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3 years ago

8

Find the slope of the line.

1 answer:

siniylev [52]3 years ago

4 0

Good day ^-^///////////

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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

What is the volume of a cylinder with base radius 333 and height 888?

ozzi

Answer:

V≈3.09×108

Step-by-step explanation:

Shape: Cylinder

Solved for volume

Radius: 333

Height: 888

Formula: Radius, Height

Exact answer: V≈3.09×108

<u><em>Hope this helps.</em></u>

4 0

3 years ago

Caitlin says the difference in their ages is 24 years. In two or more complete sentences, explain whether or not Caitlin is corr

Paraphin [41]

~Hello There!~

$\frac{m}{s} =\frac{2}{5}$

Rearrange for s

$s = \frac{5m}{2}$

After 8 years, the new equation would be:

$\frac{m+8}{s+8} =\frac{1}{2}$

Cross multiply

$2m+16 = s+8$

Subtract 8

$2m+8=s$

Substitute old equation

$2m+8 = \frac{5m}{2}$

Solve to get m as 16.

s = 40.

Their current ages are 16 and 40 and the different is 24 years. Therefore, Caitlin is correct.

Hope This Helps You!

Good Luck :)

Have A Great Day ^_^

- Hannah ❤

3 0

3 years ago

Please help i will mark brainiest answer please

DENIUS [597]

Answer:

-2

Step-by-step explanation:

Coefficient is usually the number in front of the variable so, in this case it would be -2.

6 0

3 years ago

is the relationship between the amount of the orange juice concentrate c and the amount of water w proportional? Explain. Zoe us

cluponka [151]

Answer:

B.12 ounces

Step-by-step explanation:

step 1

Find out the ounces of orange juice concentrate used yesterday

Let

x ----> ounces of orange juice concentrate used yesterday

y ---> ounces of water used yesterday

we know

that

----> equation A

----> equation B

substitute equation B in equation A

solve for x

step 2

today she wants to make twice as much orange juice.

To find out how much orange juice concentrate she needs, multiply the ounces of orange juice concentrate used yesterday by 2

so

3 0

3 years ago

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