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2 years ago

9

I understand the switching of positive and negative signs but I don’t understand how to get to the next step which is the answer

. It’s factoring.

1 answer:

Finger [1]2 years ago

6 0

2ab - 3a = a.(2b-3)

now the same thing

let's say n=1

a.(2b-3) + n.(2b-3) = (2b-3).(a+n)

Understood?

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

SHOW YOUR WORK! Marking the best response with brainliest:) thank u

sdas [7]

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

where

l is the length

w is the width

From the question

The length is 3x + 7

The width is 2x + 2

The perimeter is

<h3>2( 3x + 7) + 2( 2x + 2)</h3>

Simplify

6x + 7 + 4x + 4

Group like terms

6x + 4x + 7 + 4

We have the final answer as

<h3>10x + 11</h3>

Hope this helps you

6 0

3 years ago

How would you solve (-1,4),y=3x+5

astraxan [27]

Answer:

y = 12x

Step-by-step explanation:

-1 times 4 equals -4 so you have -4,y = 3x + 5 so you do 5 + 3 so it is 8x then you have -4,y = 8x so you add 4 to each side and it becomes y = 12x

5 0

3 years ago

Summer campers were surveyed about their favorite fruit. The resulting table shows the data collected from the survey. Use the i

NemiM [27]

Answer:

Step-by-step explanation: 90

7 0

3 years ago

Read 2 more answers

Use the first and last data points to find the slope intercept equation of a trend line.

andriy [413]

Answer:

y = $\frac{16}{3}x-79$

Step-by-step explanation:

From the given table,

Two points are (1, 15) and (7, 47)

If the two points $(x_1,y_1)$ and $(x_2,y_2)$ are lying on a line then slope 'm' of the line will be,

m = $\frac{y_2-y_1}{x_2-x_1}$

= $\frac{47-15}{7-1}$

= $\frac{32}{6}$

= $\frac{16}{3}$

Let the equation of a line passing through (h, k) is,

y - h = m(x - k)

If the line passes through (1, 15)

y - 1 = $\frac{16}{3}(x-15)$

y = $\frac{16}{3}x-\frac{16}{3}(15)+1$

y = $\frac{16}{3}x-80+1$

y = $\frac{16}{3}x-79$

4 0

3 years ago