Answers
[tex]\qquad \textit{power of a complex number} \\\\\ [\quad r[cos(\theta)+isin(\theta)]\quad ]^n\implies r^n[cos(n\cdot \theta)+isin(n\cdot \theta)] \\\\[-0.35em] ~\dotfill\\\\ z=2[\cos(104^o)~~ + ~~i\sin(104^o)] \\\\\\ z^2=2^2[\cos(2\cdot 104^o)~~ + ~~i\sin(2\cdot 104^o)] \\\\\\ z^2=\underset{polar}{4[\cos(208^o)~~ + ~~i\sin(208^o)]}~\hfill \implies ~\hfill z^2\approx \underset{rectangular}{\stackrel{4\cos(208^o)}{-3.532}~~,~~\stackrel{4\sin(208^o)}{-1.878} i}[/tex]
Related Questions
If one angle in a linear pair is 110 degrees, what is the measureof the other angle?
Answers
The other angle = 70°
Explanations:When two angles are form a linear pair , then they are supplementary. That is, they add up to give <180°
The first angle = 110°
Let the second angle be x
110 + x = 180
x = 180 - 110
x = 70°
The measure of the other angle is 70°
Error Analysis
Louie and Nicky were asked to find point P that divides the directed line segment FG so that the ratio of FP
to PG is 4 to 1. Louie says the coordinate of point P is (-4,- 4), while Nicky says the coordinate of point P
is (2, 5). Who is correct? Describe the mistake that was made by the student who was incorrect.
Answers
Using proportions, it is found that Louie is correct, while Nicky's mistake was in building the proportional equation.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using operations such as multiplication and division.
The endpoints of the line segment are given as follows:
G(-6,-7) and F(4,8).
Point P divides the ratio of FP to PG is 4 to 1, meaning that the following equation is built:
P - F = 4/5(G - F)
Hence the x-coordinate of P is found as follows:
x - 4 = 4/5(-6 -4)
x - 4 = -8
x = -4.
The y-coordinate is found as follows:
y - 8 = 4/5(-7 - 8)
y - 8 = -12
y = -4.
Hence Louie is correct, while Nicky's mistake was in building the proportional equation, as he found the wrong coordinates.
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how do you solve 3/4 % of 387?
Answers
To calculate the 3/4% of 387, you have to use cross multiplication:
The fraction 3/4 can be expressed as a decimal value to make the calculations easier: 3/4=0.75
100% is 387
0.75% is x
Both relations are at the same ratio, so that
[tex]\begin{gathered} \frac{387}{100}=\frac{x}{0.75} \\ x=\frac{387}{100}\cdot0.75 \\ x=2.9025 \end{gathered}[/tex]This means that the 3/4% of 387 is 2.9025
Salary 75000Salary increase to 81000 in 4 years Future earnings in any given year y= Toms salary X=number of years worked Use the data given to find the rate of Chamorro the salary increase per year Use the data given and the slope value from step 1 to write the slope intercept form of the lineBased on your equation from step 2 what will Toms salary be in Ten years?
Answers
Given that Tom's initial salary is;
[tex]y_0=\text{ \$}75000[/tex]In four years the salary increases to;
[tex]y_4=\text{ \$}81000[/tex]The rate at which his salary increase per year is;
[tex]\begin{gathered} m=\frac{y_4-y_0}{4}=\frac{81000-75000}{4}=\frac{6000}{4} \\ m=1500 \end{gathered}[/tex]The rate at which his salary increase per year is;
[tex]\text{ \$}1500\text{ per year}[/tex]Using the given initial salary and the slope(rate) abo
6 3/8 - 2 5/8 what is the value of this expression?A) 3B) 3 6/8C) 4 2/8D) 5
Answers
6 3/8 - 2 5/8
=4 3 - 5/8
= 3 8 + 3 - 5/8
= 3 6/8
Option B) 3 6/8
the radius of a circle in 6 miles. what is the area of a sector bounded by a 126° arc?
