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2 years ago

Is 0, 3, 8, 15, 24, 35 an arithmetic sequence

Mathematics

1 answer:

Marta_Voda [28]2 years ago

5 0

Answer:

Yes, the sequence is an arithmetic sequence

Step-by-step explanation:

Notice that each consecutive number is being added by the next odd number up:

0+3=3

3+5=8

8+7=15

15+9=24

24+11=35

We can represent this as the arithmetic sequence $a_n=n(n+2)$

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A contaminant is leaking into a lake at a rate of R(t) = 1700e^0.06t gal/h. Enzymes that neutralize the contaminant have been ad

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Answer:

16,460 gallons

Step-by-step explanation:

This is a differential equation problem, we have a constant flow of contaminant into the lake, but also we know that only a fraction of that quantity of contaminant remains because of the enzymes. For that reason, the differential equation of contaminant's flow into the lake would be:

$\frac{dQ}{dt} =1700exp(0.06t)*exp(-0.32t)\\\frac{dQ}{dt} =1700exp(-0.26t)\\$

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$\int\limits^0_t {dQ}=\int\limits^0_t {1700exp(-0.26t)dt}\\Q(t)=\frac{1700}{-0.26} exp(-0.26t)+C \\$

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$t_{0} =0\\Q_{0}=10,000\\Q_{0}=-6538exp(-0.26*0)+C\\C=10,000+6538=16538$

Then, we reorganize the equation and we replace t for 17 hours, in order to determine the quantity of contaminant at that time:

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3 years ago

Which student correctly used guess and check to determine the unknown number?

Alenkasestr [34]

<h2>Explanation:</h2><h2></h2>

Hello! Remember you need to write complete questions in order to get good and exact answers. Here we know nothing about the students so I can only help you providing the correct steps to find <em>the product of a number and eight is 104:</em>

<em />

Let that number be $n$ , then the statement can be written in a mathematical language as follows:

$n\times 8=104 \\ \\ \\ \text{Dividing both sides by 8:} \\ \\ \frac{n\times 8}{8}=\frac{104}{8} \\ \\ \boxed{n=13}$

Finally, <em>the unknown number is 13</em>

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