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3 years ago

Simplify 8 over the quantity of 2 plus 2i.

1 answer:

5 0

$\dfrac{8}{2+2i}=\dfrac{8}{2(1+i)}=\dfrac{4}{1+i}=\dfrac{4}{1+i}\cdot\dfrac{1-i}{1-i}=\dfrac{4(1+i)}{1^2-i^2}\\\\=\dfrac{4(1+i)}{1-(-1)}=\dfrac{4(1+i)}{1+1}=\dfrac{4(1+i)}{2}=2(1+i)=2+2i\\\\Used:\\(a-b)(a+b)=a^2-b^2\\\\i=\sqrt{-1}\to i^2=-1$

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Find an for the arithmetic series with s16 = -288 And a1 =-21

Maru [420]

If $d$ is the common difference between terms in the sequence $\{a_n\}$ , then

$a_1=-21$
$a_2=a_1+d=-21+d$
$a_3=a_2+d=-21+2d$
...
$a_n=a_{n-1}+d=\cdots=-21+(n-1)d$

You're told that $S_{16}=-288$ (the sum of the first 16 terms in the sequence, presumably). Well, we know that

$S_{16}=\displaystyle\sum_{n=1}^{16}a_n=\sum_{n=1}^{16}(-21+(n-1)d)$
$S_{16}=\displaystyle(-21-d)\sum_{n=1}^{16}1+d\sum_{n=1}^{16}n$

Recall that

$\displaystyle\sum_{n=1}^kn=\frac{k(k+1)}2$

so that we have

$-288=16(-21-d)+\dfrac{16(16+1)}2d\implies d=\dfrac25$

So we get

$\begin{cases}a_1=-21\\\\a_n=-21+\dfrac25(n-1)\end{cases}$

8 0

3 years ago

(7 - 3)^2 / 8 - 1 as an evaluated expression

hodyreva [135]

Step-by-step explanation:

((7²-2×7×3+3²)/8)-1=( 16/8)-1=2-1=1

7 0

3 years ago

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Please i need help ASAP!

madam [21]

With what? I need a picture or type the answer

7 0

3 years ago

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Kimmy saving accounts has a balance of $76.23 in June by September her balance is 5 time as much as her June balance between Sep

hammer [34]

Answer:

Kimmy balance in December will be $545.21.

Step-by-step explanation:

Given:

Balance in account in June = $76.23

Now Given, by September her balance is 5 time as much as her June

It means that Balance in account till September is 5 times Balance in account in June.

framing in equation form we get;

Balance in account till September = $5\times \$76.23 = \$381.15$

Also Given:

Balance Deposited in account between September and December = $87.83

Now We need to find balance till December.

Kimmy balance till December will equal to sum of Balance in account in June and Balance in account till September and Balance Deposited in account between September and December.

framing in equation form we get;

Kimmy balance till December = $\$76.23+ \$381.15+\$87.83 = \$545.21$

Hence Kimmy balance in December will be $545.21.

3 0

3 years ago

The graphs below have the same shape. f(x) = x2<br> What is the equation of the graph of g(x)?

mariarad [96]

Answer:

g(x)=(x-2)^2

Step-by-step explanation:

the equation of of the graph of g(x) is:

g(x)=(x-2)^2, since the following transformation has been done to it:

right one unit

since the equation in vertex form is g(x)=a(x-h)^2+k, it is moved two units to the right and not to the left

since g(x) has the same shape, it had not been compressed or stretched by any means, meaning that a is 1

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3 years ago

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