Answers
The area of a sector of a circle is:
[tex]A=\pi r^2\cdot\frac{\theta}{360}[/tex]Where θ is the angle of the arc and r is the radius.
In this case,
• r = 6mi
,• θ = 126º
Then:
[tex]A=\pi(6mi)^2\cdot\frac{126}{360}=\pi\cdot\frac{36mi^2\cdot126}{360}=\frac{63}{5}\pi[/tex]Thus the correct option is the 4th one:
[tex]\frac{63}{5}\pi\text{ }mi^2[/tex]Using the design below, you plan to make a rectangular wall hanging to decorate yourbedroom. Th e green rectangle is 16 ft by 10 ft, the blue square is 7 ft by 7 ft, the orangetriangles have a height of 1.73 ft and a side length of 2 ft, and the yellow circle has adiameter of 3 ft. You plan to glue the pieces together and then outline each piece withblack cord.a. How much black cord does the design use?b. How much fabric of each color does the design show?c. At a craft store, fabric comes in bolts that are a fixed number of inches wide.You can only buy fabric by the whole yard. If each bolt is 48 in. wide, what isthe least amount of each color that you need to buy? Explain.please I try to solve it but I did not understand it please need help thank you so much.
Answers
To know the total amount of fabric we need per color, we need to find the area of each color.
The green rectangle.[tex]A_{green}=16\cdot10=160ft^2[/tex]The blue square.[tex]A_{blue}=7\cdot7=49ft^2[/tex]The orange triangles.[tex]A_{orange}=4(\frac{1}{2}\cdot1.75\cdot2)=\frac{14}{2}=7ft^2[/tex]The yellow circle.[tex]A_{circle}=\pi r^2=3.14\cdot(1.5)^2=3.14\cdot2.25=7.065ft^2[/tex]Now, the bolts are sold in fixed yards, we know that 48 inches are equivalent to 1.333... yards, or 4 feet. But, we are using areas so, 48 to the square power in square inches would be equivalent to 16 square feet.
Then, we divide each area by 16 square feet.
[tex]b_{green}=\frac{160}{16}=10[/tex]We need 10 bolts of green fabric.
[tex]b_{blue}=\frac{49}{16}=3.0625[/tex]We need 4 bolts of fabric since if we use 3 we would need a bit more.
[tex]b_{orange}=\frac{7}{16}=0.4375[/tex]We just need 1 bolt of orange fabric.
[tex]b_{yellow}=\frac{7.065}{16}=0.44[/tex]We need 1 bolt of yellow.
What is the solution to the equation below?A.x = B.x = 25C.x = D.x = 9
Answers
The given equation is
- 3 + √(3x - 11) = 5
Adding 3 to both sides of the equation, we have
- 3 + 3 + √(3x - 11) = 5 + 3
√(3x - 11) = 8
Square both sides. It becomes
[√(3x - 11)]^2 = 8^2
3x - 11 = 64
Adding 11 to both sides of the equation, we have
3x - 11 + 11 = 64 + 11
3x = 75
Dividing both sides by 3,
3x/3 = 75/3
x = 25
Fill in the blanks to correctly complete the sentence.To perform the division x-3)x³ + 6x² + 4x, begin by writing the synthetic division problem shown below.0)1040
Answers
The division is given by
x^3+6x^2+4x : (x-3)
therefore
The answer is
3 1 6 4 0
2. Which of the following cannot be a part of a rational expression?O-7x⁰3x²3x² - 4x + 5043x² - 4√x
Answers
To be part of a rational expression, we need to have a polynomial expression.
By definition, all the exponents of a polynomial expression are positive integer values (including 0).
We know that:
[tex]\sqrt{x}=x^{\frac{1}{2}}[/tex]So the last option is not a polynomial.
Answer: The last option
Evaluate the expression when y=5 and x=20.x - 4y
Answers
To evaluate the expression we need to replace with the given values, as follows:
x - 4y =
= 20 - 4*5 =
= 20 - 20 =
= 0
Round to nearest foot
Answers
Using the law of sines and relations in a right triangle, the ground distance AB is of:
AB = 3745 ft.
