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3 years ago

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Consider the line through (-1, -4) and (1, 2). What is the slope (m) of the line?

1 answer:

zloy xaker [14]3 years ago

5 0

Answer:

<u><em>3</em></u>

Explanation:

$\bold{\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}}$

$\bold{\left(x_1,\:y_1\right)=\left(-1,\:-4\right),\:\left(x_2,\:y_2\right)=\left(1,\:2\right)}$

$\bold{m=\frac{2-\left(-4\right)}{1-\left(-1\right)}}$

Refine

<u><em>m = 3</em></u>

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In 2012, the world population was 7.02 billion. The birth rate had stabilized to 134 million per year and is projected to remain

xeze [42]

Answer:

$(a)\ \frac{dP}{dt} = 0.078- 0.000857t$

$(b)\ P = 0.078t- 0.0004285t^2 + 7.02$

$(c)\ 9.37\ billion$

Step-by-step explanation:

Given

In 2012

$P(t) = 7.02\ billion$

$R_1 = 134\ million/year$ --- Birth rate

$R_2 = 56\ to\ 80$ -- Death rate from '12 to '40

Solving (a): Equation for population from 2012

In 2012, we have the addition in population to be:

$\triangle P= Birth - Death$

$\triangle P= 134 - 56$

$\triangle P = 78$ million

From 2012 to 2040, we have the death rate per year to be:

$Rate/yr = \frac{80 - 56}{2040 - 2012}$

$Rate/yr = \frac{24}{28}$

$Rate/yr = \frac{6}{7}$ million/year

So, the differential equation is:

$\frac{dP}{dt} = \triangle P - Rate/yr * t$ where t represents time

$\frac{dP}{dt} = 78 - \frac{6}{7} * t$

$\frac{dP}{dt} = 78 - \frac{6t}{7}$

Express in millions

$\frac{dP}{dt} = \frac{78}{1000} - \frac{6t}{7000}$

$\frac{dP}{dt} = 0.078- 0.000857t$

Solving (b): The solution to the equation in (a)

$\frac{dP}{dt} = 0.078- 0.000857t$

Make dP the subject

$dP = (0.078- 0.000857t)dt$

Integrate both sides

$\int dP = \int (0.078- 0.000857t)dt$

$P = \int (0.078- 0.000857t)dt$

This gives:

$P = 0.078t- \frac{0.000857t^2}{2} + c$

$P = 0.078t- 0.0004285t^2 + c$

Solve for c.

When t = 0; P = 7.02

So, we have:

$7.02 = 0.078*0- 0.0004285*0^2 + c$

$7.02 =0-0 + c$

$7.02 =c$

$c = 7.02$

So:

$P = 0.078t- 0.0004285t^2 + c$

$P = 0.078t- 0.0004285t^2 + 7.02$

Solving (c): The population in 2050

We have:

$P = 0.078t- 0.0004285t^2 + 7.02$

In 2050, the value of t is:

$t = 2050 - 2012$

$t = 38$

So, the expression becomes

$P = 0.078*38- 0.0004285*38^2 + 7.02$

$P \approx 9.37\ billion$

3 0

3 years ago

What are the first four terms if the sequence represented by the expression n (n-1) -4?

shepuryov [24]

We have that
<span>n (n-1) -4

for n=1
a1=1*(1-1)-4------> a1=-4

for n=2
</span>a2=2*(2-1)-4------> a2=-2

for n=3
a3=3*(3-1)-4------> a3=2

for n=4
a4=4*(4-1)-4------> a4=8

the answer is
-4,-2, 2, 8

5 0

4 years ago

Line segment EF is shown on the coordinate grid:

Masja [62]

Answer:

im guessing C

Step-by-step explanation:

I dont have this exam let me know is I'm right

6 0

2 years ago

Read 2 more answers

pogonyaev

Answer:

The correct answer is: c. {-3, 0, 4, 11}

Step-by-step explanation:

A function consists of ordered pairs. In the ordered pairs, the first element is the input and second value is the output.

All the possible set of inputs for a function are called domain.

Given function is:

{(-3, 6), (0, 2), (4, 7), (11, 15)}

The domain set will consist of the first elements of all the ordered pairs.

The domain of this function is: {-3,0,4,11}

Hence,

The correct answer is: c. {-3, 0, 4, 11}

5 0

3 years ago

16/5 x 36/12 x 25/18

solmaris [256]

Answer

$\frac{16}{5}$ * $\frac{36}{12}$ * $\frac{25}{18}$ = $\frac{4}{1} *\frac{2}{3} *\frac{5}{1}=\frac{40}{3} =13\frac{1}{3}$

Step-by-step explanation:

6 0

3 years ago