Match each complex number with its equivalent expression.
i
-1
1
-i
i^48
i^223
i^113
i^82
Answers
Remember that i = √(-1), so that
• i ² = -1,
• i ³ = i x i ² = i x (-1) = -i
• i ⁴ = i x i ³ = i x (-i) = -i ² = -(-1) = 1
Multiplying by i again gives i ⁵ = i and the cycle starts over.
The main observation to make here is that raising i to any multiple of 4 returns 1. So,
i ⁴⁸ = (i ⁴)¹² = 1¹² = 1
i ²²³ = i ²²⁰⁺³ = i ²²⁰ x i ³ = (i ⁴)⁵⁵ x i ³ = 1⁵⁵ x (-i) = -i
i ¹¹³ = i ¹¹²⁺¹ = i ¹¹² x i = (i ⁴)²⁸ x i = 1²⁸ x i = i
i ⁸² = i ⁸⁰⁺² = i ⁸⁰ x i ² = (i ⁴)²⁰ x i ² = 1²⁰ x (-1) = -1
i^48 = 1
i^223 = -i
i^113 = i
i^82 = -1
Related Questions
In this figure, ∠1 and ∠2 are located on a line.
Let m∠1=x° and m∠2=(14x)°.
What is the value of x?
Enter your answer in the box.
Answers
In a straight line, all angles sum up to 180°
====================================
[tex]\hookrightarrow \sf x +\dfrac{1}{4} x = 180[/tex]
[tex]\hookrightarrow \sf \dfrac{4x}{4} +\dfrac{1}{4} x = 180[/tex]
[tex]\hookrightarrow \sf \dfrac{4x+x}{4} = 180[/tex]
[tex]\hookrightarrow \sf 4x+x= 180(4)[/tex]
[tex]\hookrightarrow \sf 5x= 720[/tex]
[tex]\sf \hookrightarrow x = 144[/tex]
Answer:
x = 144°
Step-by-step explanation:
Since the larger line is a straight line, ∠1 and ∠2 are a linear pair. A linear pair is such a pair where two angles sum up to 180°.
⇒ ∠A + ∠B = 180°
Substitute the measure of ∠A and ∠B
⇒ x + x/4 = 180° [∠A = x; ∠B = x/4]
⇒ 4x/4 + x/4 = 180° [Rewrote x as 4x/4]
⇒ 5x/4 = 180°
Using cross multiplication
⇒ 5x = 180 × 4 = 720
⇒ x = 720/5 = 144°
what is the square root of 12?
Answers
Find the area can i get the answer ASAP pls......................
Answers
For the second problem, we can notice that the shape is a trapezoid. The way we find the area of a trapezoid is by taking the average of the bottom length and the top length, and multiply it by the height. The first step is to do 16+8 to get 24. Next, you need to divide 24 by 2 since you’re finding the average of the two numbers. Finally, to finish multiply the height by 12. In this case you do 16*12, to get 192 feet squared.
Answer to A: 3456 Yards Squared
Answer to B: 192 Feet Squared
The ratio of dogs to cats is 6:11. if i have 18 dogs, how many total animals do i have
Answers
Answer:
51
Step-by-step explanation:
6 dogs: 11 cats
12 dogs: 22 cats
18 dogs : 33 cats
18 + 33 = 51
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A manufacturer makes chocolate squares that have a target weight of 8 g. Quality control engineers sample 30 chocolate squares to see whether H0: μ = 8 vs. Ha: μ ≠ 8 where μ is the true average weight of the chocolate squares. They calculate the sample mean of the 30 squares to be 8.3 g. Suppose the population standard deviation is 0.87 g and the true weight is 8.5 g. At the 5% level of significance, calculate the power for the test. For full credit, include all steps as described in class.
