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3 years ago

9

8. Factor Bab + 12ay - 14b - 21y

1 answer:

Natalka [10]3 years ago

8 0

The answer is a, you factor by regrouping in pairs and undistributing the greatest common factor of each of the 4 pairs you regroup

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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

7. Sarah bought a lawnmower for $320. She signed up for the buy now pay later plan at the store with the following conditions: $

erastova [34]

Amount financed
320−100=220

Total paid
100+25×12=400

Interest paid
400−320=80

Interest rate=(2yc)÷(m (n+1))
I=(2×12×80)÷(220 (12+1))
I=(2×12×80)÷(220×13)
I=0.67×100
I=67%

4 0

3 years ago

Read 2 more answers

The width of a rectangle is 4 less than half the length. If L represents the length, what equation can be use to find the width,

strojnjashka [21]

Answer:

W = 1/2L - 4

Step-by-step explanation:

The width is 4 less than 1/2 of the length.

w = 1/2L - 4

6 0

3 years ago

PLZ HELP ASAP!!!!<br><br> Solve for X:<br> 2X^3 = 54

mariarad [96]

X=3

Divide both sides of the equation by 2
X^3 =27

Write the number in exponential form with an exponent of 3
X^3=3^3

Since the exponents are the same, set the bases equal
X=3

6 0

3 years ago

A weather station on the top of a mountain reports that the temperature is currently 0 and has been falling at a constant rate o

dlinn [17]

Answer:

Because I SAVAGE

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6 0

2 years ago