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3 years ago

1, 4, 3, 6, 5, ... Find the pattern

Mathematics

1 answer:

Brut [27]3 years ago

4 0

the pattern goes as adding 3 then subtracting with 1,

1+3=4

4-1=3

3+3=6

6-1=5

so its like that now we have to continue it like:

5+3=8

8-1=7

so the pattern goes like 1,4,3,6,5,8,7

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3 years ago

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3 years ago

Element X decays radioactively with a half life of 11 minutes. If there are 870 grams of Element X, how long, to the nearest ten

serg [7]

Answer:

It would take 27.5 minutes the element to decay to 154 grams.

Step-by-step explanation:

The decay equation:

$\frac {dN}{dt}\propto -N$

$\Rightarrow \R\frac {dN}{dt}=-\lambda N$

$\Rightarrow \frac {dN}N=-\lambda dt$

Integrating both sides

$\Rightarrow \int \frac {dN}N=\int-\lambda dt$

$\Rightarrow ln|N|=-\lambda t+c$

When t=0, N= $N_0$ = initial amount

$ln|N_0|=-\lambda .0+c$

$\Rightarrow c=ln|N_0|$

$ln|N|=-\lambda t+ln|N_0|$

$\Rightarrow ln|N|-ln|N_0|=-\lambda t$

$\Rightarrow ln|\frac{N}{N_0}|=-\lambda t$

Decay equation:

$ln|\frac{N}{N_0}|=-\lambda t$

Given that, the half life of of element X is 11 minutes.

For half life, $N=\frac12 N_0$ , t= 11 min.

$ln|\frac{N}{N_0}|=-\lambda t$

$\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11$

$\Rightarrow ln|\frac12}|=-\lambda . 11$

$\Rightarrow -\lambda . 11=ln|\frac12}|$

$\Rightarrow \lambda =\frac{ln|\frac12|}{-11}$

$\Rightarrow \lambda =\frac{ln|2|}{11}$ [ $ln|\frac12|=ln|1|-ln|2|=-ln|2|$ , since ln|1|=0]

N=154 grams, $N_0$ = 870 grams, t=?

$ln|\frac{N}{N_0}|=-\lambda t$

$\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t$

$\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}$

=27.5 minutes

It would take 27.5 minutes the element to decay to 154 grams.

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3 years ago

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AURORKA [14]

C & A I believe because 2+3 is 5 so that’s 5x

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3 years ago

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