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2 years ago

What is the slope of the line that passes through the point (-9,8) and (-3-1)?

Mathematics

1 answer:

natulia [17]2 years ago

5 0

Answer:

Step-by-step explanation:

(x₁, y₁) = (-9 ,8) and (x₂ , y₂) = (-3 , -1)

$Slope = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\dfrac{-1-8}{-3-[-9]}\\\\=\dfrac{-9}{-3+9}\\\\=\dfrac{-9}{6}\\\\=\dfrac{-3}{2}$

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During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

Answer! The amount of time it takes to complete a reading assignment might be a function of which of the folowing ?

sladkih [1.3K]

Amount is a function of what means
the amount is dependent on what variable

well, the amount of time to read would be depending on the number of pages or your reading speed

looking at the options, A is clearly the answer

5 0

3 years ago

Read 2 more answers

Rotating a polygon in Quadrant II 270° clockwise is the same as what?

lora16 [44]

The answer to this question would be: <span>rotating it 90° counterclockwise.

When you rotate up an object 360</span>°, it will revert into its original places. That mean, if you rotate it more than 180°, then rotating it to the opposite direction will be easier/closer than you do. In this case, you rotate the polygon 270° so it will equal to 360° - 270°= 90° of opposite direction, which means counterclockwise. The quadrant shouldn't have any meaning in this question.

8 0

3 years ago

An athlete plains to run 3 miles. Each lap around th school yard is 3/7 miles how many laps will the athlete run

kati45 [8]

Answer: 7 laps

Step-by-step explanation:

The athlete planned to run 3 miles

1 lap = 3/7 miles

x laps = 3 miles

by proportion :

x × 3/7miles = 3 miles

x = 3 ÷ 3/7

x = 3 x 7/3

x = 7

Therefore: the athlete will run 7 laps

3 0

3 years ago

Approximately how many times bigger was the 1908 siberian asteroid than the diameter of the chelyabinsk asteroid

elena-14-01-66 [18.8K]

1908 Siberian Asteroid is known to be 130 feet/ 18 meters in diameter while on the other hand Chelyabinsk Asteroid is known to be 59 feet/40 meters in diameter. To find how many times Siberian Asteroid is bigger than Chelyabinsk Asteroid we just have to divide Siberian by Chelyabinsk here we get:

10/59=2.2 = 1908 Siberian Asteroid is 2.2 times bigger than Chelyabinsk Asteroid.

4 0

3 years ago