The complex number z = –1 + 3i can be expressed in trigonometric form as:

The Complex Number Z = 1 + 3i Can Be Expressed In Trigonometric Form As:
The Complex Number Z = 1 + 3i Can Be Expressed In Trigonometric Form As:
The Complex Number Z = 1 + 3i Can Be Expressed In Trigonometric Form As:
The Complex Number Z = 1 + 3i Can Be Expressed In Trigonometric Form As:

Answers

Answer 1
[tex]\bf z=\stackrel{a}{-1}\stackrel{b}{+3}i\qquad \begin{cases} r=\sqrt{a^2+b^2}\\ \theta =tan^{-1}\left( \frac{b}{a} \right) \end{cases}\qquad \qquad z=r[cos(\theta )i~sin(\theta )]\\\\ -------------------------------\\\\ r=\sqrt{(-1)^2+3^2}\implies r=\sqrt{10} \\\\\\ \theta =tan^{-1}\left( \frac{3}{-1} \right)\implies \theta \approx -71.57\implies \theta \approx\stackrel{360-71.57}{288.43^o}\\\\ -------------------------------\\\\ z=\sqrt{10}\left[ cos(288.43^o)+i~sin(288.43^o) \right][/tex]

now, the calculation in the choices, show 289.5°, which I take it is due some early rounding up.

Related Questions

Compare the decimals 17.20 and 17.2. Which comparison is correct? A. 17.20 > 17.2 B. 17.20 < 17.2 C. 17.20 = 17.2

Answers

Hello!

I believe the correct answer is C. 17.20 = 17.2

Hope this helps! ☺♥
Compare the decimals 17.20 and 17.2. Which comparison is correct?

c) 17.20 = 17.2


He for got his pin code. 20% of his pin code was 246.8. What was his pin code?

Answers

So if 20% of his pin code was 246.8, then we want to know 5 times that since 20% * 5 = 100%.

So 246.8 * 5 = 1234

So his pin was 1234.

The Mississippi River is about 4,000 kilometers long. An M&M is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Estimate how many M&Ms it would take to measure the length of the Mississippi River

Answers

To be able to determine the number of M&Ms that are needed in order to measure the length of Mississippi River, we convert the units to a common one. For this purpose, we convert kilometers to centimeter such that,
 
Length of Mississippi River = (4000 km)(1000 m/1 km)(100 cm/1 m)
                       = 400,000,000 cm

Since there are 400,000,000 cm in the entire length of the river, the answer would also be 400,000,000. 

To measure the approximately 4,000 km long Mississippi River with M&Ms, we will need about 400,000,000 M&Ms, as there are 100 cm in a meter and 1,000 m in a km.

The question involves estimating the length of the Mississippi River using the size of M&Ms as a unit of measurement. Since the river is about 4,000 kilometers long and the standard unit of length in the SI system is the meter, we need to convert kilometers to centimeters to match the size of an M&M, which is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Therefore, we have:

Convert kilometers to meters: 4,000 km x 1,000 m/km = 4,000,000 m.Convert meters to centimeters: 4,000,000 m x 100 cm/m = 400,000,000 cm.

Now, since each M&M is 1 centimeter, the number of M&Ms needed to measure the length of the Mississippi River is equal to the total number of centimeters:

400,000,000 M&Ms would be required to measure the approximate length of the Mississippi River.

Can anyone help me Plot a parabola through the points? Cause i dont understand what to do

Answers

There are youtube videos on how to this operation. :)
Since the vertex is (0,0), and the parabola passes through -1 and +1, then it opens upward with a minimum of (0,0).

Join the Vetex to -1 and + 1 It will have the shape of U

5 less than a third of a number is at most 15

Answers

1/3x - 5 < = 15 ...this is ur inequality

***
5 less....- 5
1/3 of a number....1/3x
so 5 less then 1/3 of a number....1/3x - 5
is at most 15....means it can be 15 or less.....< = 

calculate the cost of fuel. 40 L at 65.7cents/L

Answers

26 dollars and 28 cents

$26.28 
Multiply 65.7 × 40 = 2,628 
Then add the decimal between 26 and 28

A relation is plotted as a linear function on the coordinate plane starting at point E at
(0, 27)
and ending at point F at
(5, −8).

What is the rate of change for the linear function and what is its initial value?

