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3 years ago

13

What is the midpoint of a segment in the complex plane with endpoints at 6-2i and -4+6i?

1 answer:

Ilia_Sergeevich [38]3 years ago

8 0

Answer:

1+2i

Step-by-step explanation:

midpoint: (6 + -4)/2 + (-2 + 6)/2 i

= 1+2i

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How would you find the volume of this?

Oduvanchick [21]

4*4*6(7/10)=volume^3

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4 years ago

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Find the sequence of differences for the given sequence. Next, find a closed form solution for the following sequence. (Be sure

padilas [110]

Let $a_n$ denote the given sequence with $n\ge1$ :

$\{a_n\}_{n\ge1}=\{1,5,11,19,29,41,\ldots\}$

Let $b_n$ be the sequence of the forward differences of $a_n$ , so that $b_n=a_{n+1}-a_n$ for $n\ge1$ :

$\{b_n\}_{n\ge1}=\{4,6,8,10,12,\ldots\}$

$b_n$ follows an arithmetic progression with a difference of 2 between terms, so that

$b_n=4+2(n-1)=2n+2$

Then we have

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

so that $a_n$ is given recursively by

$\begin{cases}a_1=1\\a_{n+1}=a_n+2(n+1)&\text{for }n\ge1\end{cases}$

By substitution, we can try to find a pattern:

$a_2=a_1+2\cdot2$

$a_3=a_2+2\cdot3=a_1+2(2+3)$

$a_4=a_3+2\cdot4=a_1+2(2+3+4)$

$a_5=a_4+2\cdot5=a_1+2(2+3+4+5)$

and so on, with the general pattern

$a_n=a_1+2(2+3+4+\cdots+n)$

and since $a_1=1$ we can write this as

$a_n=1+2(2+3+4+\cdots+n)$

$a_n=-1+2+2(2+3+4+\cdots+n)$

$a_n=2(1+2+3+4+\cdots+n)-1$

Recall that

$\displaystyle\sum_{i=1}^ni=1+2+3+\cdots+n=\dfrac{n(n+1)}2$

Then

$a_n=2\dfrac{n(n+1)}2-1\implies\boxed{a_n=n^2+n-1}$

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3 years ago

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Answer:

A

Step-by-step explanation:

when the line is solid its greater, smaller or equal to

when the line is dashed its greater or smaller

When the shade is above the y is greater

When the shade is coming from down its less than

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You deposit $800 in an account that pays 5.7%annual

bagirrra123 [75]

A(t) 800 0.057t
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3 years ago

Bob has some 10 lb weights and some 3 lb weights. Together, all his weights add up to 50 lbs. If x represents the number of 3 lb

Romashka [77]

Total weight = 50 lb
x = number of 3-lb weights
y = number of 10-lb weights

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weight of 10-lb weights = 10y
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equation
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