one.

Answers

Answer:

250.

The area of the larger box is 30,000 cm squared. Once you find the total area of the small box, divide that by the area of the larger box and you have your answer.

Answer:

205

Step-by-step explanation:

How many ?!!!!
?!!!
?!!

Answers

15

hope this helps you alot☺✌❤

A recipe calls for 1 1/2
teaspoons of cinnamon to make 2 oatmeal cookies.

How many teaspoons
of cinnamon are needed to make 60 oatmeal cookies?

Answers

Answer:

45

Step-by-step explanation:

How do I solve problems like

5 + 2y = 1

Answers

Answer:

y=-2

Step-by-step explanation:

its like in the paper sorry it if crops out

A. 0.75s+0.4t=980

B. 0.75s-0.4t=980

C. 0.75s+0.04t=980

D. 0.75s-0.04t=980

Answers

c is the correct answer

Simplify
92
97

1. 95
2.1/99
3.1/9-5
4. 1/95

Answers

Answer:

D : 1/9^5

Step-by-step explanation:

you would first start off by subtracting the powers ( 7-2 ), which gives us 5. That then gives you 9^5, however, 9^5 gives you 59049, and the original problem's answer was 1/59049. When you divide 1 by 9^5, you get 1/59049, which is the same as the original answer.

6. In his car, John can drive 75 miles on 5 gallons of gas. He drove
825 miles to visit his sister, how many gallons of gas did he use?

Answers

Answer: 55 Miles

Step-by-step explanation:

75x11=825

11x5=55

PLZ HELP I BEG U!!!!!! ILL MARK U BRAINLIEST
Create a story using the inequality symbols , ≤,≥,≠ . the story must be creative, detailed, coherent, and written clearly. it does not have to be solely math related.

Answers

Answer:

T_T said to 个_个: Hallo, I am so happee!!!

Step-by-step explanation:

Plz mark as Brainliest!

There are 31 guests at your home for a dinner party. In how many ways could the guests arrange themselves on a four person couch?

Answers

Answer:

7.75

Step-by-step explanation:

The total number of ways could the guests be arranged on a four person couch is 31465.

What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.

Given is that there are 31 guests at your home for a dinner party.

The total number of ways could the guests be arranged on a four person couch is -

C{31, 4} = 31!/{(31 - 4)!4!}

C{31, 4} = (31 x 30 x 29 x 28 x 27!/27! x 4!) = (31 x 30 x 29 x 28)/24 = 31465

C{31, 4} = 31465

Therefore, the total number of ways could the guests be arranged on a four person couch is 31465.

To solve more questions on equations, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ5

PLS HELP ME I CANT DO IT AND JMBEING TIMED

Answers

Answer:

For A+B

a. 0.3+0.8 = 1.1

b. 1.2+1.4 = 2.6

c. 3.4 + 4.2 = 7.6

d. 2.25 + 2.95 = 5.20

For B-A

a. 0.8-0.3 = 0.5

b. 1.4-1.2 = 0.2

c. 4.2-3.4 = 1.2

d. 2.95-2.25 = .070

hvfygcicgdigcigcicticigcdbgvbug​

Answers

Answer:

This is a hw site pls dont post this, if you dont need help. I dont want your account to be deleted. :) Hope u have a great day tho, but in the future dont post this.

Step-by-step explanation:

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