I assume you're talking about a fraction,
(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²)
Remember that i ² = -1; from this it follows that
i ³ = i ² × i = -i
i ⁴ = i ³ × i = (-i ) × i = -i ² = -(-1) = 1
i ⁵ = i ⁴ × i = i
i ⁶ = i ⁵ × i = i ² = -1
and so on. In particular, raising i to some integer multiple of 4 reduces to 1.
Using the above pattern, we find
i ²⁰ = 1
i ⁴² = i ⁴⁰ × i ² = 1 × (-1) = -1
i ¹⁰¹ = i ¹⁰⁰ × i = 1 × i = i
So, we have
(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²) = (2 - 1) / (i - (-1)) = 1 / (i + 1)
We can stop here, but usually it's more useful to have complex numbers written in standard a + bi form. To get this result, multiply the numerator and denominator by the complex conjugate of i + 1:
(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²) = 1 / (i + 1) × (-i + 1) / (-i + 1)
… = (-i + 1) / (-i ² + 1²)
… = (-i + 1) / (-(-1) + 1)
… = (1 - i ) / 2
or equivalently,
… = 1/2 - 1/2 i
The list price on a winter coat is $84. It is being sold at a 23% discount. What is the sale price of the coat?
A)$64.68
B)$61.32
C)$47.48
D)$22.68
Answer:
A) $64.68
Step-by-step explanation:
Note that 23% = 23/100 = 0.23
First, multiply $84 with 0.23:
84 x 0.23 = 19.32
Next, subtract 19.32 from the total cost:
84 - 19.32 = 64.68
A) $64.68 is your answer.
~
Answer:
A)$64.68
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
GIVING 20 POINTS, HELP ASAP!! DUE IN 45 MIN!!!!!
Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The graph below represents what Health Club B charges.
The equation of line is solved and Health Club B costs $ 7 less in monthly membership fees that Health Club A
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 3 , 106 )
Let the second point be Q ( 6 , 187 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 187 - 106 ) / 3
Slope m = 27
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 106 = 27 ( x - 3 )
y - 106 = 27x - 81
Adding 106 on both sides , we get
y = 27x + 25 be equation (1)
Now , let the equation of line be represented as B
And , the value of B is
Let the first point be R ( 3 , 105 )
Let the second point be S ( 6 , 165 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 165 - 105 ) / 3
Slope m = 20
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 105 = 20 ( x - 3 )
y - 105 = 20x - 60
Adding 105 on both sides , we get
y = 20x + 45 be equation (2)
Now , when x = 1
Substitute the value of x = 1 in equation (1) and equation (2) , we get
y₁ = 27 + 25 = $ 52
y₂ = 20 + 45 = $ 65
So , health club B costs $ 7 less than health club A every month
Hence , the equation of lines is solved
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ1
Please help me i really need it please
Answer:
1. 12 outcomes 2. 24 outcomes
Step-by-step explanation:
Tell me 5 things you have learned about scientific notation.... pls
Answer: 1) If the decimal is being moved to the right, the exponent is negative. 2) It’s it’s moved to the left, the exponent is positive.
Step-by-step explanation:
fnejfkenfejdb that’s all I know that is correct.
what is x? (7x+1)=(9x-7)
Step-by-step explanation:
Given
7x + 1 = 9x - 7
9x - 7x = 1 + 7
2x = 8
x = 8 / 2
x = 4
Hope it will help :)❤
A restaurant has a total of 30 employees there are 14 who work in the evening and the rest work during the day what is the ratio of employees who work in the evening to employees who work during the day?
A: 7:8
B: 7:15
C: 8:7
D: 8:15
Maria has 64 flowers. She makes 8 bouquets with the flowers. How many bouquets of flowers will she have if she has 80 flowers?
Answer:
10 bouquet of flowers
Step-by-step explanation:
64÷8=8
80÷8=10
URGENT PLEASE !!!! Please answer correctly !!Will mark Brianliest !!!!!!!!!!
Answer:
Step-by-step explanation:
Square Root of 85
Jocelyn said that the triangle below is not a right triangle. Her work is shown below. Explain what she did wrong and show Jocelyn the correct solution.
Complete Question:
Jocelyn said that the triangle below is not a right triangle. Her work is shown below. Explain what she did wrong, and show Jocelyn the correct solution.
We need to check if 27² + 45² = 36² is a true statement. The left side of the equation is equal to 2,754. The right side of the equation is equal to 1,296. That means 272 + 452 = 362 is not true, and the triangle shown is not a right triangle
Answer/Step-by-step explanation:
Jocelyn used a wrong equation and statement.
Here's what she should have stated and done.
Using the converse of Pythagorean Theorem, which says that a triangle with sides a, b, and c is a right triangle if it satisfy the statement: a² + b² = c².
Where, c is the hypotenuse which is the longest leg. While a and b are the side lengths of the other two legs.
Therefore, in this case,
c = 45
b = 27
a = 36
Thus, what we need to check to be true would be:
36² + 27² = 45² (this is where Jocelyn made a mistake. Jocelyn wrote 27² + 45² = 36² rather)
Let's check if it's true.
2,025 = 2,025 (this is true)
Therefore, the triangle is a right triangle.
PLEASE ANSWER WILL GIVE POINTS!!!!!!!!!!!!!!!!
(7)From the diagram
cos 34=y/37
y=37 × cos34
y=30.673 approximately 31
and x+y=52
therefore we have our x=21 and y=31
lillian works 7 hours each day for 5 days a week. she earns £420 each week. how much does she earn per hour?
need ASAP I will mark beainlist for correct t answer
Answer:
Lillian gets paid $12 an hour.
