Answers
The complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6). (Correct choice: C)
How to transform a complex number in rectangular form into polar formComplex numbers are elements of the form z = a + i b, where [tex]a, b \in \mathbb{R}[/tex]. In other words, represents a generalization from real numbers. The polar form of a complex number is shown below:
[tex]z = r\cdot (\cos \theta + i \,\sin \theta)[/tex] (1)
Where:
r - Normθ - Direction, in radians.The norm is determined by Pythagorean theorem and the direction by inverse trigonometric reason. If we know that z = (5√3 / 4) - i 5/4, then its polar form is shown below:
Norm
[tex]r = \sqrt{\left(\frac{5\sqrt{3}}{4} \right)^{2}+\left(-\frac{5}{4} \right)^{2}}[/tex]
r = 5/2
Direction
[tex]\theta = \tan^{-1} \left[\frac{\left(-\frac{5}{4} \right)}{\left(\frac{5\sqrt{3}}{4} \right)} \right][/tex]
θ = 11π/6 rad
Thus, the complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6).
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Related Questions
3 divided by 3.40 i am sorry
Answers
If the diameter of a youth softball is 3.5 inches and the diameter of an adult softball is 3.8 inches, what is the approximate difference in their volumes? use 3.14 for pi. round to the nearest tenth of a cubic inch. recall the formula sphere volume = four-thirds pi r cubed. 6.3 cubic inches 51.1 cubic inches 67.0 cubic inches 409.2 cubic inches
Answers
Answer:
A because the volume of the adult softball is 28.7309120146 inches and the youth softball is 22.4492975038 inches and when u subtract them u get about 6.3 cubic inches :)
Step-by-step explanation:
:)
Answer: IT A!
Step-by-step explanation:
Choose the best definition for the following phrase: combining like terms (1 point)
Group of answer choices
A letter that holds the place for some unknown value in mathematics
A process where you must look for terms that have identical variable parts and then combine their coefficients
A process where if two things are equal, one can be put in the place of the other and nothing will change
Terms that have identical variable parts
Answers
Answer:
A process where you must look for terms that have identical variable parts and then combine their coefficients
Step-by-step explanation:
Combining like terms is adding or subtracting terms that have the same variable parts.
Answer: A process where you must look for terms that have identical variable parts and then combine their coefficients
A rectangular patio is 9 ft by 6 ft. when the length and width are increased by the same amount, the area becomes 88 sq ft. ginger is using the zero product property to solve the equation (6 x)(9 x) = 88. what does the value of x in her solutions represent?
Answers
Answer:
x=2
9+2=11
6+2=8
8x11+88
Step-by-step explanation:
We can use radicals if needed, and we need to simply.
Answers
Answer:
x = √41 which is 6.40 to the nearest hundredth.
Step-by-step explanation:
x^2 = 4^2 + 5^2 (By the Pythagoras theorem)
x^2 = 16 + 25 = 41
x = √41.
In a word game, 1 letter is worth 1 point. this dot plot shows the scores for 20 common words.what is the median score? pointswhat is the first quartile (q1)?
points
what is the third quartile (q3)?
points
what is the interquartile range (iqr)?
Answers
The median is 6.5.
The first quartile is 5.
The third quartile is 8.
The interquartile range is 3.
What are the statistics of the data plot?The numbers in the dot plot are: 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 22
Median is the number in the middle of the dataset.
Median = 1/2 ( n + 1)
1/2 x 21 = 11.5th number = (6+ 7) / 2 = 6.5
First quartile = 1/4 x (n + 1)
1/4 x 21 = 5.25th number = 5
Third quartile = 3/4 x (n + 1)
3/4 x 21 = 15.75th number = 8
Interquartile range = 8 - 5 = 3
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please help meeee, much appreciated!!!!!!
Answers
Answer:
expected value is $4.5
Step-by-step explanation:
expected value is $4.5
The question is in the picture.
Answers
Answer:
x² - 22x + y² + 18y + 58 = 0
Step-by-step explanation:
Using the equation of a circle :
(x - h)² + (y - k)² = r²
Solving :
Substitute 11, -9, 12 in place of h, k and r respectively.
