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3 years ago

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1 answer:

kotegsom [21]3 years ago

8 0

Answer:

Jesus because eveybody loves jesus lol

the 90's because everthing was better in the 90's

i was married to donald trump

Id want apple pie

not going to school

Step-by-step explanation:

You might be interested in

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

Which transformations are needed to change the parent cosine function to y = 3 cosine (10 (x minus pi))?

Alekssandra [29.7K]

Answer:

See Explanation

Step-by-step explanation:

Given

New function: $y = 3 \cos(10 (x -\pi))$

We can assume the parent function to be:

$y = \cos (x)$

The new function can be represented as:

$y = A*\cos((\frac{2\pi}{B})(x-c))$

Where

A = Vertical stretch factor

B = Period

C = Right shift

By comparison:

$y = A*\cos((\frac{2\pi}{B})(x-c))$ to $y = 3 \cos(10 (x -\pi))$

$A = 3$

$c = \pi$

$\frac{2\pi}{B} = 10$

Solve for B

$B = \frac{2\pi}{10}$

$B = \frac{\pi}{5}$

Using the calculated values of $A,\ B\ and\ c.$ This implies that, the following transformations occur on the parent function:

<em>Vertically stretched by </em> $3$ <em />
<em>Horizontally compressed by </em> $\frac{\pi}{5}$ <em />
<em>Right shifted by </em> $\pi$ <em />

5 0

3 years ago

Read 2 more answers

The first two terms of the perfect square trinomial are given, find "c".

Naddik [55]

Answer:

A.) 36

Step-by-step explanation:

For a perfect square trinomial, a = 1 b = 2x c = x². For an example, (x+3)² = x² + 6x + 9.

For this trinomial, divide "b" by 2 to get 6. Square this number and you will have 36.

x² + 12x + 36

7 0

3 years ago

Read 2 more answers

There are 220 students in the seventh grade, and 10% are in the Environmental Club. How many students are in the Environmental C

siniylev [52]

Answer:

22 students are in the environmental club

Step-by-step explanation:

220 / 10 = 22

7 0

3 years ago

What is the area of an isosceles triangle whose equal sides 5 cm and base side 6 cm

zaharov [31]

Answer:

12 cm^2

Step-by-step explanation:

6 0

3 years ago