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3 years ago

7

Which undefined geometric term is described as a two - dimensional set of points that had no beginning or end

2 answers:

Nana76 [90]3 years ago

4 0

A line is the answer

Nikitich [7]3 years ago

3 0

Answer:line

Step-by-step explanation:

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Simplfiy the expression -5+i/2i

Elodia [21]

-5i/2i. is the answer because all you have to do is add the -5 and the i.

8 0

3 years ago

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

2 years ago

A. 7 ft<br><br> B. 8 ft<br><br> C. 49 ft<br><br> D. 576 ft

AleksAgata [21]

Your equation is gonna be a^2-24^2=25^2 and your answer is 7.

4 0

2 years ago

Read 2 more answers

Using your answer from #3, how many hours will

Sphinxa [80]

Answer:

5 hours cuz 75 divided by 15 is 5 or 15 x 5 is 75

3 0

3 years ago

Read 2 more answers

A man invests $2000 in an account that pays 6.5% interest per year, compounded quarterly.

skelet666 [1.2K]

Answer:

The correct answer is a. $2275.28; b. 17.04 years

Step-by-step explanation:

Principal to be invested is $2000

Interest rate (r) per year is 6.5 quarterly.

Interest is calculated compoundly.

a. Time (t) for the investment is given to be 2 years.

Amount after two years is = Principal × $( 1+ \frac{r}{100n}) ^ {nt}$ where the value of n is 4.

⇒ A = 2000 × $( 1+ \frac{6.5}{400}) ^ {8}$

⇒ A = $2275.28.

b. Now the value of A is given to be triple the principal = $ (3 × 2000).

Therefore we need to find the value of t.

⇒ 3 × 2000 = 2000 × $( 1+ \frac{6.5}{400}) ^ {4t}$

⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)

⇒ t = 17.04

Therefore it would take 17.04 years for the principal to triple.

5 0

3 years ago