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2 years ago

Evaluate the expression -[-16.9 + 10]

Mathematics

2 answers:

Alenkinab [10]2 years ago

8 0

I believe it would be -6.9‍♀️

tekilochka [14]2 years ago

3 0

its 6.9 i took the test.

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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,

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

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

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.

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

Then

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

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

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

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

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

6 0

1 year ago

What ÷ 30 =160 this equation is already estimated plz don't put a remader in this equation

Kobotan [32]

5.333 OR 5 1/3
just plug it in the calculator
you will get your answer

3 0

2 years ago

Read 2 more answers

Kayleigh babysat for 11 hours this week that was 5 fewer than 2/3 as manyas she baby sat last week, h write an equation to repre

mars1129 [50]

Answer:

10.5 hours

Step-by-step explanation:

To find the number of hours she babysat last week subtract 5 from 11 which is 7 hours. 7 hours is equal to 2/3 of the many hours. If she babysat h hours last week then solve for h using 2/3 h = 7.

Solve the equation by multiplying each side by the reciprocal.

3/2 * 2/3h = 7*3/2

h = 21/2

h = 10.5 hours

3 0

2 years ago

How much is 1638074%283363+7336-736362886 is?

ArbitrLikvidat [17]