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dimaraw [331]
3 years ago
7

What is the value of

smiddle" class="latex-formula"> of the geometric series?
A.-\frac{12}{9}
B.-\frac{1}{9}
C.1
D.12

Mathematics
1 answer:
julia-pushkina [17]3 years ago
8 0
The correct awnser is a or c i hope i helped
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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
In engineering, equilateral triangles can support the most weight and so are commonly found in the design of bridges and buildin
Dafna1 [17]

Answer:

60°

Step-by-step explanation:

Am equilateral triangle is a triangle that has all its sides and angles equal. Note that an equilateral triangle has 3 sides and angles.

Let the angles be a, b and c

The sum of angle in a triangle is 180°, hence;

a+b+c = 180°

Since a = b = c

The equation becomes;

a+a+a = 180°

3a = 180

a = 180/3

a = 60°

Hence the measure of the angles of an equilateral triangle is 60° for the three angles.

4 0
3 years ago
Assume: c = 40 + 0.8(y - t) g = 10 i = 20 t = 0, where t are taxes. (a) calculate y at equilibrium. (b) calculate c, i, and g at
Sonja [21]

(a). To calculate Y at equilibrium

Y = C + I + G

Y = 40 + 0.8(Y – 0 + 10 + 20)

Y = 350

 

(b). To calculate C, I and G at Equilibrium

C = 40 + 0.8 Y

Since Y = 350

C = 40 + 0.8(350)

C = 40 + 280

C = 320

I = 20

G = 10

 

(c).To find equilibrium Y

Given,

EX = 4 + 3EP/P

IM = 8 + 0.1 (Y - T) - 2EP/P

E = 3

P = 1

P = 1.5

Y = 170

3 0
3 years ago
A state university locks in costs for a student once a student starts attending the university. The total cost is $23,500. A stu
Anestetic [448]

Answer:

720

Step-by-step explanation:

24500 (total) subtracted by (10,700 + 5000 + 1600) =7200. 7200 divide by 10 mo=720

7 0
3 years ago
Which statement describes the first step to solve the equation by completing the square?
Readme [11.4K]

Answer:

It's Multiply both sides of the equation by 1/2, I literally just took the quiz.  

6 0
3 years ago
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