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guajiro [1.7K]
4 years ago
8

How will the solution of the system y > 2x + 2/3 and y < 2x + 1/3 change if the inequality sign on both inequalities is re

versed to y < 2x + 2/3 and y > 2x + 1/3.

Mathematics
1 answer:
Valentin [98]4 years ago
7 0

Answer:Infinite solution

Step-by-step explanation:

For Inequalities

y>2x+\frac{2}{3}

3y-6x>2

and y

3y-6x<1

The required Inequalities have no solution because they do not share the common region for a common solution

But if signs of both inequalities  is changed then the system has infinite number of solution.

y

3y-6x<2

and y>2x+\frac{1}{3}

3y-6x>1

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World poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year. Assume tha
dezoksy [38]

Answer:

A) P(t)=77.2\cdot e^{0.016t}

B) 89.157 million tons.

C) In year 2017.

Step-by-step explanation:

We have been given that world poultry production was 77.2 million tons in the year 2004 and increasing at a continuous rate of 1.6% per year.

A). We know that a continuous growth function is in form y=a\cdot e^{kx}, where,

a = Initial value,

k = Growth rate in decimal form.

1.6\%=\frac{1.6}{100}=0.016

Upon substituting our given values, we will get:

P(t)=77.2\cdot e^{0.016t}

Therefore, our required function would be P(t)=77.2\cdot e^{0.016t}, where, P represents world poultry production, in million tons, as a function of the number of years, t, since 2004.

B) To find the world poultry production in the year 2013, we will substitute t=2013-2004=9 in above formula as:

P(9)=77.2\cdot e^{0.016(9)}

P(9)=77.2\cdot e^{0.144}

P(9)=77.2\cdot 1.1548841085249135

P(9)=89.1570531781\approx 89.157

Therefore, the world poultry production in the year 2013 would be 89.157 million tons.

C) To find the number of years it will take for world poultry production to be over 95 million tons, we will equate our function with 95 as:

95=77.2\cdot e^{0.016t}

Divide both sides by 77.2:

1.2305699481865285=e^{0.016t}

Take natural log of both sides:

\text{ln}(1.2305699481865285)=\text{ln}(e^{0.016t})

\text{ln}(1.2305699481865285)=0.016t\text{ln}(e)

0.20747743456981035=0.016t*1

Divide both sides by 0.016:

t=12.9673396606

t\approx 13

Therefore, 13 years after in 2017 world poultry production goes over 95 million tons.

4 0
3 years ago
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3 years ago
The sum of three numbers is 12 . The sum of twice the first​ number, 3 times the second​ number, and 4 times the third number is
Harlamova29_29 [7]

Given:

The sum of three numbers is 12 .

The sum of twice the first​ number, 3 times the second​ number, and 4 times the third number is 37 .

The difference between 7 times the first number and the second number is 25.

To find:

The three number.

Solution:

Let the three numbers are x, y and z respectively.

According to the question,

x+y+z=12           ...(i)

2x+3y+4z=37         ...(ii)

7x-y=25           ...(iii)

From (iii), we get

-y=25-7x

y=-25+7x

Put y=-25+7x value in (i).

x+(-25+7x)+z=12

8x-25+z=12

8x+z=12+25

8x+z=37        ...(iv)

Put y=-25+7x value in (ii).

2x+3(-25+7x)+4z=37

2x-75+21x+4z=37

23x+4z=37+75

23x+4z=112          ...(v)

Now, Multiply equation (iv) by 4 and subtract the result from (v).

23x+4z-4(8x+z)=112-4(37)

23x+4z-32x-4z=112-148

-9x=-36

x=4

Put x=4 in (iv).

8(4)+z=37

32+z=37

z=37-32

z=5

Put x=4 in y=-25+7x.

y=-25+7(4)

y=-25+28

y=3

Therefore, the three numbers are 4, 3 and 5 respectively.

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3 years ago
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There are 11 skateboards and 9 bikes.

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3 years ago
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