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Ahat [919]
3 years ago
12

For the equation ae^ct=d, solve for the variable t in terms of a,c, and d. Express your answer in terms of the natural logarithm

.
Mathematics
1 answer:
saveliy_v [14]3 years ago
5 0

We have been given an equation ae^{ct}=d. We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

\frac{ae^{ct}}{a}=\frac{d}{a}

e^{ct}=\frac{d}{a}

Now we will take natural log on both sides.

\text{ln}(e^{ct})=\text{ln}(\frac{d}{a})

Using natural log property \text{ln}(a^b)=b\cdot \text{ln}(a), we will get:

ct\cdot \text{ln}(e)=\text{ln}(\frac{d}{a})

We know that \text{ln}(e)=1, so we will get:

ct\cdot 1=\text{ln}(\frac{d}{a})

ct=\text{ln}(\frac{d}{a})

Now we will divide both sides by c as:

\frac{ct}{c}=\frac{\text{ln}(\frac{d}{a})}{c}

t=\frac{\text{ln}(\frac{d}{a})}{c}

Therefore, our solution would be t=\frac{\text{ln}(\frac{d}{a})}{c}.

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a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers starte
ankoles [38]

Answer:

<em>Worker B needs 9 days to finish the rest of the work</em>

Step-by-step explanation:

<u>Proportions</u>

Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.

Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do

\frac{1}{12}+\frac{1}{16}=\frac{7}{48}

After 3 days they have completed:

3*\frac{7}{48}=\frac{7}{16}

parts of the project, this means it still remains:

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\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9

days to complete the project.

Worker B needs 9 days to finish the rest of the work

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3 years ago
Radium-226 is a metal with a half-life of 1600 years. If you start with 1 kilogram of radium-226, how much will remain after 20,
erica [24]
Ending Amount = Beginning Amount / 2^n 
where 'n' = # of half lives
n = 20,000 / 1,600 = 12.5 half-lives

Ending Amount = 1 kg / 2^12.5
Ending Amount = 1 kg / <span> <span> <span> 5,792.6
</span></span></span>Ending Amount = <span> <span> <span> 0.00017263 kilograms = </span></span></span><span>0.17263 grams


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<u>The television station has received/A many complaints about/B the clothing advertisements, which some/C viewers condemn to be/D </u><u>tasteless</u><u>. No error/E</u>

The correct option is D.

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What is a television station called?

  • Most often the term "television station" refers to a station which broadcasts structured content to an audience or it refers to the organization that operates the station.
  • A terrestrial television transmission can occur via analog television signals or, more recently, via digital television signals.

Learn more about television station

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