Answers
i ⁴³⁵ = i ⁴³²⁺³ = i ⁴³² • i ³
i ⁴³⁵ = i ⁴³² • i ³
i ⁴³⁵ = (i ⁴)¹⁰⁸ • i ³
i ⁴³⁵ = 1¹⁰⁸ • (-i)
i ⁴³⁵ = -i
The value of the imaginary number i⁴³⁵ is : i ⁴³⁵ = -i.
Here, we have,
To evaluate the expression i⁴³⁵, we need to understand the properties of the imaginary unit, denoted by i.
The imaginary unit i is defined as the square root of -1, meaning i² = -1.
When raising i to an exponent, we can use the pattern of powers of i to simplify the expression.
The pattern of powers of i repeats every four exponents:
i¹ = i
i² = -1
i³ = -i
i⁴ = 1
Since i⁴ = 1, we can divide the exponent 435 by 4 to find the remainder:
435 divided by 4 gives a remainder of 3.
Therefore, i⁴³⁵ is equivalent to i³.
Using the pattern of powers of i, we know that i³= -i.
So, i⁴³⁵ = -i.
i.e. we get,
i ⁴³⁵ = i ⁴³²⁺³ = i ⁴³² • i ³
i ⁴³⁵ = i ⁴³² • i ³
i ⁴³⁵ = (i ⁴)¹⁰⁸ • i ³
i ⁴³⁵ = 1¹⁰⁸ • (-i)
i ⁴³⁵ = -i
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Related Questions
Solve the following. 5 ice cream cones cost $8.25. At this rate, how much do 2 ice
cream cones cost?
Your answer
Answers
Answer:
$3.30
Step-by-step explanation:
5x = 8.25
divide by 5
one ice cream equals $1.65
multiply by 2 to get $3.30
5/2x - 2000 what does x equal
Answers
Target is advertising a Back to School sale on pens. A pack of 30 sells for $8.90, whereas a 15-pack of me same brand costs $4.39. Which is the better buy? How do you know?
Answers
Answer: Well you don't really need to do math. You have to think half of 30 is 15. So then you would multiply 4.39 times 2 and you get 8.78. So the 15 pack is a better deal.
Step-by-step explanation: Hope this helps! Feel free to ask any other questions in the comment section :)
At the sewing store, Bridgette bought a bag of mixed buttons. The bag included 90 buttons, of which 20% were large. How many large buttons did Bridgette get?
Answers
Answer:
18 large buttons
Step-by-step explanation:
Given that :
A bag of mixed button was purchased ;
Total number of buttons in the bag = 90
Percentage number of large buttons on bag = 20%
Number of large buttons in bag :
(Percentage Number of large buttons * total number of buttons)
= 20% * 90
= 0.2 * 90
= 18
Hence, there are 18 large buttons in the bag.
11. List the steps to constructing the line of reflection.
Answers
Answer:
Construct a perpendicular from A to the line of reflection. Measure the length from A to the intersection point. Copy this length on the perpendicular bisector starting at the intersection point to find A'. You have located ONE vertex of the image.
WILL GIVE BRAINLIEST
Mickey Mouse was finally buying a pair of shoes that fit! The shoes he chose cost $120. The store was offering a 25% discount. How much did Mickey save with the discount?
(PLEASE SHOW WORK!)
Answers
He saved 30 dollars
3. Jack received $75 for his birthday. He spent $25 on a new baseball glove, S45 on a new pair of shoes, and $5
on digital music
(a) What portion of his birthday money went toward new shoes? Express the value as a simplified
fraction. Then, convert the fraction to a percent Show your work
(b) What portion of his birthday money went toward music? Express the value as a simplified fraction.
Then, convert the fraction to a decimal. Round the decimal to the nearest hundredth or indicate it as
repeating. Show your work
(C) Write the ratio of money Jack spent on music to money Jack spent on shoes. Simplify your answer.
What does the ratio mean? What fraction is equivalent to the ratio?
Answers
Answer:
a) What portion of his birthday money went toward new shoes? Express the value as a simplified
fraction. Then, convert the fraction to a percent Show your work
Step-by-step explanation:
a) What portion of his birthday money went toward new shoes? Express the value as a simplified
fraction. Then, convert the fraction to a percent Show your work
Adele swam the length of the pool in 32.56 seconds. Alexandria swam the length of the pool in 29.4 seconds. How many seconds faster was Alexandria's time than Adele's time?
