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3 years ago

6

Consider the expression 35.86 divided by 2.2 .

1 answer:

Anastasy [175]3 years ago

3 0

Answer:

a = 100, b = 100
16.3

Step-by-step explanation:

<h3>Part A</h3>

a = 100 will convert the number on the numerator to whole number
b = 10 will convert the number on the denominator to whole number

But we need a = b in order not to change the value of the fraction, therefore we choose

a = b = 100

<h3>Part B</h3>

Multiplying both numerator and denominator by 100 will make the fraction:

35.86*100/2.2*100 =
3586/220 =
16 66/220 =
16 3/10
16.3

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Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

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and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

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Then

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$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

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and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

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3 years ago

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cluponka [151]

Answer:

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1 year ago