Answers
Using the normal distribution and the central limit theorem, it is found that the power of the test is of 0.9992 = 99.92%.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is [tex]\mu = 8.5[/tex].The standard deviation is [tex]\sigma = 0.87[/tex].A sample of 30 is taken, hence [tex]n = 30, s = \frac{0.87}{\sqrt{30}} = 0.1588[/tex].The power of the test is given by the probability of a sample mean above 8, which is 1 subtracted by the p-value of Z when X = 8, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8 - 8.5}{0.1588}[/tex]
[tex]Z = -3.15[/tex]
[tex]Z = -3.15[/tex] has a p-value of 0.0008.
1 - 0.0008 = 0.9992.
The power of the test is of 0.9992 = 99.92%.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
Get Fit Gym currently has 96 members participating in their aerobic classes, and this number has been increasing by 2 people per
week. The cycling classes have a total of 80 members who participate, and this number
has been decreasing by 3 people per
week. In how many weeks will the number of people working out in the aerobics classes be double the number of people
attending the cycling classes?
Answers
Step-by-step explanation:
mx + b = y
2x + 96 = y
-3x + 80 = z
What we want is y to be twice z, or y = 2z
If we're going to make 2z, then that means its equation needs to be doubled as well:
2x + 96 = 2(-3x + 80)
2x + 96 = -6x + 160
8x = 64
x = 8
Now to check our answer:
2 * 8 + 96
16 + 96 = 112
-3 * 8 + 80
-24 + 80 = 56
56 * 2 = 112
hope it helps :)
Solve this system of equations algebraically:
y – 10 = 11x + x2
y – 12x = 30
The first solution is (–4, –18).
The second solution is
Answers
Answer:
5,90
Step-by-step explanation:
got it correct :)
The second solution for the system of equations is (5, 90).
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given the system of equations,
y - 10 = 11x + x² and
y - 12x = 30
Consider second equation.
y - 12x = 30
⇒ y = 30 + 12x
Substitute y = 30 + 12x in the equation y - 10 = 11x + x², we get,
(30 + 12x) - 10 = 11x + x²
12x + 20 = 11x + x²
12x - 11x - x² + 20 = 0
-x² + x + 20 = 0
x² - x - 20 = 0
Discriminant = [tex]\sqrt{(-1)^{2} -(4*1*-20)}[/tex] = √(1 + 80) = √81 = ±9
x = (1 + 9)/2 and x = (1 - 9) / 2
x = 5 and x = -4
The solution x = -4 and y = -18 is given.
Other solution is,
x = 5
y = 30 + 12x = 30 + 60 = 90
Hence the second solution is (5, 90).
Learn more about Linear Equations here :
https://brainly.com/question/19770987
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Help help ASAP pelsss thanks
Answers
Answer:
(5,1)
Step-by-step explanation:
6(x-1)=9(x+2) what's the answer?
Answers
Answer:
x=-8
Step-by-step explanation:
Slove for x
Show all work
Answers
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
[tex](x)(y)=9(4)[/tex]
[tex]\sqrt{x^2} =\sqrt{36}[/tex]
[tex]x=6[/tex]
~
A car rents for $280 per week plus $0.15 per mile. Find the rental cost for a three-week trip of 900 miles.
Answers
Answer:
$975
Step-by-step explanation:
The car is rented for 3 weeks
the rent is for a week is $280 so for three weeks it would be
3*28 = $840
now we need to add the per mile price to this
1 mile = $0.15 for 900 miles it would be
900*(0.15) = 135
So the total rental cost is
$840 + $135 = $975
Which describes the slope of the given line?
A) positive
B) zero
C) negative
D) undefined
Answers
Answer:
C) Negative
Step-by-step explanation:
This is because the top is left and going right
Answer:
negative
Step-by-step explanation:
2x = 1/32 find the value of x
Answers
Answer:
x = 64
Step-by-step explanation:
2/x = 1/32
cross multiply
2 × 32 = x × 1
64 = 1x
64 = x
I need help please please
Answers
Answer:
A
Step-by-step explanation:
Reflects across the y axis then rotates 180 degrees.
