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marusya05 [52]
4 years ago
7

Find the prime factorization of 210. 2 X 3 X 5 X 7 2 X 3 X 35 2 X 7 X 15

Mathematics
2 answers:
Ne4ueva [31]4 years ago
8 0

Answer: 2 X 3 X 5 X 7

Step-by-step explanation:

The given number to find the prime factorization =210

We know that 210 can be written as 21\times10

Also , 21 can be written as 3\times7.

And 10 can be written as 2\times5

Then , the  prime factorization of 210 is given by :-

210=21\times10\\\\=3\times7\times2\times5

Hence, the prime factorization of 210= 2 X 3 X 5 X 7

lara31 [8.8K]4 years ago
6 0
The answer is:  [A]:  " 2 × 3 × 5 × 7 " .
________________________________________________________

210 = 70 * 3 ;

70 * 3 = 35 * 2 * 3 ;

35* 2* 3 = 7 * 5 * 2 * 3 ; which corresponds to "Answer choice:  [A]." .
________________________________________________________
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A
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Answer:

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Step-by-step explanation:

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2 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}

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So

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
What is the domain of the relation?<br><br> Express your answer using inequalities.
son4ous [18]

Answer:

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  -    -

Step-by-step explanation:

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Good luck! Hope I'm not late!

8 0
3 years ago
Read 2 more answers
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