Step-by-step explanation:
I multiplied 7 times 5, which gives you 35. The you divide 420 by 35, which then gives you 12 dollars
Paragraph One
He drives a racecar 80 miles per hour. He motivates audiences of hundreds. He's earned awards for his performance on and off the racetrack, and he's traveled the country to compete. Did we mention that he's 13 years old? One look at his accomplishments and it is easy to see that Noah "Little Gator" Cornman is on the fast track to success. "Little" might be a part of his nickname, but it does not describe his determination to succeed and his heart to make a difference for kids like him.
In paragraph 1, which sentence implies that the author is impressed with the teen's accomplishments?
He drives a racecar 80 miles per hour.
He motivates audiences of hundreds.
Did we mention that he's 13 years old?
He's traveled the country to compete.
Answer:
Did we mention that he's 13 years old?
Step-by-step explanation:
because he inspire alot of people by driving a racecar 80 mph that is fast for a kid at his age.
Answer:
Did we mention that he's 13 years old?
Step-by-step explanation:
Did this in middle school 1 year ago it right
LE
Majid rents a bicycle to ride around the city.
There is AED 80 deposit plus AED 22 per hour charge.
If Majid pays AED 146, Majid can ride the bicycle for
hour
B
22
12
80
Answer:
3 hours
Step-by-step explanation:
The rent of the bicycle comes with a charge of:
Initial deposit = AED 80
cost per hour = AED 22
If Majid pays AED 146, then;
AED 146 - AED 80 = AED 66
Given that the charge per hour is AED 22, then to determine the number of hours that Majid can ride;
number of hours = [tex]\frac{AED 66}{AED 22}[/tex]
= 3
Majid would be able to ride the bicycle for 3 hours when he pays AED 146.
Solve x2 - 10 = 0. If necessary, round to the nearest hundredth.
9514 1404 393
Answer:
3.16 or -3.16
Step-by-step explanation:
Add 10 and take the square root.
x^2 = 10
x = ±√10 ≈ ±3.16
x is 3.16 or -3.16
A cube has a side length of 4 feet. What is the volume of the cube?
48 ft3
64 ft3
96 ft3
12 ft3
Answer:
64 square ft^3
Step-by-step explanation:
If the side lengh is 3 then you would have 4^3 which is 64.
Answer:
64
Step-by-step explanation:
Select the correct answer.
What is the value of y?
A.3
B.8
C.4
D.16
12 NEED HELP ASAP WILL GIVE BRAINLY
Answer:
x = 4
8(4) - 2 = 30
15(4) = 60
All triangles equal 180 degrees and there is already a right angle. 60 plus 0 is 90, and 90 plus 90 (or 90 times 2) is 180
60 + 30 = 90
90 + 90 = 180
Step-by-step explanation:
Please Help!!! I'll give brainliest
If x+3/3 = y+2/2, then x/3 = ______
who can help me with some math homework
Answer:
I can help you dude if any trouble (:
Three sides of a kite measure 8 inches, 10 inches, and 8 inches. What is the perimeter of the kite?
A 26 inches
B. 28 inches
C. 34 inches
D. 36 inches
Answer:
26
Step-by-step explanation:
8+10+8=26
The Perimeter of the Kite whose dimensions 8 in., 10 in. and 8 in. is 26 inches.
What is the Perimeter of Kite?
A kite has two pairs of equal size. Total distance around the outside is called the perimeter of a kite. This distance can be found by calculating the sum of the lengths of each pair.
Here, the perimeter of kite = a + b + c
= 8 + 10 + 8
= 26 inches.
Thus, the Perimeter of the Kite whose dimensions 8 in., 10 in. and 8 in. is 26 inches.
Learn more about Perimeter of Kite from:
https://brainly.com/question/5028901
#SPJ2
How to find the slope for (2,2) and (-1,2)
Answer:
Slope = 0
slope is the same as gradient, so you will use the formula
M = y2 - y1 / x2 - x1 in this case (2,2) and (-1.2)
the first 2,is x1.then the other 2 in the first coordinate is y1 , for the last coordinate -1 is x2 and 2 is y2, use the formula I gave you , you will see that the answer is 0
How do i find "40% is 80 of what number?"
Answer:
hhhsunf
Step-by-step explanation:
2y-4x=-18 slope intercept form
Answer:
y=−2x−9
Step-by-step explanation:
Write an equation of the line that passes through (1,2) and is parallel to the line y = -5x+4
Answer:
y =-5x + 7
Step-by-step explanation:
y = -5x + 4
Slope = -5
Parallel lines have same slope
Slope of the parallel line to this line = -5
(1 , 2)
y -y1 =m(x - x1)
y - 2 = -5(x - 1)
y -2 = -5x + 5
y = -5x + 5 + 2
y = -5x + 7
What is the next term of the geometric sequence?
48,-36,27....
Answer:
-15 is the next number in the sequence
Mac Cosmetics sells a lip gloss for $15.50, but it only costs the company $6 to make it. What is the percentage markup on the lip gloss? Show all of your work and record your final answer in the space below.
Answer:
258 percent
Step-by-step explanation:
15.5/6 is 2.58, which is 258 percent
HELP ANSWER GETS BRANLIEST ANSWER!
Answer: -5/4
Step-by-step explanation: You can use the graph to count the slope. The change in y is -5 and the change in x is 4, and slope is change in y over change in x.
Yoo Helpppp meee outt
Answer:
I going to go with B $2378.30
Answer:
I going to go with B $2378.30
Step-by-step explanation:
what's 5x-4y=-12 need help