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3 years ago

What is the value of r for 19 and 20?

Mathematics

1 answer:

nata0808 [166]3 years ago

4 0

Answer:

19.) r = -4 20.) r = 1

Step-by-step explanation:

19.) Because we know the slope and have some points, we can use point-slope form to find the equation.

Point-slope form is:

y - y1 = m(x - x1)

Substitute the numbers into the equation:

y - 3 = 7/6(x - 1)

y - 3 = 7/6x -7/6

y = 7/6x + 11/6

Now that we know the equation, we can put in the x value to find the y (In this case, y = r):

r = 7/6(-5) + 11/6

r = -35/6 + 11/6

r = -4

20.) Because the slope is undefined, that means on the graph, the line will appear straight and vertical. This means the equation will be something like x = a number.

We have the point (1,4). Since we know that the x value will never change, we know that r will have to equal 1 as well.

r = 1

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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

3 years ago

Melanie's room measures 10 ft by 12 ft. Her rug covers 90 ft². Explain how to determine the percent of floor covered by the rug.

Inessa [10]

$\huge \bf༆ Answer ༄$

Here's the solution ~

Area of floor is ;

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:10 \times 12$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:120 \: ft {}^{2}$

Area covered by rug is ;

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:90 \: ft {}^{2}$

So, the percentage of floor covered by rug is ~

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \dfrac{90}{120} \times 100$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \dfrac{3}{4} \times 100$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:3 \times 25$

${ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \:75 \%$

5 0

2 years ago

Read 2 more answers

I'm spending lots of points so please help ahaha-

umka2103 [35]

(2x+24)
(11b-33)
(8s-8)
(36+6y)
(25z-100)
(35w-70)

5 0

3 years ago

Read 2 more answers

Please help me with these.. i am stuck

SCORPION-xisa [38]

Answer:

Both are irrational

12√3 = 20.784

9√6 = 22.045

Hopefully this is what you're looking for :)

4 0

3 years ago

How would I solve this problem in steps pls

gregori [183]

In order to solve for a, we must isolate it. To do this, we should add c to both sides, making a the only term on the left.

Final answer: a=c+d-r

3 0

3 years ago