(x - 11)² + (y + 9)² = (12)²x² - 22x + 121 + y² + 18y + 81 = 144x² - 22x + y² + 18y + 202 = 144x² - 22x + y² + 18y + 58 = 0Zahara asked the students of her class their gymnastic scores and recorded the scores in the table shown below:
Gymnastic Scores
Score Number of Students
0 1
1 1
2 2
3 6
4 4
5 3
6 2
Based on the table, what is the mean gymnastic score? (1 point)
2.5
3.5
5.2
9.4
Answers
Answer:
B. 3.5
Step-by-step explanation:
I believe this is correct :')
Measure the angle shown below.
a protractor showing an angle going through the fifteenth tick mark after two hundred sixty five degrees
272°
275°
279°
280°
Answers
The measure of the angle shown is 280°
Calculating anglesFrom the question, we are to determine the measure of the angle shown
For the given protractor,
The measure between any two lines is 10°.
Also, there are 10 tick marks between any two lines.
∴ 15 tick marks will have a measure of 15°
Then,
The measure of a protractor showing an angle going through the fifteenth tick mark after two hundred sixty five degrees will be
265° + 15° = 280°
Hence, the measure of the angle shown is 280°
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Please help me with this PROBABILITY question! I'm really stuck and would really appreciate your help.
Please don't post nonsense answers and I'd love it if you could add working out.
Thanks :))
Answers
Answer: The probability of picking a black bead is 4/7, because there are 4 black beads out of seven. But if you took the first black bead out of the equation then the probability is now 3/7.
Colin gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many cola bottles as smarties. He also picks twice as many smarties as marshmallows. What proportion of the bag of sweets are cola bottles?
Give your answer in its simplest form.
Answers
The simplest form of the proportion is 2/3
here , it is give that colin picks 3 times as many cola bottles as smarties and twice as many smarties as marshmallows. To simplify this let us suppose colin pic a number of marshmallows then number of smarties he pic will be 2a and also the number of cola bottles will be 6a.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Therefore, the proportion of the bag of sweets are cola bottles will be :
[tex]\begin{aligned}\frac{6a}{a+2a+6a}&=\frac{6}{9}\\&=\frac{2}{3}\end{aligned}[/tex]
Therefore, The simplest form of the proportion is 2/3
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what is 9x7 equal to i been stuck
Answers
Answer:
9x7=63
Step-by-step explanation:
just use a calculator for multiplication
The product of 9 and 7 is 63. In other words, the result of multiplying 9 and 7 is 63.
To find the result of multiplying 9 and 7, by follow a step-by-step process.
First, start by writing the multiplication expression as 9 multiplied by 7.
Next, multiply the digit in the ones place of the first number (9) with the digit in the ones place of the second number (7).
In this case, 9 multiplied by 7 equals 63.
Then, move to the tens place of the second number (7) and multiply it with the digit in the ones place of the first number (9).
Since there is no digit in the tens place of the first number, skip this step.
Finally, add the products obtained from the previous steps.
In this case, there is only one product, which is 63.
Therefore, the result of multiplying 9 and 7 is 63.
Multiplication is a fundamental arithmetic operation used to determine the total value when a number is repeated a certain number of times. In this case, multiplying 9 by 7 represents adding nine 7s together.
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solve the quadractic formula 3x+x-3=0
Answers
Answer: x = 0.75
Step-by-step explanation:
3x+x - 3 =0
4x - 3=0
4x = 3
x = 0.75
Process:
4x-3=0
4x=3
X=3/4
Decrease £40 by 25%
(Hegarty maths)
Answers
Answer:
the answer to your question is 10
Step-by-step explanation:
if you divide 40 by 25% then you will get 10
Expand and simplify
4(2x + 3) + 4(3x + 2)
Answers
Answer: 20x + 20
Step-by-step explanation:
We will distribute the four into the expressions to expand, then we will simplify.