Answer:
reflection then rotation
Step-by-step explanation:
because to get 2 you reflect then 3 is rotated
Which of the following shows figure T rotated 90° clockwise around the Orgin ?
Answers
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
It's the 4th one because it's the only one that rotated at 90° clockwise and around the origin.
if sin(θ)=7/25, when π/2<θ<π, use the given information about θ to find the exact value of sin(θ/2)
Answers
we know that π/2 < θ < π, which is another way of saying that θ is in the II Quadrant, so half that angle will most likely be located on the I Quadrant, where cosine as well as sine are both positive.
Now, let's keep in mind that θ itself is in the II Quadrant, where the cosine is negative whilst the sine is positive.
[tex]\textit{Half-Angle Identities} \\\\ sin\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1-cos(\theta)}{2}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\theta )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{25}}\qquad \textit{let's now find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]
[tex]\pm\sqrt{25^2-7^2}=a\implies \pm\sqrt{576}=a\implies \pm 24=a\implies \stackrel{II~Quadrant}{-24=a} \\\\[-0.35em] ~\dotfill\\\\ cos(\theta )=\cfrac{\stackrel{adjacent}{-24}}{\underset{hypotenuse}{25}} \\\\\\ sin\left(\cfrac{\theta}{2}\right)\implies \pm \sqrt{\cfrac{1-\left( -\frac{24}{25} \right)}{2}}\implies \pm \sqrt{\cfrac{1 +\frac{24}{25} }{2}}[/tex]
[tex]\pm\sqrt{\cfrac{~~\frac{49}{25} ~~}{2}}\implies \pm\sqrt{\cfrac{49}{50}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{49}{50}}}\implies \cfrac{\sqrt{49}}{\sqrt{50}}\implies \cfrac{7}{5\sqrt{2}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{\cfrac{7}{5\sqrt{2}}\cdot \cfrac{\sqrt{2}}{\sqrt{2}}\implies \cfrac{7\sqrt{2}}{5\sqrt{2^2}}}\implies \cfrac{7\sqrt{2}}{10}[/tex]
please help me
NO LINKS!!
Answers
Answer:
D
Step-by-step explanation:
π/3
Coterminal angle:-
π+π/34π/3Or
π-π/3=2π/3Option D
Hello Can Someone Please Answer This Math Question
Answers
Step-by-step explanation:
the answer is in the picture
Please solve this linear algebra equation for 15 points.
Answers
Answer:
[6
-1.5]
the six and 1.5 are in the same bracket the 6 in ontop
Find the value of xx, yy, and zz in the parallelogram below..
Answers
Answer:
36, y = 10, and z = -25
Step-by-step explanation:
99 and -3z +6 are same side interior angles, so they sum to 180 degrees.
99 -3z + 6 = 180
-3z = 75
z = -25
Opposite angles of a parallelogram are congruent
2x + 9 = -3x + 6
2x + 9 = 75 + 6
2x = 81 - 9
2x = 72
x = 36
9y + 9 = 99
9y = 90
y = 10
Please help I don’t understand please I really need helppppppppp
Answers
Answer:
it's 4
Step-by-step explanation:
you just divide 8 and 4
8÷4= 4
Working together, Bill and Tom painted a fence in 8 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but took 12 hours less than Tom took. How long did Bill and Tom take, when each was painting alone?
Answers
Answer:
Tom paints the fence in 24 hours and Bill paints the fence in 12
Step-by-step explanation:
T = 1 fence / x hours
B = 1 fence / x - 12 hours
B + T = 1 fence / 8 hours
( 1 fence / x - 12 hours ) + ( 1 fence / x hours ) = 1 fence / 8 hours
( 1 / x - 12 ) + ( 1 / x ) = 1 / 8
multiply through all the denominators to get:
8x + 8 (x - 12 ) = x( x - 12 )
8x + 8x - 96 = x^2 - 12x
combine like terms to get:
x^2 - 28x + 96 = 0
factor to get:
( x - 4 ) ( x - 24 ) = 0
x = 4, 24
4 won't work, because that would mean Bill would take a negative amount of time to paint the fence by himself, so that means
Tom paints the fence in 24 hours and Bill paints the fence in 12
The floor of a NYC subway car measures approximately 12 feet. How many cubic feet of space are there in a subway car?
