Answer:
a) The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex], b) [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].
Step-by-step explanation:
a) The standard form of the complex number is [tex]z = a + i\cdot b[/tex], [tex]\forall \,a,b \in \mathbb{R}[/tex]. If we get that [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex], whose standard form is obtained by algebraic means:
1) [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] Given
2) [tex]z = (4\cdot \cos 60^{\circ})+i\cdot (4\cdot \sin 60^{\circ})[/tex] Distributive and Associative properties.
3) [tex]z = 2 + i\cdot 2\sqrt{3}[/tex] Multiplication/Result.
The standard form of [tex]z = 4\cdot (\cos 60^{\circ}+i\cdot \sin 60^{\circ})[/tex] is [tex]z = 2 + i\cdot 2\sqrt{3}[/tex].
b) The De Moivre's Theorem states that:
[tex]z = (a+i\cdot b)^{n}= r^{n}\cdot (\cos \theta + i\cdot \sin \theta)[/tex]
Where:
[tex]r =\sqrt{a^{2}+b^{2}}[/tex] and [tex]\theta = \tan^{-1} \left(\frac{b}{a}\right)[/tex].
If we know that [tex]z = (2+i\cdot 3)^{6}[/tex], then:
[tex]r = \sqrt{2^{2}+3^{2}}[/tex]
[tex]r =\sqrt{13}[/tex]
[tex]r \approx 3.606[/tex]
[tex]\theta = \tan^{-1}\left(\frac{3}{2} \right)[/tex]
[tex]\theta \approx 56.310^{\circ}[/tex]
The resulting expression is:
[tex]z = 3.606^{6}\cdot (\cos 56.310^{\circ}+i\cdot \sin 56.310^{\circ})[/tex]
[tex]z = 1219.585+i\cdot 1829.381[/tex]
Therefore, [tex]z = (2+i\cdot 3)^{6} = 1219.585 + i \cdot 1829.381[/tex].
Help me plzzz 100pts
Answer:
Yen, Hana, Tyrell
Step-by-step explanation:
took on edge 2020
If you get this you are a critical thinker.
I enter the garden.
There are 34 people.
You kill 30.
How many people are in the garden.
Answer:
5
Step-by-step explanation:
If you killed 30 and there were 34 people there not including me then there would be 5 left.
How to solve this problem
Answer: [tex]\sqrt100=10[/tex]
Step-by-step explanation:
[tex]\sqrt[n](-4-4)^{2} +(-3-3)^{2} \\\sqrt64+36\\\sqrt100\\=10[/tex]
Rozalie spent $26.75 at a parking garage in downtown Orlando. The garage charged a base fee of $7.50 for the first hour, and an hourly rate of $2.75 for each additional hour. The following sign is displayed to show the prices for the first 4 hours.
Answer:
Rozalie spent 7 hours at the parking garage.
Step-by-step explanation:
The equation for the above Question can be given as:
$7.5 + 2.75x
Where x = hourly rate
We are told that Rozalie spent $26.75
The number of hours Rosalie spent at the parking garage is calculated as:
$7.5 + 2.75x = $26.75
2.75x = $26.75 - $7.5
2.75x = 19.25
x = 19.25/2.75
x = 7 hours
Therefore the number of hours Rozalie spent at the parking garage was 7 hours.
To which substance does ferredoxin transfer an electron? photosystem I photosystem II NADP+ NADPH
Answer:
NADP+
Step-by-step explanation:
Answer:
C. NADP+
Step-by-step explanation:
You spend $168 on materials to start a business making silk flower arrangements. Each arrangement sells for $12. You decide to create a linear graph to model the relationship between profit, P, and sales, x. Which statements are true about the graph?
Answer:
B) The graph models P(x) = 12x − 168.
C) The x-axis represents the number of sales.
D) The break-even point for the number of sales and profit is (14, 0)
Step-by-step explanation:
Answer:
B) The graph models P(x) = 12x − 168.
C) The x-axis represents the number of sales.
D) The break-even point for the number of sales and profit is (14, 0)
Step-by-step explanation:
The x-axis represents the number of sales.
The graph models P(x) = 12x − 168
The break-even point for the number of sales and profit is (14, 0)
The x-axis represents independent values, such as the number of sales.
Profit = 12(#sales) − cost of materials → P(x) = 12x − 168
0 = 12x − 168 → x = 14 → (14, 0) is the break-even point.
Debra bought 7 boxes of chocolates. Each box cost $9.55. How much did she spend?
Answer:
$66.85
Step-by-step explanation:
One box equals $9.55.
There are seven boxes, so multiply the $9.55 by 7 to get your answer:
7 × 9.55 = 66.85.
Debra spent $66.85 for all seven boxes of chocolates.
Identify the data set's level of measurement.