Given:
4(2x + 3) + 4(3x + 2)
Distribute:
8x + 12 + 12x + 8
Combine like terms with addition:
20x + 20
20x + 20
Nathan has 40 coins.Of coins,1/5 are nickels,1/5 are dimes,and the rest are quarters.What Is the ratio of Nathan’s nickels to dimes to quarters?
Answers
The ratio of Nathan's nickels to dimes to quarters is 4 : 4 : 17.
What is the ratio ?Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).
Number of dimes = 1/5 x 40 = 8 Number of nickels = 1/5 x 40 = 8 Number of quarters = 40 - 8 - 8 = 34The ratio = 8 : 8 : 34 = 4 : 4 : 17
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Find the measures of angles a=(2x+3) and b=(2x-3),if their sum is 120 degrees
Answers
Answer:
angle A is 63 degrees,
angle B is 57 degrees
Step-by-step explanation:
first, let's create the equation. Pretty simple, because angles a and b become 120 degrees when added up, this this will become:
2x+3+2x-3=120
now, we make it simpler. In this case, just add up the numbers that we can add up. this eventually becomes:
4x=120
now, all we need to do is divide 120 by 4, which becomes 30. So, x=30.
substitute the 30 into the x in the original equation, and this becomes:
60+3+60-3=120
63+57=120
thus, angle A is 63 degrees, and angle b is 57 degrees.
Please help me thanks!!!
Answers
Problem 9
r+h = 9
SA = 2*pi*r^2 + 2*pi*r*h = 54pi
2*pi*r^2 + 2*pi*r*h = 54pi
2pi*r(r + h) = 54pi
r(r+h) = 27
r(9) = 27
9r = 27
r = 27/9
r = 3
r+h = 9
h = 9-r
h = 9-3
h = 6
Answers: r = 3 and h = 6 are the radius and height respectively.
==========================================================
Problem 10
d = diameter = 68 mm
r = radius = d/2 = 68/2 = 34 mm
SA = surface area of a sphere
SA = 4*pi*r^2
SA = 4*pi*34^2
SA = 4264pi
Answer: 4264pi square mm
==========================================================
Problem 11
Plug V = 3000 into the sphere volume formula and isolate r.
V = (4/3)pi*r^3
3000 = (4/3)pi*r^3
(4/3)pi*r^3 = 3000
4pi*r^3 = 3*3000
4pi*r^3 = 9000
r^3 = 9000/(4pi)
r = cube root( 9000/(4pi) )
r = ( 9000/(4pi) )^(1/3)
r = 8.947002 approximately
Now we can determine the surface area of this sphere.
SA = 4pi*r^2
SA = 4*pi*( 8.947002 )^2
SA = 1005.923451
Answer: 1005.923451 square feet approximately
==========================================================
Problem 12
We'll follow the same idea as problem 11, but in reverse.
SA = 4*pi*r^2
400pi = 4pi*r^2
r^2 = (400pi)/(4pi)
r^2 = 100
r = sqrt(100)
r = 10
Luckily we get a nice whole number for the radius r. Use it to find the volume.
V = (4/3)*pi*r^3
V = (4/3)*pi*10^3
V = (4000/3)pi
Answer: (4000/3)pi cubic inches exactly
==========================================================
Problem 13
The diagram is missing. I don't have enough info to be able to answer.
19. What are equivalent statements to a + 3 = 18 and 4 b = 32?
a = 18-3 and b = 32/4
a=18/3 and b = 32/4
a = 18/3 and b = 32-4
a = 18-3 and b = 32 - 4
Answers
Answer:
The choice second . a=18/3 and b = 32/4
Step-by-step explanation:
[tex]a + 3 = 18 \\ a = 18 - 3[/tex]
[tex]4b = 32 \\ \\ b = \frac{32}{4} [/tex]
24. Taylor wants to purchase an $80 purse. She has
found three stores that have the purse originally priced
at $80 but are offering 3 different sales this weekend:
1
●
Store A: off original price
• Store B: 10% off original price
Store C: $15 off original price
Which of the following is a true statement?