Law of sinesThe ratios between the sine of an angle and the length of the opposite side to the angle are the same in a triangle.
The sum of the measures of the internal angles of a triangle is of 180º, hence the missing angle is of:
180 - (74 + 49) = 57º.
Then the bottom side of the blue triangle is found as follows:
sin(57º)/3300 = sin(74º)/x
x = 3300sin(74º)/sin(57º)
x = 3782 ft.
Ground distanceThe ground distance can be found considering that:
The adjacent side to the angle of 8º is the ground distance.The hypotenuse is of 3782 ft.Hence the ground distance is calculated as follows:
cos(8º) = AB/3782
AB = 3782 x cos(8º)
AB = 3745 ft.
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the quotient of 7 subtracted from a number c and 4
Answers
The quotient of 7 subtracted from a number c and 4 which is 2 , 4 +3 = 7 and c=3. The quotient is the outcome of splitting two numbers.
What is meant by quotient?In mathematics, the quotient is the result of performing division operations on two numbers. It is essentially the outcome of the division procedure. In arithmetic division, the terms divisor, dividend, quotient, and remainder are employed in four different ways.A quotient in mathematics is the amount created by dividing two numbers. n mathematics, the word "quotient" is widely used, and it is sometimes referred to as the integer part of a division, a fraction, or a ratio. The quotient is the outcome of splitting two numbers.To learn more about quotient refer to:
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The diagram represents a set of beams that form part of a bridge support. Label AB and BD with their lengths, rounded to the nearest foot.Enter the correct answers in the boxes.
Answers
BD = 12 ft
AB is 15 ft
Explanation:The two triangles are right angled, so we would apply pythagoras' thorem:
Hypotenuse² = opposite² + adjacent²
First we would go for the second triangle as two of the sides are given.
Hypotenuse = 14, adjacent = 7, opposite =BD
14² = BD² + 7²
196 = BD² + 49
BD² = 196 - 49 = 147
BD = √147 = 12.12 ft
To the nearest foot, BD = 12 ft
1st triangle:
Hypotenuse = AB,
opposite = BD = √147
adjacent = 9 ft
AB² = (√147)² + 9²
AB² = 147 + 81 = 228
AB = √228 = 15.0997
To the nearest foot, AB is 15 ft
PLEASE HELP!!! - 55 pts
1.) Mrs. Zech babysits for extra money.
-The job pays $250 for twenty hours of work
-She needs to make $750
How many hours of babysitting would Mrs. Zech need to work to earn the $750?
Answers
Answer: Mrs. Zech would need to work 60 hours to earn $750.
Step-by-step explanation: 250 x 3 = 750, Every 20 hours Mrs. Zech makes $250 therefore 20 x 3 = 60 hours of work.
Answer:
60 hours
Step-by-step explanation:
if $250 is for 20hrs, $750 is for x hours (let the number of hours be x)
$250=20hrs
$750=x hrs
then you cross multiply. Which will be represented as
250x= (750x 20)
Divide both sides by 250
X =750x 20/ 250
X = 15000/250
X = 60 hours
Panama wants to solve the equation 1/3 ( x - 7) = 4To begin , she multipiles both sides of the equation by 3 what should she do next?
Answers
Question:
[tex]\frac{1}{3}(x-7)=4[/tex]Step 1: Multiply both sides by 3
[tex]\begin{gathered} \frac{1}{3}(x-7)=4 \\ 3\times\frac{1}{3}(x-7)=4\times3 \\ 1(x-7)=12 \\ x-7=12 \end{gathered}[/tex]Step 2: To find the value of x, Add 7 to both sides
[tex]\begin{gathered} x-7=12 \\ x-7+7=12+7 \\ x=19 \end{gathered}[/tex]Hene,
The final answer is add 7 to both sides
Answer:
Add 7 to each side
Step-by-step explanation:
1/3 ( x - 7) = 4
After multiplying both sides by 3
3*1/3 ( x - 7) = 4*3
( x - 7) = 12
We want to isolate x
Add 7 to each side
x - 7+7 = 12+7
x = 19
Options for the first box: (0,1), (0,0), (1,0) Options for the second box: increases and decreases Options for the third box: x=-1, x=1, x=0 Options for the fourth box: Decreases to negative infinity and increases to positive infinity
Answers
To answer this question we can use the graph of the logarithm:
From this graph we conclude that:
Function f crosses the x-axis at (1,0). As x increases the function increases. As x approaches its vertical asymptote of x=0, the function decreases to negative infinity.