Ages of students in a statistic class
The ages of students in a statistic class is classified as a nominal data.
For the given statistics class, the age of the student is Nominal data in nature.
Nominal data are “labeled” data which can be divided into various groups that do not overlap.This type of data ar not measured or evaluated but are categorized into groups. Examples of nominal data include race, sex, age etc.Hence the ages of students in a statistic class is classified as a nominal data.
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Answer:
Question :Identify the data set's level of measurement.
Ages of students in a statistic class.
RatioOrdinalNominal Interval Answer :The ages of students in a statistic class is identify as a nominal data.
Additional Information :
Levels of measurement
There are 4 levels of measurement, which can be ranked from low to high:
Nominal : the data can only be categorized.Ordinal : the data can be categorized and ranked.Interval : the data can be categorized and ranked, and evenly spaced.Ratio : the data can be categorized, ranked, evenly spaced and has a natural zero.elena and emily are twins. together they have saved a total of $72. elena saves twice as much as emily. how much has each girl saved?
Answer:
Emily: 24 Elena:48
Step-by-step explanation:
el + em = 72
el = 2em
2em + em = 72
3em = 72
em = 24
el = 2*24 = 48
If this helped, please give brainliest
Evaluate 3 + 11t - 9u when t=9 and u=11
Answer:
3
Step-by-step explanation:
given
3 + 11t - 9u
if t = 9, and u = 11, substitute these numbers into the equation:
3 + 11(9) - 9(11)
= 3 + 99 - 99
= 3
Answer: 3
Step-by-step explanation:
3+11t-9u=3+11(9)-9(11)
=3+99-99
=102-99
=3
к L
-12 -9 -6 -3 0 3 6 9 12 15 18
What is KL?
Answer:
kl is a volume with sides that are equal
If the point K is over -9 and L is over 15 then the value of KL is 24.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
A number line is a horizontal line that has equally spread number increments.
On the number line K is over -9 and L is over 15
We need to find the distance of KL.
KL=OL-OK
Where the OL is 15 and OK is -9.
Now plug in these values in KL
KL=15-(-9)
When minus and minus are multiplied we get positive.
=15+9
Add fifteen and nine we get twenty four.
=24
Hence, if the point K is over -9 and L is over 15 then the value of KL is 24.
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Rachel wants to purchase a new I-Tablet on Black Friday for $450. Better Buy offers two
installment plans for purchasing this item.
Plan A: a fixed weekly payment of $25
Plan B: a $120 initial payment, followed by weekly payments of $5
After 12 weeks, how much money would Rachel spend on each plan?
A Plan A: $300; Plan B: $60
B Plan A: $300; Plan B: $180
C Plan B: $300; Plan A: $60
D Plan B: $300; Plan A: $180
Answer:
hmmmmm im not sure
Step-by-step explanation:
Answer:
C.plan B: $300;planA:$60
not completely sure this is the answer but I hope this helps
Step-by-step explanation:
ײ⅖ idkk
My teacher jst put this
Answer:
the answer is x 12/5
Step-by-step explanation:
helpppppp meeeee pleaseeeee
Answer:
B) -2 degrees
Step-by-step explanation:
If the temperature went down 10 degrees the equation you need to use is 8-10=x.
Once simplified/solved you will get -2
-2
In the morning it was 8 degrees celsius, and in the night it was 10 degrees lower. You are trying to find a number that's 10 degrees lower than 8. So you would do:
8-10
That would result in -2
Which of the following lines has a slope of -1?
Answer:
I do not see any lines
Step-by-step explanation:
Angel got a new phone with Verizon. They charged Angel $50 each month for service, plus an additional $15 per gigabyte of data used. Write an equation that models the total price of Angel's phone bill as 'y' based on the number of gigabytes used, 'x'.
Answer: 15y+50=x
Step-by-step explanation:
Which quadratic function opens up?
Y= -x^2+ 3
Y= -(x + 3)^2
Y= -3x^2
Y= x^2- 3
Answer:
y = x^2 - 3
Step-by-step explanation:
Quadratic function in general form:
y = ax^2 + bx + cThe graph opens up if a>0, opens down if a < 0
The function that opens up is:
y = x^2 - 3The 16th percentile in a Normal distribution is 25 and 2.5% of the values in the distribution are greater than 40.
Which of the following are the best estimates for the mean and standard deviation of the distribution?
(a) mean = 32.5; standard deviation = 2.5
(b) mean = 32.5; standard deviation 5
(c) mean 32.5; standard deviation = 10
(d) mean = 30; standard deviation - 2.5
(e) mean = 30; standard deviations
This question is not complete
Complete Question
The 16th percentile in a Normal distribution is 25 and 2.5% of the values in the distribution are greater than 40.
Which of the following are the best estimates for the mean and standard deviation of the distribution?
