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ZanzabumX [31]
4 years ago
8

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

Mathematics
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?
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False. This number can be written as a fraction, \frac{1}{9}
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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
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<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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8 0
3 years ago
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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.

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3 years ago
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