Answers
Answer:
3.16
Step-by-step explanation:
Answer:
Adele was 3.14 seconds faster than Alexanderia
Step-by-step explanation:
Alexamdria - Adele
1. Write the product as one power. a8 • a5
Answers
Answer:
a8.a5= a 13
from the law of indices
Help please this is very much difficult and I have an "f" in her class. :(
Answers
Answer:
10.
average rate of change in this interval=-9
Step-by-step explanation:
i will do for one question.
10.
interval [4≤x≤6]
average rate of change=(18-36)/(6-4)=-18/2=-9
Which of the following linear equations when graphed on a
coordinate grid has the steepest slope?
Y=5/2x-1
Y=3x+1/4
Y=4x+3/5
Y=1/3x-2
Answers
Answer:
y = 4x + 3/5
Step-by-step explanation:
The slopes are 5/2, 3, 4, 1/3.
The larger the absolute value of the slope is, the steeper the graph is.
The largest slope is 4, so that equation has the graph with the steepest slope.
Answer: y = 4x + 3/5
Bobs car wash had to close 26 days because of bad weather. If last year had 365 days, what is the ratio of days open for Bob's car wash
Answers
Answer:
= x² + 8x - 33
Step-by-step f(x) • g(x)
= ( x - 3 )( x + 11 )
= x² + 8x - 33 explanation:
Caffeine in the body decays by a factor of every 2 hours.
Answers
Answer:
Exponential, because the function grows by a common factor.
Ashley uses of 3/4 a cup of milk when making pancakes for 1 person. How many cups of milk does she need to make pancakes for 6 people?
Answers
Answer:
18/4 or 4 1/2
Step-by-step explanation:
Find the equation of the line use exact numbers y =___ x + _____ PLEASE HELP
Answers
The equation of the graphed line, in slope-intercept form, is: y = -3x + 7.
How to Find the Equation of a Line in Slope-intercept Form?To find the equation of the line that is given above, we need to find the slope of the line (m) and the y-intercept (b), then substitute the values into y = mx + b.
Find the slope:
Slope of a line (m) = change in y / change in x = rise/run
The line declines, so, the value of the slope would be negative.
Rise (change in y) = 3 units
Run (change in x) = 1 unit
Slope (m) = - (3 units/1 unit)
Slope (m) = -3
The y-intercept (b) would be the point where the line cuts the y-axis, which is: 7.
Y-intercept (b) = 7
Write the equation by substituting b = 7 and m = -3 into y = mx + b:
y = -3x + 7.
Thus, the equation, in slope-intercept form, is: y = -3x + 7.
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i don't understand this!
Answers
Answer:
at the left of the image, is it 37 or 57
Step-by-step explanation:
What is the slope of the line that passes through the points (2, 0) and (32, -5)? Write your answer in simplest form.
Answers
Answer:
-1/6
Step-by-step explanation:
The slope of the line passing through the given points (2, 0) and (32, -5) is [tex]\frac{-1}{6}[/tex]
Given the following points:
Points on the x-axis = (2, 32)Points on the y-axis = (0, -5)To find the slope of the line passing through the given points (2, 0) and (32, -5):
The slope of a line refers to the gradient of a line and it is typically used to describe both the direction and steepness of an equation of a straight line.
Mathematically, the slope of a line is given by the following formula;
[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substituting the given points into the formula, we have;
[tex]Slope. \;m = \frac{-5 \;- \;0}{32\; - \;2}\\\\Slope. \;m = \frac{-5}{30}\\\\Slope. \;m = \frac{-1}{6}[/tex]
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Manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15-gallon buckets. Manny would like a mixture of 60% detergent and 40% water in 5-gallon buckets. To make this, he combines some 80/20 mixture with some pure water in each 5-gallon bucket. How many gallons of pure water does Manny add to each 5-gallon bucket? Express your answer as a decimal to the nearest hundredth.
Answers
Answer:
1.25 gallons of pure water
Step-by-step explanation:
Manny's cleaning supply store receives a mixture of 80% detergent and 20% water in 15-gallon buckets.
0.80 d + 0.20w = 15 gallon
Manny would like a mixture of 60% detergent and 40% water in 5-gallon buckets.
0.60d + 0.40w = 5 gallon
0.80 d + 0.20w = 15 ....... Equation 1
0.60d + 0.40w = 5 ......….. Equation 2
Using elimination method
Multiply Equation 1 with 0.60
Multiply Equation 2 with 0.80
We eliminate d
0.80 d + 0.20w = 15 × 0.6
0.60d + 0.40w = 5 × 0.8
=
0.48d + 1.2w = 9....... Equation 4
0.48d + 3.2w = 4..... Equation 5
Subtract Equation 5 from 4
= - 2.0w = -5
w = -5/-2
w = 2.5 gallons.
