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4 years ago

8

What are the next two numbers in this pattern? 3, â9, 27, â81, . . ?

1 answer:

hjlf4 years ago

4 0

729, <span>â6561 is the answer</span>

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If The number 0.1111... repeats forever; therefore, irrational number true or false?

Kazeer [188]

False. This number can be written as a fraction, $\frac{1}{9}$

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3 years ago

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A local school requires 3 teachers for every 93 students. Which equation represents this relationship, where t is the number of

bearhunter [10]

<span>t is the number of teachers and s is the number of students
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<span>The school requires 3 teachers for every 93 students.
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<span>So, 3t = 93 s ⇒⇒⇒ divide by 3
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<span>∴ 3t/3 = 93s/3
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<span>∴ t = 31 s
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The <span>equation represents this relationship is ⇒⇒⇒ t = 31 s
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3 years ago

Vertical angles are non-adjacent angles.<br><br>True or False

Harrizon [31]

The correct answer would be True

7 0

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.

5 0

3 years ago

Simplify 1/2(4a+b)-1/4(4a+b)

gogolik [260]

So this can be rewritten as 2/4(4a+b)-1/4(4ab) so this can be simplified more easily, 2/4-1/4=1/4. The simplified version is 1/4(4a+b)

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3 years ago

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