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3 years ago

How do you find (2+4i)^3 in rectangular form?

Mathematics

2 answers:

marshall27 [118]3 years ago

8 0

$(2+4i)^3=8+48i-96-64i=-88-16i$

Paha777 [63]3 years ago

4 0

note that (a + b)³ = a³ + 3a²b + 3ab² + b³

(2 + 4i)³ ← with a = 2 and b = 4i noting that i² = (√-1)² = -1

= 2³ + (3 × 4 × 4i ) + ( 3 × 2 × 16i² ) + ( 4i )³

= 8 + 48i - 96 - 64i

= - 88 - 16i

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Perform the indicated operation.(3/a+2) + (4/a-5)

kipiarov [429]

Answer:

$\frac{7(a-1)}{(a+2)(a-5)}$

Step-by-step explanation:

To solve this operation we need to find the common multiple of both denominators and solve for a.

$\frac{3}{a+2} + \frac{4}{a-5} =\frac{3(a-5)+4(a+2)}{(a+2)(a-5)} =\frac{3a-15+4a+8}{(a+2)(a-5)} =\frac{7a-7}{(a+2)(a-5)} =\frac{7(a-1)}{(a+2)(a-5)}$

Thus, the solution is 7(a -1) / (a+2)(a-5)

8 0

4 years ago

Simplify the expression 3^7/3^5

Setler79 [48]

Answer:

Step-by-step explanation:

3 0

3 years ago

Does anyone know how to solve for a proof like this??? PLEASE PLEASE HELP ME.

Sonbull [250]

You are supposed to make a claim then prove it using evidence you are already given.

5 0

3 years ago

Anja collected data about the number of dogs 9th-grade students own. She created this histogram to represent the data and determ

igomit [66]

Anja is correct that the histogram is skewed to the right

According to the statement

we have given that the anja collected the data and created the histogram and after analyzing we have to tell that her claim is correct or not.

So, she collected the data:

A graph shows number of dogs labeled 0 to 2 on the horizontal axis and frequency on the vertical axis. 0 dogs at frequency 20. 1 dog at frequency 15. 2 dogs at frequency 12.

we know that the

Histogram is is an approximate representation of the distribution of numerical data.

and after making the histogram we see that

The histogram is skewed to the right because there is less data on the right side.

So, Anja is correct that the histogram is skewed to the right.

Learn more about Histogram here brainly.com/question/25983327

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4 0

2 years ago

Given the following data: X 1 4 6 7 Y 9 7 8 1 a) Find the coefficient of correlation. b) Find the equation of the regression lin

Viktor [21]

Answer:

a) r=-0.719

b) y=10.642-0.976x

c)Predicted y=7.714

Step-by-step explanation:

sumx=1+4+6+7=18

sumy=9+7+8+1=25

sumxy=1*9+4*7+6*8+7*1=92

sumx²=1²+4²+6²+7²=102

sumy²=9²+7²+8²+1²=195

n=number of observation=4

The correlation coefficient is computed by following formula

$r=\frac{nsumxy-(sumx)(sumy)}{\sqrt{[nsumx^{2} -(sumx)^2][nsumy^2-(sumy)^2]}}$

$r=\frac{4(92)-(18)(25)}{\sqrt{[4(102) -(18)^2][4(195)-(25)^2]}}$

$r=\frac{368-450}{\sqrt{[408 -324][780-625]}}$

$r=\frac{-82}{\sqrt{[84][155]}}$

$r=\frac{-82}{\sqrt{13020}}\\r=\frac{-82}{114.1052}\\r=-0.7186$

By rounding r to 3 decimal places we get r=-0.719.

The regression equation can be written as y=a+bx

We have to find "a" and "b" for regression equation

$b=\frac{nsumxy-(sumx)(sumy)}{{nsumx^{2} -(sumx)^2}}$

$a=ybar-b(xbar)$

$b=\frac{4(92)-(18)(25)}{{4(102) -(18)^2}}$

$b=\frac{-82}{{84}}$

b=-0.976

xbar=sumx/n

xbar=18/4=4.5

ybar=sumy/n

ybar=25/4=6.25

a=ybar-b(xbar)

a=6.25-(-0.976)4.5

a=6.25+4.392

a=10.642

Thus, the regression equation is

y=a+bx

y=10.642-0.976x

The predicted value of y for x=3 can be computed by putting the value of x in regression equation

y=10.642-0.976(3)

y=10.642-2.928

y=7.714

Hence, the predicted y-value for x=3 is 7.714.

4 0

4 years ago