1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kodGreya [7K]
2 years ago
12

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)
Mathematics
1 answer:
Andru [333]2 years ago
6 0

Answer:

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

Step-by-step explanation:

To consider the autonomous system

x' =x (12 -x - \dfrac{1}{2})

y' = y( 20 -y - x)

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

i.e.

x' =x (12 -x - \dfrac{y}{2}) = 0

\dfrac{x}{2} (24 -2x - y) = 0

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

Also

y' = y( 20-y-x) = 0

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)

You might be interested in
4x+y=17
faltersainse [42]

Answer:

x=4

y=1

Step-by-step explanation:

4x=7y+9

4x+y=17

7y+9+y=17

8y=17-9

8y=8

y=1

so

4x=7*1+9

4x=16

x=16/4

x=4

4 0
2 years ago
Which sentence is an example of the distributive property
Marrrta [24]

The distributive property of multiplication is a very useful property that lets you simplify expressions in which you are multiplying a number by a sum or difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of the products – in this case, 6(5) – 6(2).

 

Remember that there are several ways to write multiplication. 3 x 6 = 3(6) = 3 • 6.

3 • (2 + 4) = 3 • 6 = 18.

 

Distributive Property of Multiplication over Addition

 

<span>The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2.</span>

 

3(10 + 2) = ?

 

According to this property, you can add the numbers and then multiply by 3.

<span>3(10 + 2) = 3(12) = 36. Or, you can first multiply each addend by the 3. (This is called distributing the 3.) Then, you can add the products.</span>

The multiplication of 3(10) and 3(2) will each be done before you add.

3(10) + 3(2) = 30 + 6 = 36. Note that the answer is the same as before.

 

You probably use this property without knowing that you are using it. When a group (let’s say 5 of you) order food, and order the same thing (let’s say you each order a hamburger for $3 each and a coke for $1 each), you can compute the bill (without tax) in two ways. You can figure out how much each of you needs to pay and multiply the sum times the number of you. So, you each pay (3 + 1) and then multiply times 5. That’s 5(3 + 1) = 5(4) = 20. Or, you can figure out how much the 5 hamburgers will cost and the 5 cokes and then find the total. That’s 5(3) + 5(1) = 15 + 5 = 20. Either way, the answer is the same, $20.

 

The two methods are represented by the equations below. On the left side, we add 10 and 2, and then multiply by 3. The expression is rewritten using the distributive property on the right side, where we distribute the 3, then multiply each by 3 and add the results. Notice that the result is the same in each case.

 

7 0
3 years ago
Read 2 more answers
Please helps thank you
LUCKY_DIMON [66]
The best answer would be C.

Hope this helps:)
3 0
3 years ago
The ramp for a moving truck is 8 feet long If the bed of the truck is 5 feet off of the ground , how from the back of the truck
Elodia [21]
It would be about 3 feet
6 0
3 years ago
Please help me with this geometry question? Picture is there
Harlamova29_29 [7]
It is a Kite because right now we are learning about that
3 0
3 years ago
Other questions:
  • Three consecutive whole numbers are such that if they be divided by 5,3 and 4 respectively, the sum of the quotient is 40. What
    9·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Cint%5Climits%5E4_3%7Bx%5E%7B2%7D-x%20%7D%20%5C%2C%20dx" id="TexFormula1" title="\int\limits
    15·1 answer
  • A 20 foot ladder is leaning against a tree. The bottom of the ladder is 12 feet away from the bottom of the tree. Approximately
    7·1 answer
  • (04.05 MC)
    14·1 answer
  • F(x) = x2+3x+2 x2+5x+4 Why is there no zero at x = –1?
    7·1 answer
  • Which Of The Following Is A Geometric Sequence?
    12·1 answer
  • I'm really confused I'm not that good in math
    6·1 answer
  • Line m passes through points P(–1, 5) and Q(2, 3) on an xy-coordinate plane. Write an equation for the line that is perpendicula
    14·1 answer
  • Question 8 of 10<br> Simplify (7 + 1)2 – (11 + 32) - 4.
    5·1 answer
  • Two angels are called complementary when their measures add to 90. Two angels are called supplementary when their measures add u
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!