Answers
The cubic feet of space that is in the subway car is the volume of the subway car which is 5,502.
How many cubic feet of space are there in a subway car?The shape of a subway car is in the form of a rectangular prism. In order to determine the cubic feet of space, the volume of the car has to be determined. The formula for the volume of a rectangular prism would be used.
Volume = width x height x length
12 x 51 x 8.5 = 5205
Here is the complete question:
The floor of an NYC subway car measures approximately 51 feet by 8.5 feet. The height of the NYC subway car measures approximately 12 feet. How many cubic feet of space are there in a subway car?
To learn more about the volume of a cuboid, please check: https://brainly.com/question/26406747
Simplify to create an equivalent expression.
20-n – 3) – 7(5 + 2n)
Choose 1 answer:
-16n – 37
-16n - 41
16n - 41
16n +41
Answers
Answer:
by the way u typed in your answer I got -15n-12
Step-by-step explanation:
let me know If it is written another way
Answer:
its b
Step-by-step explanation:
On January 22 in 1943, the town of Spearfish, South Dakota, set the record for the world’s fastest temperature change.
At 7:30 a.m., the temperature was `-4`°F.
By 7:32 a.m., the temperature was `45`°F.
By 9:00 a.m. the same day, the temperature was `54`°F.
By 9:27 a.m., the temperature was `-4`°F.
How many degrees did the temperature change each minute from 7:30 to 7:32?
Answers
Answer:6 degrees
Step-by-step explanation:
For the polynomial below,what is the power of the term with the coefficient of 1? x^3+1/3x^4+6x+5
Answers
Hi! I hope you're enjoying your day!
Please remember that the coefficient is the number before a variable.
Also, if we have no coefficient, then we have a coefficient of 1.
Here we have
x^3 (no coefficient)
the power is after the ^ symbol or written above a number (like [tex]\bold{t^h}[/tex]) where h is the power of t
Hence, the answer is
[tex]\boxed{\boxed{\bold{3}}}[/tex]
Hope everything is clear.
Let me know if you have any other questions; if so, feel free to use the comment section.
#LearningDoesn'tEnd
#LearningIsFun
How do I subtract 8 1/2 - 6 7/8
Answers
Hope this helps :)
HELP ME PLEASE I NEED HELP
Find the value of g(25) for the function below.
g(x) = 24(x − 39)
A.
561
B.
-14
C.
-336
D.
-911
Answers
Answer:
C.-336
Step-by-step explanation:
g(25)=24(25‒39)
=24(‒14)
=‒336
i hope it helps you
Step-by-step explanation:
g(x) =24(x-39)
g(25)=24(25-39)
=24(-14)
=-336
=c
PRECAL EDGE HELPPPPP
The water level at a pier is modeled by the function y= 2.5 cos(2pi/12.5) +12, where y represents the water level
measured in meters, and x represents the number of hours since the last high tide. After how many hours is the water
first expected to reach a depth of 12 meters? Round to the nearest tenth of an hour.
Answers
Answer:
3.1
Step-by-step explanation:
Answer:
3.1
Step-by-step explanation:
edg 2021
Martin and Eva pool their loose change to buy snacks on their coffee break. One day, they spent $5.80 on 1 carton of milk, 2 donuts, and 1 cup of coffee. The next day, they spent $6.75 on 3 donuts and 2 cups of coffee. The third day, they bought 1 carton of milk, 1 donut and 2 cups of coffee and spent $6.05. How much is the price of a carton of Milk? (Write only the amount, example, $2.50)
Answers
Answer:
250
Step-by-step explanation:
gsv