(a) mean = 32.5; standard deviation = 2.5
(b) mean = 32.5; standard deviation = 5
(c) mean 32.5; standard deviation = 10
(d) mean = 30; standard deviation = 2.5
(e) mean = 30; standard deviations = 5
Answer:
(e) mean = 30; standard deviations = 5
Step-by-step explanation:
From the question, we are told that the 16th percentile in a Normal distribution is 25
Hence the standard deviation is calculated as √of the 16th percentile in a normal distribution
= √25
= 5
Hence, the standard deviation = 5
In other to obtain the mean, we used the formula of z score.
z score formula =(x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question
x = 40, σ = 5
We are told that 2.5 % of the values is greater than 40
This means The percentile for this values = 100 - 2.5 %
= 97.5%
The z-score for a 97.5th percentile = 1.96
Hence,
z = (x-μ)/σ
1.96 = (40 - μ) / 5
Cross Multiply
= 1.96 × 5 = 40 - μ
= 9.80 = 40 - μ
μ = 40 - 9.80
μ = 30.2
≈ 30
Hence, the Mean = 30
A normal distribution is symmetric about the mean.
The mean of the distribution is 30The standard deviation is 5Given
[tex]P_{16} = 25[/tex] ---- 16th percentile
First, we calculate the standard deviation as follows:
[tex]\sigma = \sqrt{P_{16}[/tex]
So, we have:
[tex]\sigma = \sqrt{25[/tex]
[tex]\sigma = 5[/tex]
Next, we have:
[tex]2.5\%[/tex] of the value are greater than 40
This means that:
[tex]x =40[/tex] and 97.5% are less.
So: the z-score of 97.5% is:
[tex]z = 1.960[/tex]
Using z formula:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
Substitute values for z, x and [tex]\sigma[/tex]
So, we have:
[tex]1.960 = \frac{40 - \mu}{5}[/tex]
Multiply through by 5
[tex]5 \times 1.960 = 40 - \mu[/tex]
[tex]9.8 = 40 - \mu[/tex]
Collect like terms
[tex]\mu = 40 - 9.8[/tex]
[tex]\mu = 30.2[/tex]
Approximate
[tex]\mu = 30[/tex]
Hence, the mean is 30 and the standard deviation is 5
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X/10 > 3 solution to the inequality
Djduhdbevzhzjsvvsyshavahsysjsjsj
simplify 14+ 18/2 * 18-7
Answer:
the solution is 169
Step-by-step explanation:
Answer:
169
Step-by-step explanation:
14 +18/2 x 18-7
14+9 x 18-7
14+162-7
169
URGENT WILL GET BRAINLIEST!!!!
Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measure.
m∠1=(50x)∘, m∠8=150°
Answer:
Alt. Ext. Angles Theorem.
m∠1 = 150
Step-by-step explanation:
∠1 and ∠8 are alternate exterior angles formed when the transversal line cuts across the 2 parallel lines. According to the alternate exterior angles theorem, both are congruent. Therefore,
m∠1 = m∠8
m∠1 = (50x)°
m∠8 = 150
Set both equal and solve for x
50x = 150
Divide both sides by 50
50x/50 = 150/50
x = 3
Unknown angle:
m∠1 = (50x) = 50*3 = 150°
Show all you work plzzz
Answer:
[tex]4+3n[/tex]
Step-by-step explanation:
[tex]4+8n-5n[/tex]
Solve [tex]8n-5n=3n[/tex]
[tex]4+3n[/tex]
If f(x) = 5x + 3 and g(x) = x – 4, then f(x) + g(x) =
Answer:
C. 6x-1
Step-by-step explanation:
Add 5x+3 by x-4 (5x+3+x-4), then simplify by combining like-terms. So, add 5x+x, which will be 6x and then do 3-4, which will be -1. So, the answer should be 6x-1. Hope this helps!
Bob bought a Ford Expedition for his family. After 5 years, the SUV was
worth $10,000 less than what he paid for it. What integer represents the
how much value the SUV lost each year?*
Answer:
500$
Step-by-step explanation:
Answer:
2,000
Step-by-step explanation:
10,000/5=2000
Which symbol makes the number sentence true?
-2.50 ? -10/4
A) <
B) >
C) =
Answer:
C) =
Step-by-step explanation:
-10/4 simplifies to -2.5 which is also equal to -2.50.
Which expression has a value of 1?
(Need answer ASAP)
Answer:I am adding the brackets to show in which order the expressions will be evaluated:
A.
(4 ÷ 4) + 4 – 4 = 1+4-4 = 1 (the correct answer)
B.
(4 · 4) – (4 ÷ 4)= 16-1 = 15
C.
4 –( 4 ÷ 4) – 4= 4-1-4 = -1
D.
