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3 years ago

Express the complex number in trigonometric form. 2 - 2i

2 answers:

8 0

Trigonometric form of the complex number : z = 2 - 2 i :
z = r ( cos t + i sin t )
r = | z | = √ ( 2² + (-2)² ) = √(4+4) = √8 = 2√2
t ( theta ) = tan^(-1) (-2 / 2 )= tan^(-1) (- 1 ) = - π / 4
z = 2√2 · ( cos (-π/4) + i sin (-π/4) ) =
= 2√2 · ( cos π/4 - i sin π/4 )

JulijaS [17]3 years ago

5 0

Answer:

a+ib=2sqrt2(cos7pi/4+isin7pi/4)

Step-by-step explanation:

a+ib=r (cos theta+isin theta)

r=sqrt a^2+b^2

r=sqrt (2)^2 +(-2)^2

r=2sqrt 2

theta=tan^-1(y/x) or (a/b)

theta= tan^-1(-2/2)

theta=-45 degrees

Now, I know that theta is in the fourth quadrant because cos (x-value) is positive. So, I am going to subtract my value from 360 degrees.

360-45= 315

theta=315

I can convert degrees to radians (if need be): 315 times pi/180= 7pi/4

Theta=7pi/4 r=2sqrt2

Substitute: a+ib=2sqrt2(cos7pi/4+isin7pi/4) this is radian format

or... a+ib=2sqrt2(cos 315+isin315) this is degree format

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Slope=3/5, y-intercept=2

aev [14]

Answer:

Step-by-step explanation:

becuase the slope is 3/5 and the y-intercept is 2 so it will be y=3/5x+2

4 0

3 years ago

Read 2 more answers

A dog trainer is trying to find a triangular area behind his house that encloses 1800 square feet for his dog to run. He has the

aliina [53]

Answer:

$C = (30,500)$

Step-by-step explanation:

Given

$Area = 1800ft^2$

$A = (6,0)$

$B = (0,25)$

$C(x,y) = (30,y)$

Required

Determine the coordinates of C

The area of triangle is calculated as thus:

$Area = \frac{|A_x(B_y - C_y) + B_x(C_y - A_y) + C_x(A_y - B_y)|}{2}$

This gives:

$1800= \frac{|6(25 - y) + 0(y - 0) + 30(0 - 25)|}{2}$

$1800= \frac{|6(25 - y) + 30(0- 25)|}{2}$

$1800= \frac{|6(25 - y) + 30(-25)|}{2}$

$1800= \frac{|150 - 6y -750 |}{2}$

$1800= \frac{|150 -750- 6y |}{2}$

$1800= \frac{|-600- 6y |}{2}$

Multiply through by 2

$2 * 1800= |-600- 6y|$

$3600= |-600- 6y|$

$3600= |-(600+ 6y)|$

$3600= 600+ 6y$

Solve for 6y

$6y = 3600 - 600$

$6y = 3000$

Solve for y

$y = 3000/6$

$y = 500$

Hence:

The point is:

$C = (30,500)$

7 0

3 years ago

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 blanket per d

Sauron [17]

Answer:

Since Darcie wants to crochet a minimum of 3 blankets and she crochets at a rate of 1/5 blanket per day, we can determine how many days she will need to crochet a minimum of 3 blankets following the next steps:

- Finding the number of days needed to crochet one (1) blanket:

\begin{gathered}1=\frac{1}{5}Crochet(Day)\\Crochet(Day)=5*1=5\end{gathered}

Crochet(Day)

Crochet(Day)=5∗1=5

So, she can crochet 1 blanket every 5 days.

- Finding the number of days needed to crochet three (3) blankets:

If she needs 5 days to crochet 1 blanket, to crochet 3 blankets she will need 15 days because:

\begin{gathered}DaysNeeded=\frac{NumberOfBlankets}{Rate}\\\\DaysNeeded=\frac{3}{\frac{1}{5}}=3*5=15\end{gathered}

DaysNeeded=

Rate

NumberOfBlankets

DaysNeeded=

=3∗5=15

- Writing the inequality

If she has 60 days to crochet a minimum of 3 blankets but she can complete it in 15 days, she can skip crocheting 45 days because:

AvailableDays=60-RequiredDaysAvailableDays=60−RequiredDays

AvailableDays=60-15=45DaysAvailableDays=60−15=45Days

So, the inequality will be:

s\leq 45s≤45

The inequality means that she can skip crocheting a maximum of 45 days since she needs 15 days to crochet a minimum of 3 blankets.

Have a nice day!

3 0

3 years ago

One third of a number t is equal to 7

Novosadov [1.4K]

7 / 1/3
therefore
21 x 1/3= 7

3 0

3 years ago

Read 2 more answers

Brian is finishing a meal at his favorite restaurant. The check shows that the cost of the food is 42 dollars. He adds a 15% tip

Serga [27]

$42 \times (100\% + 15\%) \\ = 42 \times 115\% \\ = 48.3$

Total amount of Brian paid is $48.30.

Hope this helps. - M

6 0

3 years ago

Read 2 more answers