Mike read of a novel. Katy read as much of the same novel as Mike. How much of the novel did Katy read?
What type of comparison is shown in the question above?
A.
additive comparison
B.
multiplicative comparison
Answers
The type of comparison shown is multiplicative comparison.
As the number of novel increase in the case of Mike, the number for Katy will also increase simultaneously.
For example, if the novel read count for Mike is 3 then the novel read count for Katy will be also 3.
Additive comparison defines a relationship between two quantities by specifying or saying how much greater or less one is than the other.
Multiplicative Compare - compares two values and multiplies one by a specified number to get the other.
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(-3, -3) , (-3, -5)find the slope of the line through the given points
Answers
Using the slope formula with the points (-3, -3) and (-3, -5), we have:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{-5-(-3)}{-3-(-3)}=\frac{-5+3}{-3+3}=\frac{-2}{0}=\propto\text{ (Undefined Slope)}[/tex]We can see that the slope is undefined.
Distribute 4,350$ among John, Maria, and Betsy, so that Maria receives twice as much as John and Betsy recieves 3 times as much as john
Answers
To solve this problem we must generate a system of equations that models its behavior.
To make the problem easier, the money distributed to Jhon, Maria and Betsy will be identified by their initials J, M and B.
[tex]\begin{gathered} M+J+B=4350\to(1) \\ M=2J\to(2) \\ B=3J\to(3) \end{gathered}[/tex]The first thing we are going to do is replace the value of equations (2) and (3) in equation (1)
[tex]\begin{gathered} 2J+J+3J=4350 \\ 6J=4350 \\ J=\frac{4350}{6} \\ J=725 \end{gathered}[/tex]Now we know that John will receive $725 now we plug this value into (2) and (3) to find when Maria and Betsy will receive
[tex]\begin{gathered} M=2J \\ M=2(725) \\ M=1450 \end{gathered}[/tex][tex]\begin{gathered} B=3J \\ B=3(725) \\ B=2175 \end{gathered}[/tex]The distribution of the $4350 would be as followsMaria = $1,450John = $725Betsy = $2,17530 cars are in a race. In how many different ways can cars finish in the top 3 positions?
Answers
Given:
There are 30 cars in a race.
The number of ways that cars finish in the top 3 positions is given as,
[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ n=30,r=3 \\ ^{30}P_3=\frac{30!}{(30-3)!} \\ =\frac{30!}{27!} \\ =28\times29\times30 \\ =24360 \end{gathered}[/tex]Answer: There are 24360 ways that cars finish in the top 3 positions.
-
Solve the following equation using the zero product property 5(-v-5)(v-8)=0
Answers
The expression to be solved is:
[tex]5\cdot(-v-5)\cdot3\cdot(v-8)\text{ = 0}[/tex]The zero product property states that the solution to this equation is the values of each term equals to 0.
[tex]\begin{gathered} (-v\text{ - 5) = 0} \\ -v\text{ = 5} \\ v\text{ = -5} \end{gathered}[/tex][tex]\begin{gathered} (v\text{ - 8) = 0} \\ v\text{ = 8} \end{gathered}[/tex]The answers are -5 and 8.
6. Mishell bought some sugar and strawberries to make strawberry jam.Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound.Mishell spent a total of $19.40. Which point on the coordinate plane couldrepresent the pounds of sugar and strawberries that Mishell used to makejam?*
Answers
Okay, here we have this:
We obtain the following equation.