(4 ÷ 4) + 4 + 4 = 1+4+4 =9
hope this help yu the answer is A
hope this hlpe
Step-by-step explanation:
What is 6.92 x 10^ -3 written in standard form ?
Answer:
6.92 x 1,000= 6,920
Step-by-step explanation: Hope this helps
Reflect on the concept of polynomial and rational functions. What concepts (only the names) did you need to accommodate these concepts in your mind? What are the simplest polynomial and rational function you can imagine? In your day to day, is there any occurring fact that can be interpreted as polynomial and rational functions? What strategy are you using to get the graph of polynomial and rational functions?
Answer:
Given below
Step-by-step explanation:
A rational function is a function containing rational numbers.
It can be an algebraic function in which both the numerator and denominators can be polynomials.
Any number which can be expressed in the form of a fraction p/q where p and q are integers and q is not equal to zero is called a rational number. Positive integers, negative integers ,zeros and common fractions belong to the system of rational numbers. P can be equal to zero.
A polynomial function is a function consisting of polynomials. A polynomial is an algebraic expression consisting of one or more terms in each of which the exponent of the variable is zero or positive integer. Thus 2,3x, x²+ 3x-4 etc are polynomials.
A polynomial consisting of a single term is monomial e.g, 2, 3x , xy
A polynomial consisting of two terms is binomial e.g, 2+3x , xy- 5z etc.
A polynomial consisting of three terms is trinomial e.g, 2+3x +xy
Terms containing the same variable and same corresponding exponents are known as like terms.
Terms having different variables or same variable but different exponents are called unlike terms.
Polynomials are used to sketch curves or daily life problems.
To sketch the graphs first we find the intercepts, then the vertical asymptotes and the horizontal asymptote, by solving.
The vertical asymptotes divide the number line into regions after which the graph is sketched.
The first thing that comes to the mind is the form of p/q for rational functions and algebraic expressions for the polynomial functions.
The fundamental difference between the graphs of the polynomial function and rational function is that the graph of the polynomial function is continuous in nature while the graph of the rational function is discontinuous in nature as the denominator will be zero at some point.
The strategy are using to get graph of polynomial and rational function given below.
Polynomial is an expression comprising variables and coefficients.
The rational expression is fractions involving polynomials
Polynomial: A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
An example of a polynomial of a single indeterminate, x, is x² − 4x + 7
Polynomial Function : A polynomial function is a function which involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation, cubic equation
Rational: The definition of rational is something that makes sense or that could be based in fact or someone who behaves and thinks logically.
Rational Function: A rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K.
Polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides.
Process for Graphing a Rational Function and Polynomials given below.
Find the intercepts, if there are anyFind the vertical asymptotes by setting the denominator equal to zero and solving. Find the horizontal asymptote, if it exists, using the fact above.The vertical asymptotes will divide the number line into regions.Sketch the graph.The fundamental difference between the graphs of the polynomial function and rational function is that the graph of the polynomial function is continuous in nature while the graph of the rational function is discontinuous in nature as the denominator will be zero at some point.
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I will give brainliest answer
Answer:
Please see attached image
Step-by-step explanation:
Recall that for a reflection of the triangle, we proceed to reflect its vertices across the given line. A reflection places the image of the three vertices at exactly the same number of units on the other side of the line as the original vertex was.
Please see attached image for description.
We go from vertex A straight perpendicular towards the line, and count two divisions to reach the line, so we move in the exact same down direction two divisions on the other side of the given line and mark its image (point A').
We do similarly with point B (six divisions to reach the given line, and continue also 6 divisions to the other side to create its image B'.
Finally vertex C is 5 divisions from the given line, and we continue 5 divisions on the other side of the line to place its image.
Once this is done, we simply join the image points with segments to form the triangle.
Karina and Perry are cleaning up litter in the park for community service hours. Karina and Perry both claim they have covered the greatest area. Who is correct? Justify your answer using mathematical reasoning. Also, what is the area of both shapes?
Answer:
a. Perry covered a larger area
b. Karina covered an area of 9 units squared
Perry covered an area of 18 units squared
Step-by-step explanation:
Here, we are to justify our answer using mathematical reasoning.
Firstly, we need to deduce who out of the two has covered the greatest area.
The best way to go about this is by looking at the dimensions of the shapes in which they have individually covered.
For Karina, we have a square of sides 3 units by 3 units
While for Perry, we have a rectangle of dimension 9 units by 2 units
We know that judging by the areas of both, a square of side 3 by 3 has a smaller area compared to a rectangle of side 9 by 2
So since the rectangle has the bigger area, then Perry has covered a larger area during her community service
We are told to calculate the areas;
For Karina , we have;
3 by 3 = 3 units * 3 units = 9 units squared
For Perry, we have
9 by 2 = 9 units * 2 units = 18 units squared
