All categories

3 years ago

What is the value of 6/1+i? 2-6i 2+6i 3-3i 3+3i

Mathematics

1 answer:

kramer3 years ago

8 0

Answer:

3 - 3i

Step-by-step explanation:

I think you meant:

------------

1 + i

To simplify this, that is, to "rationalize the denominator," multiply both numerator and denominator by the conjugate of 1 + i, which is 1 - I:

6(1 - i)

----------- = 3(1 - i)= 3 - 3i

1 -(-1)

You might be interested in

Write the following comparison as a ratio reduced to lowest terms 14 nickels to 15 dimes

miskamm [114]

14x5=70
15x10=150
Answer- 7:15

7 0

4 years ago

Some types of algae have the potential to cause damage to river ecosystems. Suppose the accompanying data on algae colony densit

Phantasy [73]

Answer:

$y=-2.95836 x +234.56159$

Step-by-step explanation:

We assume that th data is this one:

x: 50, 55, 50, 79, 44, 37, 70, 45, 49

y: 152, 48, 22, 35, 43, 171, 13, 185, 25

a) Compute the equation of the least-squares regression line. (Round your numerical values to five decimal places.)For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i =50+ 55+ 50+ 79+ 44+ 37+ 70+ 45+ 49=479$

$\sum_{i=1}^n y_i =152+ 48+ 22+ 35+ 43+ 171+ 13+ 185+ 25=694$

$\sum_{i=1}^n x^2_i =50^2 + 55^2 + 50^2 + 79^2 + 44^2 + 37^2 + 70^2 + 45^2 + 49^2=26897$

$\sum_{i=1}^n y^2_i =152^2 + 48^2 + 22^2 + 35^2 + 43^2 + 171^2 + 13^2 + 185^2 + 25^2=93226$

$\sum_{i=1}^n x_i y_i =50*152+ 55*48+ 50*22+ 79*35+ 44*43+ 37*171+ 70*13+ 45*185+ 49*25=32784$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=26897-\frac{479^2}{9}=1403.556$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=32784-\frac{479*694}{9}=-4152.22$

And the slope would be:

$m=-\frac{-4152.222}{1403.556}=-2.95836$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{479}{9}=53.222$

$\bar y= \frac{\sum y_i}{n}=\frac{694}{9}=77.111$

And we can find the intercept using this:

$b=\bar y -m \bar x=77.1111111-(-2.95836*53.22222222)=234.56159$

So the line would be given by:

$y=-2.95836 x +234.56159$

7 0

3 years ago

30 power of 2 muilpity by pie

Ulleksa [173]

Answer: 30^2 * pi = 2827.43.

7 0

3 years ago

Read 2 more answers

How do you do 7-12? How do you do 13-18?

eimsori [14]

7-12 is like a negative number so it will be -5. And 13-18 would be -5 also.

7 0

4 years ago

Read 2 more answers

A crew of a highway workers paved 2/15 mile in 20 minutes if they work at the same rate what portion of a mile will they pave in

Brut [27]

<span>the answer will be
396763</span>

5 0

3 years ago

Read 2 more answers