Let's take x as pounds of sugar, and y as pound of strawberries:
x(Sugar Costs)+y(Strawberries cost)=Total Cost
x(1.80)+y(2.50)=19.40
We are going to replace the coordinates of each point to see which one satisfies the total cost:
Point A (0,0):
x(1.80)+y(2.50)=19.40
0(1.80)+0(2.50)=19.40
0+0=19.40
0=19.40 (We can see that this equality is false, therefore the option is incorrect)
Point B (8,2):
x(1.80)+y(2.50)=19.40
8(1.80)+2(2.50)=19.40
14.4+5=19.40
19.40=19.40 (This equality is true, therefore this option may be correct, however let's analyze the rest)
Point C (6,1)
x(1.80)+y(2.50)=19.40
6(1.80)+1(2.50)=19.40
10.8+2.5=19.4
13.3=19.4 (We can see that this equality is false, therefore the option is incorrect)
Point D (7, 5)
x(1.80)+y(2.50)=19.40
7(1.80)+5(2.50)=19.40
12.6+12.5=19.40
25.1=19.4 (We can see that this equality is false, therefore the option is incorrect)
Finally we obtain that the correct answer is the Point B.
Write the following decimal number in standard form Two and four hundredths
Answers
ANSWER
[tex]The\text{ standard form of 2.04 is 2.04}\times10^0[/tex]STEP-BY-STEP EXPLANATION
We are two convert decimal numbers to standard form
Given information
Two and four hundredths
Step 1; write the above data in decimal
[tex]\begin{gathered} \text{four hundredths } \\ 4\text{ x }\frac{1}{100} \\ \frac{4}{100\text{ }}\text{ = 0.04} \end{gathered}[/tex]Step 2: Add the four hundredths to two
[tex]\text{ 2 + 0.04 = }2.04[/tex]Step 3: convert the decimal to standard form
[tex]2.04\text{ }\times10^0[/tex]1/11 as an decimal for long division
Answers
Question: 1/11 as an decimal for long division??
Answer: 1/11 as a decimal is 0.090909090909091.
Step-by-step explanation:
÷= 1
÷=.
(×)÷= .
1÷11=0.0
(×)÷= ,,,
1÷11=0.09 , 1 . ÷=.…
÷=.
: )✨
Two planes fly in opposite directions. One travels 400 mi/h and the other 500 mi/h. How long will it take before they are 2700 miles apart?
Answers
The time taken for the two planes to be apart is 3 hours.
What is the time taken?We have to know that the distance that is covered is the product of the speed and the time. The speed is the rate at which the distance changes with respect to the time.
Now we are looking at the time that it would take for the two airplanes that are flying in different directions to be 2700 miles apart as we can see from the question.
We now have;
400t + 500t = 2700
900t = 2700
t = 2700/900
t = 3 hours
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Find loss and loss percent.
cost price = 850
selling price = €595
Answers
231m 31 cm - 14m 48 cm
Answers
Answer:
26183cm
Step-by-step explanation:
convert to cm only 1m=100cm
23131cm-1448cm
=21683cm
16. Read the following passage below and solve the questions based on it.
There are seven professors P,Q,R,S,T,U and V teaching seven subjects History, Geography,
Physics, Chemistry, Maths, Biology and English from Monday to Friday at Nkrumah University.
Each professor teaches a different subject and not more than two subjects are taught on any one
of the days.
i. Chemistry is taught by professor Q on Tuesday
ii. Professor S teaches on Friday but neither Geography nor Physics
iii. Professor U teaches History but neither on Thursday nor on Friday
iv. Professor P teaches English on the day on which History is taught
v. Professor R teaches Maths on Monday
vi. Geography and Chemistry are taught on the same day
vii. Professor V teaches on Thursday
Answer the below questions:
Answers
After solving simple arithmetic we have found that, Professor V teaches physics as Professor P = English, Professor Q =Chemistry, Professor R = Maths, Professor S = Biology, Professor T= Geography, Professor U = history.