Answers

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 0}} &,&{{ 27}}~) % (c,d) &&(~{{ 5}} &,&{{ -8}}~) \end{array} \\\\\\ % slope = m \stackrel{\stackrel{average}{rate~of~change}}{slope}= {{ m}}\implies \cfrac{\stackrel{rise}{{{ y_2}}-{{ y_1}}}}{\stackrel{run}{{{ x_2}}-{{ x_1}}}}\implies \cfrac{-8-27}{5-0}\implies \cfrac{-35}{5}\implies -7[/tex]

well, when x = 0, namely at the very beginning, y = 27, thus, that IS the initial value.

The rate of change and the initial value are given as -5 and 27 respectively.

How to represent a straight line on a graph?

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

Given that,

The points for the given linear function are given as (0, 27) and (5, -8) respectively.

The rate of change is equivalent to the slope of the straight line and is given as,

(-8 - 27)/(5 - 0) = -35/7 = -5

Now, the equation of the function can be written as,

(y - 27)/(x - 0) = -5

=> y - 27 = -5x

=> y = -5x + 27

The initial value is given at x = 0 as below,

y = -5 × 0 + 27

  = 27

Hence, the rate of change for the function is -5 and its initial value is 27.

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please help me, solve for y 2x-y=5

Answers

2x−y=5

Add -2x to both sides.

2x−y+−2x=5+−2x

−y=−2x+5

Divide both sides by -1.

[tex] \frac{-y}{-1} = \frac{-2x+5}{-1} [/tex]
‌y=2x−5

Answer:

y=2x−5

What expression is equivalent to x^2+2x-24/3x+18

Answers

The equivalent expression to [tex]x^2 + 2x - 24 / (3x + 18([/tex] is (x - 4) / 3, after factoring and simplifying the common terms.

The question is asking for an expression equivalent to [tex]x^2 + 2x - 24 / (3x + 18[/tex].

This expression can be factored and simplified.

First, notice that the quadratic expression in the numerator can be factored into (x + 6)(x - 4).

Similarly, the denominator can be factored as 3(x + 6). After factoring, we have:

= (x + 6)(x - 4) / 3(x + 6)

We can now simplify the expression by canceling out the common factor of (x + 6):

= (x + 6)(x - 4) / 3(x + 6) = (x - 4) / 3

So the equivalent expression is (x - 4) / 3.

110% of 90 is what number a?
What does is a?

Answers

Hello!

110% of 90 is: 99.

I hope this was helpful! c:

HELP!!! A pentagonal pyramid is sliced parallel to its base. what shape does it make?

Answers

pentagonal
same as the base

The cross section formed would also turn out to be a pentagon. 

Good luck! =D

What is cos θ if sec θ = 2?

Answers

[tex]\bf cos(\theta)=\cfrac{1}{sec(\theta)}\qquad \qquad \boxed{sec(\theta )=2}\implies cos(\theta)=\cfrac{1}{\boxed{2}}[/tex]

Answer:

the value of cos θ is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

Since, [tex] cos\theta=\frac{1}{sec\theta}[/tex]

we are given with sec θ = 2

To find the value of cos θ , we use this fact [tex] cos\theta=\frac{1}{sec\theta}[/tex]

put sec θ = 2 in [tex] cos\theta=\frac{1}{sec\theta}[/tex]

[tex] cos\theta=\frac{1}{2}[/tex]

Therefore, the value of cos θ is [tex]\frac{1}{2}[/tex].

A bicycle went 120 miles in 5 hours. A motorcycle is three times as fast as the bicycle. Find the speed of motorcycle.

Answers

If the bicycle went 120 miles in 5 hours, and the motorcycle was three times as fast as the bicycle, then the motorcycle went 480 miles in 5 hours.

Answer:

Step-by-step explanation:

120 x 5 = 600

The motorcycle is 3 times as fast.

600 x 3 = 1800

A 6-ounce can of frozen juice costs 84. Give the unit price in cents per ounce.

Answers

Write out the "rate" as follows:      84 cents / 6 ounces

Then reduce 84/6:      84/6 cents/oz  =  18 cents/oz   (answer)

Simply (8xto4) (4x to 3) \ 7x to 2

Answers

32x^5/7 This is the answer for that equation.

If you are adding two fractions that are both less than 1/2, What must be true about the sum? Give three examples to support your thinking.

Answers

if both fractions are less than  1/2 then the sum has to be less than 1

1/8 + 3/8 = 4/8 = 1/2 , less than 1

7/16 + 1/4 = 11/16, less than 1

3/16 + 1/16 = 4/16 = 1/4, less than 1

First assume that the fractions are all positive.
Next, add 1/2 and 1/2; the sum is 1.  Thus, the two fractions must each be smaller than 1/2.

