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2 years ago

Help please pretty please i do not understand

Mathematics

2 answers:

Natalija [7]2 years ago

7 0

If i remember correctly i think you just cross multiply

hodyreva [135]2 years ago

6 0

Try cross multiplying or use photomath

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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

(1×1)-tan×(-tan) evaluate it by Determinants

andrew11 [14]

Answer:

1x1

Step-by-step explanation:

4 0

2 years ago

Sofia is comparing celluer plans. Company A charges a flat fee of 59.99 a month and .43 additional minutes. Company B charges 69

Vsevolod [243]

Answer: it will take 125 additional minutes for both costs to be equal.

Step-by-step explanation:

Let a represent the number of additional minutes that it will it take for the two to be the same.

Company A charges a flat fee of 59.99 a month and .43 additional minutes. This means that the total cost of a additional units would be

0.43x + 59.99

Company B charges 69.99 a month and .35 for additional minutes. This means that the total cost of a additional units would be

0.35x + 69.99

For the cost of the two plans to be the same, it means that

0.43x + 59.99 = 0.35x + 69.99

0.43x - 0.35x = 69.99 - 59.99

0.08x = 10

x = 125

5 0

2 years ago

Is -2.22 a rational or real or integers

mezya [45]

All because -2.22 is a real number, it’s a rational number because it can stop and a integer because it’s negative

3 0

2 years ago

Read 2 more answers

Complete the page for 15 points.

sergey [27]

Answer:

1. 15, 16, 17

2. 21, 23, 25

3. 44, 46, 48

4. -4, -3, -2

Step-by-step explanation:

Step 1. Writing an equation

Let's set x as the second number in the equation.

This means that the first number is x-1, and the third number is x+1.

We know that the sum of the three numbers is 48, so:

(x-1)+x+(x+1)=48

Step 2. Solving the equation

x-1+x+x+1=48

x+x+x-1+1=48

3x=48

x=16

So the answer is 15, 16, 17

Again, let's set x as the middle number.

Odd numbers are 2 numbers apart, so the first number is x-2, and the third is x+2.

This means that the equation must be:

(x-2)+x+(x+2)=69

x+x+x=69

3x=69

x=23

The numbers are 21, 23, and 25

x will be the middle number

Even numbers are 2 numbers apart, so the first number is x-2, and the third is x+2.

This means that:

x-2+x+x+2=138

x+x+x=138

3x=138

x=46

The numbers are 44, 46, and 48.

x will be the middle number.

x-1=first number, x+1=third number

x-1+x+x+1=-9

3x=-9

x=-3

The numbers are -4, -3, and -2.

3 0

2 years ago