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3 years ago

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Which linear equation contains the points

1 answer:

wariber [46]3 years ago

7 0

The answer is D

Because I worked it out

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Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B3%7Db%5E%7B5%7D%7D%7Ba%5E%7B4%7Db%7D" id="TexFormula1" title="\frac{a^{3}b^{5

aliina [53]

Answer:

b^4 / a

Step-by-step explanation:

I have attached the explanation above. hopefully this will help

3 0

3 years ago

Jack is 13 years younger than his older brother, Tyler. Their Dad is twice Tyler's age. The sum of their ages now is 91. Find Ja

grin007 [14]

Answer:

13 years old

Step-by-step explanation:

So to solve this we use a system of equations. Let's use "j" to represent Jack, "t" to represent Tyler, and "d" to represent the dad. Set the system up and it will look something like this:

j = t - 13 (Jack is 13 years younger than Tyler)

d = 2t (Dad is twice Tyler's age)

d + j + t = 91 (The sum of the ages is 91)

And then solve, I solved by isolating the "j" variable on the last equation, giving us j = 91 - t - d, then plugged that into the first equation, giving us 91 - t - d = t - 13, and got d = 104 - 2t. Then I plug that into d = 2t, giving us 104 - 2t = 2t, and solve for t. T is 26, meaning Tyler is 26 years old, and then I just subtract 13 from that, giving us 13 years old.

And finally, I obviously checked my answer, because now we know dad is 52, and I got 91.

5 0

3 years ago

Answer asap plz and thank you a head of time question in pic

ahrayia [7]

I think the answer is B.

3 0

3 years ago

Read 2 more answers

There are 10 friends who are trying to play and beat the video game, Breath of the Wild. There are 76 side quests in this game.

victus00 [196]

Answer:

2; 28.5 ; 34 ; 36 ; 38

Step-by-step explanation:

Given the data:

X = 25, 28, 29, 30, 34, 35, 35, 37, 38

n = 9

Values have been arranged in ascending order ;

The 5 number summary :

Maximum value : highest data value in the list = 38

Minimum value : Lowest data value in the list = 25

The lower quartile ; Q1 = 1/4(n+1)th term

Q1 = 1/4(10) th term = 2.5th term

Q1 = (2nd + 3rd) / 2 = (28+29)/2 = 28.5

Q2 = 1/2(n+1)th term

Q2 = 1/2(10) th term = 5th term

Q2 = 34

Q3 = 3/4(n+1)th term

Q3 = 3/4(10) th term = 7.5th term

Q3 = (7th + 8th) / 2 = (35+37)/2 = 36

Maximum value = 38 (highest data value in the list)

5 0

3 years ago