Let's try adding 5/16 and 7/16.  Both are smaller than 1/2.  Their sum is 12/16, or 3/4, which is less than 1.

Choose a couple other pairs of fractions which are between 0 and 1/2.  Then find the sum of each pair.  What do you observe about the size of these sums?

Which expression shows the result of applying the distributive property to 3(2x−6) ?

A. 2x−18
B. 6x−18
C. 6x−6
D. 5x−3

Answers

Your answer would be B. You have to multiply the 3 and 2 which is 6 then put the x so 6x. then your multiply 3 and 6 and get 18 so it would be 6x-18.

Answer:

b

Step-by-step explanation:

a pail hold 6 3/4 gallon of water. how much is this in cups

Answers

there are 16 cups in 1 gallon so you would have to turn the denominator in the fraction into a 16 meaning you would multiply by 4 (because 4 goes into 16, 4 times). Your new fraction is 12/16. now you do 6 gallons*16 cups and you get 96 cups. Then you add the fraction onto 96 and you would be adding 12. Your final answer is 108 cups in 6 3/4 gallons

The required, there are 108 cups of water in the pail as a pail hold 6 3/4 gallon of water.

What is a unit of measurement?

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,
To convert 6 3/4 gallons to cups, we can use the fact that there are 16 cups in one gallon.

So, we can start by multiplying 6 (the number of whole gallons) by 16 to get the number of cups in those gallons:

6 gallons × 16 cups/gallon = 96 cups

Next, we need to convert the 3/4 of a gallon to cups. To do this, we can multiply the fraction by the number of cups in one gallon:

3/4 gallon × 16 cups/gallon = 12 cups

So, the total amount of water in the pail is:

96 cups + 12 cups = 108 cups

Therefore, there are 108 cups of water in the pail.

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Over a two hour time period a snail moved 76 inches. How far is this in yards? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.

Answers

Final answer:

The snail moved a total distance of 2 1/9 yards after converting 76 inches to yards using the conversion factor of 1 yard equals 36 inches.

Explanation:

To convert the distance a snail moved from inches to yards, we use the conversion factor that 1 yard equals 36 inches. Given that the snail moved 76 inches, we divide this number by 36 to find the distance in yards.

76 inches ÷ 36 inches/yard = 2 yards and 4 inches.

Since there are 36 inches in a yard, the remaining 4 inches must be converted to a fraction of a yard by dividing by 36:

4 inches ÷ 36 = 1/9 yard.

Therefore, the snail moved 2 yards and 1/9 yard, or 2 1/9 yards in total.

17 ÷ 4520= what is the product

Answers

265 Remainder 15. That is, if you flip the divisor and the dividend around.

The student's question is related to dividing 17 by 4520. This is performed by a straight division resulting in a small decimal quotient, not a product. The calculation is best done using a calculator and rounding to the proper number of significant figures.

The equation given, 17 by 4520, is asking for the result of dividing 17 by 4520. To compute this, we simply perform the division, recognizing that since 4520 is much larger than 17, the answer will be a very small decimal value. The term 'product' in the student's question seems to be a mistake, as they are likely referring to the quotient obtained from the division.

When attempting to perform the computation mentally and simplify the process, one might attempt to find numbers that are more easily divisible or apply scientific notation to simplify calculations, much like re-expressing numbers to make them more manageable. However, for this division, no mental math trick simplifies it effectively, and using a calculator might be the best option.

When going through this process, it is also important to consider significant figures when giving the final answer, rounding as necessary based on the precision of the data provided.

The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. For the next few hours, the temperature drops 2 degrees every hour.Which equation represents the temperature, t, at hour h?

Answers

Answer: We find the equation that represents the temperature (t) at hour (t) using the slope-intercept form and it is:

t = -2 h + 32


Solution:

The temperature, t, in Burrtown starts at 32°F at midnight, when h = 0. This represents the y-interception of the right line, when h=0 hours, t=32 °F:

Point=(h,t)→Point=(0,32)=(0,b)→b=32

For the next few hours, the temperature drops 2 degrees every hour. This represents the slope of the line (m): m=-2, negative because the temperature drops.

Slope-Intercept form:

y=mx+b; y=t, m=-2, x=h, b=32

Replacing the values:

t=-2h+32


Answer:

t=-2h+32

Step-by-step explanation:

The sides of a triangle measure 76 mm, 8 CM, and 10 CM..What is the lengths of the two shorter sides

Answers

The two shorter sides are 76 mm and 8 cm(80 mm)

hich sentence is a run-on sentence?