Hence: 2.5 gallons/2
= 1.25 gallons.
Therefore, Manny adds 1.25 gallons of pure water.
Please help! What is the slope?
Answers
Answer:
1/3
Step-by-step explanation:
Frank invests $1,000 in simple interest investment account that pays 8% a year. After a number of years, he withdraws his balance of $2,200. Using the formula I = P r t, how many years was his money invested?
Answers
Answer:
The number of years is 15 years
Step-by-step explanation:
Given;
Principal amount invested, P = $1,000
rate, r = 8 % = 0.08
Amount at the end of the investment period, A = $2,200
interest on the investment, I = Amount - Principal
I = A - P
I = $2,200 - $1,000
I = $1,200
Using the formula I = P r t
t = I / pr
t = (1200) / (1000 x 0.08)
t = 15 years
Therefore, the number of years is 15 years
Answer:
The Answer is: 15 years
Step-by-step explanation:
Hope this helps
Joanna is baking cookies and
cupcakes. She has 1 cups of
sugar already. The cookies require
2 cups of sugar and the
cupcakes require į cup of
sugar.
How much more sugar does
Joanna need?
HELPP ASAPPP
Answers
Answer:
3(4/3) = 4
Step-by-step explanation:
Karen already has 1/2 cup of sugar on hand, she needs (4 - 1/2), or 3 1/2, more cups of sugar to triple the recipe.
Hope this helps ;)
A car that travels 20 miles in \frac{1}{2} 2 1 hour at constant speed is traveling at the same speed as a car that travels 30 miles in \frac{3}{4} 4 3 hour at a constant speed.
Answers
Step-by-step explanation:
If distance is 20 miles and time is (1/2) h. Its speed is given by :
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{20\ miles}{1/2\ h}\\\\v=40\ mph[/tex]
If the distance is 30 miles and the time is (3/4) hours. Its speed is given by :
[tex]v=\dfrac{d}{t}\\\\v=\dfrac{30\ miles}{3/4\ h}\\\\v=40\ mph[/tex]
So, the rate or the speed ib both the case is constant.
To rent a certain meeting room, a college charges a reservation fee of $41 and an additional fee of $8.30 per hour. The history club wants to spend at most $99.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality fort.
Answers
Answer:
7hours maxStep-by-step explanation:
let the total charges be y
and the number of hours be t
the total cost can be modelled linearly as
y=mt+c
given that
c=$41
m=$8.30
Therefore for y=99.10, we want to solve for t
99.1=8.3t+41
solve for t
99.1-41=8.3t
58.1=8.3t
t=58.1/8.3
t=7
therefore the time is 7hours max
Find the volume of a square pyramid with base edges of 48 cm and a slant height of 26 cm
Answers
Answer:
mks
Step-by-step explanation:
w mw
6. Find XY. Any answers
Answers
2a+6=36
2a=36-6
2a=30
a=15
15+6=21
Which choice shows a true conditional, with the hypothesis and conclusion identified correctly?
A:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: Two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
B:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: Two lines are perpendicular.
Conclusion: Two lines do not intersect at right angles.
C:
Two lines are parallel if the lines intersect at right angles.
Hypothesis: Two lines intersect at right angles.
Conclusion: Two lines are parallel.
D:
Two lines are perpendicular if the lines intersect at right angles.
Hypothesis: Two lines intersect at right angles.
Conclusion: Two lines are perpendicular.
Answers
Answer:A:
If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: Two lines are perpendicular.
Conclusion: Two lines intersect at right angles.
Step-by-step explanation:
ASAP ASAP ASAP
please help me with this
Answers
Answer:
b
Step-by-step explanation:
Find the Product:
[tex](9+4s)(4+s)[/tex]
Answers
Plz HELP ME! Can someone rotate this 90 degrees counter clockwise? TYSM (:
Answers
Answer:
I cant really see it but this will help 100%.
Step-by-step explanation:
Find the mode of the set of data.
59, 61, 54, 61, 38, 46, 56, 52, 63, 40, 44
O A. 61
O B. 52.2
O C. 50.5
O D. 54
Answers
Answer:
61
Step-by-step explanation:
The mode of a set of data is the value in the set that occurs most often and 61 occurred the most so its A