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hammer [34]
3 years ago
15

List the first 9 terms of the sequence defined recursively by Sn = Sn-2. (Sn-1 - 1), with S1 = 2 and

Mathematics
1 answer:
STALIN [3.7K]3 years ago
5 0

Explanation

Given that Sn = Sn-2 . (Sn-1 - 1)

Tn = Sn - Sn-1

Tn = Sn-2 . (Sn-1 - 1) - (Sn-3 . (Sn-2 - 1))

T3 = S1.(S2-1) - (S0.(S1-1)

T3 = 2.(3-1) - 1.(2-1)

T3 = 2(2) - 1(1)

T3 = 4-2

T3 = 3

T4 = S2.(S3-1) - (S1.(S2-1)

T4 =3.(-1) - 1.(2-1)

T4 = 2(2) - 1(1)

T4 = 4-2

T4 = 3

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What is the tan invers of 3i/-1-i​
postnew [5]

<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> )

<em>z</em> = 3<em>i</em> / (-1 - <em>i</em> ) × (-1 + <em>i</em> ) / (-1 + <em>i</em> )

<em>z</em> = (3<em>i</em> × (-1 + <em>i</em> )) / ((-1)² - <em>i</em> ²)

<em>z</em> = (-3<em>i</em> + 3<em>i</em> ²) / ((-1)² - <em>i</em> ²)

<em>z</em> = (-3 - 3<em>i </em>) / (1 - (-1))

<em>z</em> = (-3 - 3<em>i </em>) / 2

Note that this number lies in the third quadrant of the complex plane, where both Re(<em>z</em>) and Im(<em>z</em>) are negative. But arctan only returns angles between -<em>π</em>/2 and <em>π</em>/2. So we have

arg(<em>z</em>) = arctan((-3/2)/(-3/2)) - <em>π</em>

arg(<em>z</em>) = arctan(1) - <em>π</em>

arg(<em>z</em>) = <em>π</em>/4 - <em>π</em>

arg(<em>z</em>) = -3<em>π</em>/4

where I'm taking arg(<em>z</em>) to have a range of -<em>π</em> < arg(<em>z</em>) ≤ <em>π</em>.

6 0
2 years ago
I WILL AWARD BRAINLIEST!! PLEASE HELP!!
lara31 [8.8K]

Answer:

A(...; 7)

x =-1/5

B(8; ...)

y = 48

The slope is 5

Step-by-step explanation:

y−5x=8

A(...; 7)

We know that y=7, we need to find x

7 - 5x = 8

Subtract 7 from each side

7-7 -5x = 8-7

-5x =1

Divide by -5

-5x/-5 = 1/-5

x =-1/5

B(8; ...)

We know x = 8 we need to find y

y−5x=8

y - 5(8) = 8

y - 40 =8

Add 40 to each side

y-40+40 = 8+40

y = 48

Now we need to find the slope

y - 5x =8

Add 5x to each side

y -5x+5x = 5x+8

y = 5x+8

This is in the form y = mx+b  where m is the slope

The slope is 5

5 0
3 years ago
Can someone please please help me :/ I have to get this right. please help​
Vladimir [108]
<h3>Answer: Choice B. f(x) = 100 - 68x</h3>

Work Shown:

Solve for y. Then replace y with f(x).

680x + 10y - 1000 = 0\\\\10y - 1000 = -680x\\\\10y = -680x + 1000\\\\y = \frac{-680x + 1000}{10}\\\\y = \frac{-680x}{10} + \frac{1000}{10}\\\\y = -68x + 100\\\\y = 100 - 68x\\\\f(x) = 100 - 68x\\\\

Effectively this involves adding 1000 to both sides and subtracting 680x from both sides, afterward we divide both sides by 10 to isolate y.

4 0
3 years ago
Read 2 more answers
If n + 10 = 45.5, then what is the value of the expression n - 25?
Citrus2011 [14]

Answer: 90

Step-by-step explanation:

45.5-.5=45

45^2=90

8 0
3 years ago
A parking garage charges a 3.50$ base fee plus an hourly rate of 7.00$. If you have at most 21.50$ to pay for parking, how long
pentagon [3]

Answer:

You get a total of two hours of parking.

Step-by-step explanation:

First, you subtract the base fee of $3.50, which gives you $18.00. Then you subtract as many sevens there are in 18, which is two. And then your answer is shown, as two. Hope this helps!

3 0
3 years ago
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