A.
Dogs and hamsters are both fun pets, they relate to people in different ways.


B.
Dogs enjoy human contact; they love to fetch and chase.


C.
My hamster likes to run in his wheel, and he does not like to be held.


D.
When I try to pick up my hamster, he looks for a place to hide.

Answers

Hello!

This question has been asked under the weong subject, but I'll answer anyway.

The correct answer, I believe, would be: A. Dogs and hamsters are both fun pets, they relate to people in different ways.

I really hope this helped you out! :)

factor the expression 10x−25y

Answers

5(2x-5y) is the answer to this expression

Final answer:

To factor the expression 10x-25y, we find the greatest common factor, which is 5, and write the expression as 5(2x - 5y).

Explanation:

To factor the expression 10x−25y, we need to find the greatest common factor (GCF) that both terms share. In this case, both terms are divisible by 5. When we factor out the GCF, we get:

Identify the GCF of 10x and 25y, which is 5.

Divide both terms by the GCF: 10x/5 = 2x and 25y/5 = 5y.

Write the factored expression: 5(2x - 5y).

Thus, the expression 10x−25y factored is 5(2x - 5y)

A bus can carry 50 people per run. At least how many times does the bus have to run in order to transfer 25,000 people?

Answers

500 times, to transfer 25,000 people. Let me know if this helped.
500 times is the answer

A recipe makes 6 2/3 cups the serving size is 5/6 cup how many servings does the recipe make

Answers

ithe recipe makes precicely 8 servings,i hope this helps

The recipe can make serving 8 cups.

What is  multiplication?

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

A recipe makes 6 2/3 cups

                         =20/3 cups

And, the serving size is 5/6 cup

So, the recipe can make serving = 20/3÷ 5/6 cups

                                                      =20/3 × 6/5 cups

                                                      =8 cups

Hence, the recipe can make serving 8 cups.

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An m-bit password is required to access a system. a hacker systematically works through all possible m-bit patterns. let x be the number of patterns tested until the correct password is found. find the conditional pmf of x given that the password has not been found after k tries

Answers

Final answer:

The conditional pmf of x, the number of patterns tested until the correct m-bit password is found, given that the password has not been found after k tries, is uniformly distributed with 1/(2^m - k) for x = k+1, k+2, ..., 2^m.

Explanation:

The question deals with the topic of probability and specifically centers around the concept of a conditional probability mass function (pmf). Given that an m-bit password is systematically being guessed by a hacker and has not been found after k attempts, we need to find the conditional pmf of x, where x is the number of patterns tested until the password is found.

Since the password has not been guessed within the first k tries, the conditional probability is based on the remaining 2m - k possibilities. The distribution of x will be uniform because each subsequent attempt has an equal probability of being correct. The conditional pmf of x given that the password was not found after k tries is 1/(2m - k) for x = k+1, k+2, ..., 2m.

Evaluate each expression. Click on undefined as needed

Answers

if the 0 is in the numerator, the value is 0
if the 0 is in the denominator, the value is undefined

so 0/8 = 0
and 3/0 = undefined

suppose you deposit $25,000 in to a fund for which the annual interest rate is 5.3% compounded continuously. find the number of years it will take to double in value (round your answer to the nearest tenth of a year)

Answers

so, the principal is 25,000, when it double then, the accumulated amount is 50,000.

[tex]\bf \qquad \textit{Continuously Compounding Interest Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &\$50000\\ P=\textit{original amount deposited}\to& \$25000\\ r=rate\to 5.3\%\to \frac{5.3}{100}\to &0.053\\ t=years \end{cases} \\\\\\ 50000=25000e^{0.053t}\implies \cfrac{50000}{25000}=e^{0.053t}\implies 2=e^{0.053t} \\\\\\ ln(2)=ln(e^{0.053t})\implies ln(2)=0.053t\implies \cfrac{ln(2)}{0.053}=t \\\\\\ 13.0782486898102888\approx t\implies 13.08\approx t[/tex]

For a normal distribution, the proportion in the tail beyond z = 0.30 is p = 0.1179.
a. True
b. False

Answers

they tricked me into signing into this site to get the answer, oonly to find out they didnt have it answered, click b8

Using the normal distribution, it is found that the statement is False, thus the correct option is b.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The area on the tail beyond z is the proportion that is above z, that is, 1 subtracted by the p-value of z.

For this problem, z = 0.3 has a p-value of 0.6554.

1 - 0.6554 = 0.3446

The proportion in the tail beyond z = 0.30 is p = 0.3446, thus, the statement is False.

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