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jeka94
3 years ago
9

Determine whether the sequence converges or diverges. If it converges, give the limit. 60, 10, five divided by three, five divid

ed by eighteen, ...
Mathematics
1 answer:
vodomira [7]3 years ago
6 0
A_n = 60, 10, \frac{5}{3}, \frac{5}{18}

Using geometric sequence form, we can rewrite it as:
A_n = a_1 \cdot r^{n-1}
A_n = 60 \cdot \frac{1}{6}^{n - 1}

Since r < 1, there exists a limit, and thus, it is said to converge.
\lim_{n \to \infty} 60 \cdot (\frac{1}{6})^{n - 1}
= 0

Since the ratio is still positive, as n tends towards infinity, the graph of the sequence will never go below the horizontal. Thus, we say that the limit of the function is zero, which means that as we increase the size of n, eventually after the infinite-th time, it will hit zero.
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OPEN-UP... | GRADE
allochka39001 [22]

Answer:

The answer to your question is: 19 l

Step-by-step explanation:

Data

20 quarts to liters

Process

Rule of three

                         1 quart ------------------  0.946 l

                       20 quarts --------------     x

                           x = (20 x 0.946) / 1

                           x = 18.92 l ≈ 19 l

6 0
2 years ago
Read 2 more answers
What points can be found on the line 2y=3x+4
Olin [163]

The answer is (2,5).

Check:

2y=3x+4

2(5)=3(2)+4

10=6+4

10=10 Good

The answer is (2,5)

3 0
3 years ago
A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total s
vodomira [7]
Answer: 16

Solution:

1) Use letters to identify the variables:

Number of trumpets: t
Number of clarinets: c

2) Translate each statement into algebraic (mathematical) language.

2.1) Sold a total of 27 used trumpets and clarinets

=> t + c = 27

2.2) Trumpets cost $149 and clarinets cost $99

Total cost of the trumpets: 149t
Total cost of clarinets: 99c

Total cost = 149t + 99c

2.3) Total sales were $3223

=> 149t + 99c = 3223.

3) State the system of equations:

Equation (1) t + c = 27
Equation (2) 149t + 99c = 3223

4) Solve the system of equations:

4.1) Multiply equation 1 by 149:

=> 149t + 149c = 4023

4.2) Subtract the equation (2) from the equation obtained in 4.1

=> 149c - 99c = 4023 - 3223

=> 50c = 800

=> c = 800 / 50 = 16

5) Verify the solution:

From equation (1) t = 27 - 16 = 11

Total cost = 149*11 + 99*16 = 3223

Now you have a verified answer: they sold 16 clarinets
7 0
3 years ago
What would it mean if there was an outbreak of cholera? A. The disease has infected a few people spread out over a large distanc
Dmitry_Shevchenko [17]

Answer:

I think that it is B because its the only answer that makes sense

Step-by-step explanation:

5 0
3 years ago
boeing plans to increase its price for jetliners. with a selling price $201.5 million and a cost of $190.1 million, what was the
scoray [572]

so from 190.1 to 201.5 is 201.5 - 190.1 = 11.4.

now, if we take 190.1 as the 100%, what is 11.4 off of it in percentage?

\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 190.1&100\\ 11.4&x \end{array}\implies \cfrac{190.1}{11.4}=\cfrac{100}{x}\implies 190.1x=1140 \\\\\\ x=\cfrac{1140}{190.1}\implies x\approx 5.99684

3 0
3 years ago
Read 2 more answers
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