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3 years ago

What is the sum of the first 100 even natural numbers? S100 =

Mathematics

2 answers:

kolbaska11 [484]3 years ago

7 0

Answer:

10100

Step-by-step explanation:

E2020

Leviafan [203]3 years ago

5 0

Sn = n(n+1) = 100(101) = 10100

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A partir del resultado obtenido ;con

Ymorist [56]

Answer:

I don't understand what your asking here.

Your translation: From the result obtained; with

Step-by-step explanation:

8 0

3 years ago

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

A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.

Anvisha [2.4K]

Answer:

where is the figure?? thanks

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3 years ago

Jack made $30 mowing lawns in May and $72 mowing lawns in June. By what percent did the amount of money Jack made mowing lawns i

WARRIOR [948]

$72 - $30 = $42

It increased $42.

Now take this number and divide by the original number (first):

42 ÷ 30

This is 1.4, let's convert this to a percentage.
We now times it by 100

1.4 × 100

The answer is 140%

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3 years ago

What is the value of the expression when x = 5, y = 4, and z = 3?

Elan Coil [88]

C-75 would be your answer

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3 years ago

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