Question 3 of 10

A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021

egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

A is approximately <u>2020.022</u>

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

$\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}$

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

$\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}$

Therefore, for the last term we have;

$\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}$

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

$\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}$

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)$

Which gives;

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)$

$\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}$

A ≈ <u>2020.022</u>

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A common denominator for 1/4 and 5/6...
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5/6 = 10/12
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An airport shuttle company owns cars that have a maximum capacity of 4 passengers and vans that have a maximum capacity of 9 pas

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Answer:

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A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in

Andreyy89

So, she has 3hrs to grade all papers, for 35 students.. alrite.

the first 5, she does them in 30minutes.. what's the speed rate? well, 5/30 or 1/6

now, she has still 2 hours and a half, or 150 minutes, to do the remaining 30 papers... she has to work at a rate of 30/150 then... which is 1/5 simplified.

now if we take 1/6 as the 100%, what is 1/5 in percentage then?

$\bf \begin{array}{ccllll}
rate&\%\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
\frac{1}{6}&100\\\\
\frac{1}{5}&x
\end{array}\implies \cfrac{\frac{1}{6}}{\frac{1}{5}}=\cfrac{100}{x}\implies \cfrac{1}{6}\cdot \cfrac{5}{1}=\cfrac{100}{x}\implies \cfrac{5}{6}=\cfrac{100}{x}
\\\\\\
x=\cfrac{6\cdot 100}{5}\implies x=120$

so 1/5 is 120% in relation to 1/6... meaning the rate of 1/5 she needs to move through, namely 1 paper every 5 minutes, is 20% faster than 1/6.

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Y=-5/3x + 28/3 in standard form

Temka [501]

3y + 5x - 28 = 0

anything please ask me

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