What is arithmetic?Arithmetic is the branch of mathematics concerned with the study of numbers through various operations on them. The basic operations of math are addition, subtraction, multiplication, and division.
It is said that Each professor teaches a different subject and not more than two subjects are taught on any one which means
1 teacher = 1 subject
1 day = 2 subjects
We have given that
Chemistry is taught by professor Q on Tuesday
Professor Q is Chemistry teacher
Professor S teaches on Friday but neither Geography nor Physics
Professor U teaches History but neither on Thursday nor on Friday
Professor U is History teacher
Professor P teaches English on the day on which History is taught
Professor P is English teacher
Professor R teaches Maths on Monday
Professor R is Maths teacher
Geography and Chemistry are taught on the same day
Which means geography is taught on Tuesday
Tuesday = geography and Chemistry (1 day = 2 subjects)
Professor U and Professor P teaches history and English on the same day and it is either Monday or Wednesday as Tuesday already filled and they don't teach on Thursday or Friday.
But it couldn't be Monday as Professor R teaches Maths on Monday and there could only be two subjects
So,
Wednesday = history and English (1 day = 2 subjects)
Professor S teaches on Friday but neither Geography nor Physics and other teachers are taken for Chemistry, math, English and history, so Professor S is Biology teacher
There are seven subjects and 5 days which means three subjects are learned twice at the end of the week
Mondays = Maths and 1 other subject
Tuesday = geography and Chemistry
Wednesday = history and English
Thursday = Professor V(subject) and any of the repeated subject
Friday = Biology and any of the repeated subject
As Biology is a repeated subject we can assume that it is also learned on Monday, We have found that Professor U and Professor P teaches history and English on the same day and Geography and Chemistry are taught on the same day, so the repeated subjects are neither history, English, Geography, nor chemistry.
Which means repeated subject could only be Maths, Physics and biology
But for Friday it could only be maths or physics
As Geography could only be taught on same days with chemistry it means professor T teaches geography as Chemistry is taught by professor Q on Tuesday and Geography and Chemistry are taught on the same day so Professor V wont be teaching on that Tuesday.
Thus, we have
Professor P = English
Professor Q =Chemistry
Professor R = Maths
Professor S = Biology
Professor T= Geography
Professor U = history
Professor V = ?
Only subject left is Physics
So, professor V teaches physics
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Full question
Which of the following subjects is taught by professor V?
Consider the following graph of two functionsStep 2: Find (g-f)(-5)Step 3: Find (g.f)(1)Step 4: Find (f/g)(-3)
Answers
Answer:
• (g-f)(-5)=16
,• (g.f)(-1)=-16
,• (f/g)(-3)=-1
Explanation:
Given the graph of f(x) and g(x):
Part 2
• When x=-5, f(x)=-8.
,• When x=-5, g(x)=8
Thus:
[tex]\begin{gathered} f(-5)=-8 \\ g(-5)=8 \end{gathered}[/tex]The composition of the functions:
[tex]\begin{gathered} (g-f)(-5)=g(-5)-f(-5) \\ =8-(-8) \\ =8+8 \\ \implies(g-f)(-5)=16 \end{gathered}[/tex]The answer is 16.
Part 3
• When x=1, f(x)=4.
,• When x=1, g(x)=-4
Therefore:
[tex]\begin{gathered} f(1)=4 \\ g(1)=-4 \\ \implies(g\cdot f)(-1)=(g)(-1)\cdot(f)(-1) \\ =-4\times4 \\ =-16 \end{gathered}[/tex]The answer is -16.
Part 4
• When x=-3, f(x)=-4.
,• When x=-3, g(x)=4
Therefore:
[tex]\begin{gathered} f(-3)=-4 \\ g(-3)=4 \end{gathered}[/tex]The composition is calculated below:
[tex](\frac{f}{g})(-3)=\frac{f(-3)}{g(-3)}=-\frac{4}{4}=-1[/tex]The answer is -1.