Answers
Answer:
we need the full question
Tom opens a bank account and makes an initial deposit of 500$. Then banker tells Tom that he is going to receive an annual rate of 6% on his investment. Find the bank balance assuming Tom leaves the account untouched for 15 years. (Will give brainliest to the person who has the answer correct and will shown work.)
Answers
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=500\left(1+\frac{0.06}{1}\right)^{1\cdot 15}\implies A=500(1.06)^{15}\implies A\approx 1198.28[/tex]
. Triangle EFG has vertices E(-2, 1), F(-1, 4), and G(3, 4). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then write the coordinates of triangle E'F'G'.
Answers
Triangle EFG has vertices E(-2, 1), F(-1, 4), and G(3, 4). Graph the figure and its image after a clockwise rotation of 90° about vertex F. Then write the coordinates of triangle E'F'G'.
given set P={3,6,9}.How many subset can be formed
Answers
Answer:
8
Step-by-step explanation:
[tex]P = \{3,6,9\}\\\\\text{Number of elements,}~ n = 3\\\\\text{Number of subset} = 2^n = 2^3 = 8[/tex]
What is the polynomials of (2x^2-x+1)(x-3)
Answers
Answer:
2x^3 - 7x^2 + 4x - 3
Step-by-step explanation:
Multiply them all together.
Please help !!!!!!!!!!
Answers
Answer:
the third option in the list
Step-by-step explanation:
the numbers down below qre the coefficients of the equations above
x/9+3<4 what is the solution to the ineqaulity
Answers
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the solution to the inequality:
[tex]\star~\large\pmb{\cfrac{x}{9}+3 < 4}[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
First, subtract 3 from both sides, then multiply both sides by the denominator.Step 1.
[tex]\star~\large\pmb{\cfrac{x}{9} < 4-3}[/tex]
[tex]\star~\large\pmb{\cfrac{x}{9} < 1}[/tex]
Step 2.
[tex]\star~\large\pmb{\cfrac{x}{9}\times9 < 1\times9}[/tex]
Notice that on the left, the 9s cancel, and we're left with x.
Step 3.
[tex]\star~\large\pmb{x < 9}[/tex]
This is the solution.
Hope it helps you out! :D
Ask in comments if any queries arise.
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Answer:
x < 9
Step-by-step explanation:
Given:
[tex]\dfrac{x}{9} + 3 < 4[/tex]
1. Subtract 3 from both sides of the inequality
[tex]\dfrac{x}{9} + 3 - 3 < 4 - 3\\\\\implies\dfrac{x}{9} < 1[/tex]
2. Multiply both sides of the inequality by 9
[tex]9\left(\dfrac{x}{9}\right) < 1(9)\\\\\implies x < 9[/tex]
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Graph the lines that represent the following system of linear equations.
2s +1.5y = -60
2s + y = -50
Answers
The lines that represent the following system of linear equations.
2s +1.5y = -60
2s + y = -50
will intersect at (-15, -20)
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
Slope is a ratio of change in y-coordinate w.r.t. change in x-coordinate. The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.
Given,
System of linear equations
2s +1.5y = -60
2s + y = -50
After plotting both the graphs we can see that, point of intersection is (-15, -20)
Hence, The point of intersection is (-15, -20)
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1/2x +3x = 14
steps?
Answers
Step-by-Step Explanation:
=> 1/2x + 3x = 14
x/2 + 3x = 14 (Take 2 as LCM)
x/2 + 6x/2 = 14 (Now, shift 2 to RHS)
x + 6x = 14 * 2
x + 6x = 28
7x = 28
x = 28/7
=> x = 4
Therefore, x = 4
Answer: Heyaa! ~
Your Answer would be.. =4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.Convert the integer into a fraction:Combine the fractions:Combine the numerators:Multiply both sides by inverse fraction 2/7:Group like terms:Simplify the fraction:Multiply the fractions:Simplify the arithmetic:Hopefully this helps you ! ^^
√(2-x)-√(1-4x)=1
solve for x
Answers
Answer:
decimal form; 0.22222...
exact form; 2/9
Step-by-step explanation: