Find the cube roots of i. Round all numbers to 3 decimal places. Enter 0s or 1s in the appropriate boxes to answer 0 + i, 1+0i, etc.

Answers

Answer 1

The cube roots of i are:

0.866 + i(0.5)-0.866 + i(0.5)0 - i

Given:

cube root of i

i can be written as cosπ/2 + i sinπ/2

i = cos π/2 + i sinπ/2

general form:

i = cos (2kπ + π/2) + isin(2kπ + π/2) for k=0,1,2

= cos (4kπ+π/2) + i sin(4kπ+π/2)

= cos (4k+1)π/6 + i sin(4k+1) π/6

k = 0: i¹/³ = cos π/6 + i sin π/6

= √3/2 + i 1/2

K = 1, i¹/³ = cos(5π/6) + i sin(5π/6)

= cos(π - π/6) + i sin (π-π/6)

= - cos (π/6) + isin(π/6)

= -√3/2 + i 1/2

k = 2, i¹/³   cos(3π/6) + i sin(3π/6)

= cos (3π/2) + i sin(3π/2)

= cos(π+π/2) + i sin(π+π/2)

= -cos(π/2) - i sin(π/2)

= 0 - i

= -i

Hence we get the required roots.

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Related Questions

A clothing store specializes in blue jeans. They run a regression and get the following results: Coefficients Intercept 200.0 Price -4.5 PriceKhakis 2.2 Advertising 6.5 Weekend 10.0 price is $40, price khakis (a substitute) are $50, advertising is $2, and Weekend is a dummy variable. If it IS the weekend, find price elasticity of the blue jeans. You MUST properly round out 2 decimals exactly and include a negative sign if needed.
Using the elasticity you found before, determine what will happen to the quantity demanded of blue jeans if they drop the price by 5%?

Answers

a. The price elasticity of blue jeans on the weekend is approximately -2.14, indicating that a 1% decrease in price will result in a 2.14% increase in quantity demanded.

b. The quantity demanded of blue jeans will increase by approximately 10.7%.

a. The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Given:

Price = $40

Price of khakis = $50

Advertising = $2

Weekend (dummy variable) = 1 (indicating it is the weekend)

To calculate the price elasticity of blue jeans on the weekend, we need to use the coefficient for the "Price" variable from the regression results.

Price elasticity of demand = (Coefficient for Price * Price) / Quantity demanded

Coefficient for Price = -4.5 (from regression results)

Price = $40 (given)

Quantity demanded can be calculated using the regression equation:

Quantity demanded = Intercept + (Coefficient for Price * Price) + (Coefficient for Price Khakis * Price of khakis) + (Coefficient for Advertising * Advertising) + (Coefficient for Weekend * Weekend)

Intercept = 200 (from regression results)

Coefficient for Price Khakis = 2.2 (from regression results)

Coefficient for Advertising = 6.5 (from regression results)

Coefficient for Weekend = 10.0 (from regression results)

Quantity demanded = 200 + (-4.5 * 40) + (2.2 * 50) + (6.5 * 2) + (10.0 * 1)

Quantity demanded = 200 - 180 + 110 + 13 + 10

Quantity demanded = 153

Now we can calculate the price elasticity of demand:

Percentage change in quantity demanded = (Quantity demanded - Quantity demanded with a 5% price decrease) / Quantity demanded

Percentage change in quantity demanded = (153 - Quantity demanded with a 5% price decrease) / 153

Percentage change in price = 5% (given)

Price elasticity of demand = (Percentage change in quantity demanded / Percentage change in price) * (Price / Quantity demanded)

Price elasticity of demand = ((153 - Quantity demanded with a 5% price decrease) / 153) / 0.05 * (40 / 153)

To find the quantity demanded with a 5% price decrease, we calculate:

New price = $40 - (5% of $40) = $40 - ($2) = $38

New quantity demanded = 200 + (-4.5 * 38) + (2.2 * 50) + (6.5 * 2) + (10.0 * 1)

New quantity demanded = 200 - 171 + 110 + 13 + 10

New quantity demanded = 162

Substituting the values into the formula:

Price elasticity of demand = ((153 - 162) / 153) / 0.05 * (40 / 153)

Price elasticity of demand = (-0.059 / 0.05) * (40 / 153)

Price elasticity of demand ≈ -2.14

The price elasticity of blue jeans on the weekend is approximately -2.14, indicating that a 1% decrease in price will result in a 2.14% increase in quantity demanded.

b. We already calculated the price elasticity of demand (-2.14). Now, we can use this elasticity to determine the percentage change in quantity demanded when the price is reduced by 5%.

Percentage change in price = -5% (given)

Percentage change in quantity demanded = Price elasticity of demand * Percentage change in price

Percentage change in quantity demanded = -2.14 * (-5%)

Percentage change in quantity demanded = 10.7%

Therefore, if the price of blue jeans is reduced by 5%, the quantity demanded will increase by approximately 10.7%.

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A 36-inch diameter pie is cut into 6 slices. What is the area of one of the slices?
A. 54pi inches
B. 216pi inches
C. 6pi inches
D. 24pi inches
E. None of the above

Answers

The area of one of the slices is  54π square inches

What is the area of one of the slices?

The given parameters are

Diameter = 36 inches

Number of slices = 6

The pie represents take the shape of a circle

And the area (A) of a circle using the diameter (d) is

A= π(d/2)^2

Multiply the above area by 1/6 to get the area of a slice of the pie

So, we have

Area = 1/6 * π(d/2)^2

This means that the area of one of the slices is calculated by

Area = 1/6 * π(d/2)^2

Where

d represents the diameter of the pie i.e. d = 36 inches

So, we have

Area = 1/6 * π * (36/2)^2

Evaluate

Area = 54π

Hence, the area of one of the slices is  54π square inches

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Which of the following is not an aquatic ecosystem
A. Marsh
B. River.
C. Tundra
D. Swamp​

Answers

Answer:

marsh.

Step-by-step explanation:

hope it help goodluck bro............

PLEASE HELP,
10 POINTS + BRAINLIEST

Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for
r = 7 in.

The volume of the sphere is about ____in^3.

Answers

What we know:

3.14 pi
radius: 7in.
Result units: in^3, this is the results of in used for radius; no conversion needed
Formula volume of a sphere: (4/3)* pi * r^3

(4/3)(3.14)(7)(7)(7)
(4/3)(3.14)(343)
(4/3)(1077.02)
(1.3)(1077.02) \\repeated 3 infinite
1436.026666\\repeated 6inf

The volume of the sphere is about 1436.0266 in^3

Answer:

Step-by-step explanation:

1436 is the answer

A
5

B
10

C
6

D
4
pls help

A 5B 10C 6D 4 pls help

Answers

Answer:

Pretty sure it's C.

Step-by-step explanation:

A and B are 6 units away from each other.

Answer:

C

Step-by-step explanation:

Count the boxes

A 5B 10C 6D 4 pls help

How do I write \(\sqrt[4]{5}\) using rational exponets?

Answers

This the answer 5^1/4

Hope this help

Answer:

y=45u

Step-by-step explanation:

4 with a 5 try adding / bc its supposed to be like a check sin

help me i need help.

help me i need help.

Answers

Answer:108 inches

Step-by-step explanation:

to find the area of one of the right triangles you do.

base = 6/2 =3

3x6=18

18/2=9

there are 8 right triangles so you would do

9x8 = 72.

then you would add 72 and the area of the square in the middle

6x6=36

36+72= 108

so Area of SA = 108 inches ^2

Which equation has exactly one solution in common with the equation y=6x-2?

A. 18x - 3y = 6
B. 1/2y = 3x - 2
C. 2y = 4x - 12
D. 18x - 12 = 3y

Answers

Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Find the mean, the median, and the mode of each data set.
0 0 1 1 2 3 3 5 3 8 7

Answers

Answer:

mean is 3 median is 3 and mode is also 3

Step-by-step explanation:

brainliest helps

What is the value of this expression when x=8 and y=-(1)/(2)? 4(x^(2)+3)-2y

Answers

When x = 8 and y = -(1/2), the value of the expression 4(x^2 + 3) - 2y is 269.

The expression given is:

4(x^2 + 3) - 2y

We are asked to evaluate this expression when x = 8 and y = -(1/2). Substituting these values, we get:

4(8^2 + 3) - 2(-1/2)

Simplifying inside the parentheses first:

4(64 + 3) - 2(-1/2)

= 4(67) + 1

= 268 + 1

= 269

Therefore, when x = 8 and y = -(1/2), the value of the expression 4(x^2 + 3) - 2y is 269.

We can obtain this value by first evaluating the expression inside the parentheses, which is 8^2 + 3 = 67. Then, we multiply this result by 4 to get 4(67) = 268. Finally, we subtract 2 times the value of y, which is -1/2, from this result to get 268 - 2(-1/2) = 268 + 1 = 269.

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A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.

Answers

Slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

What is Slope of Line?

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that A cell phone company uses the equation C=$0.15t+$35.00

C is the total cost for a month of service.

t is the number of text messages.

We have to find the slope of the equation.

slope is 0.15 and 35.00 is the y intercept of the equation given.

Hence, slope is  $0.15 of the equation of cost  C=$0.15t+$35.00.

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can someone solve this with negative exponents

5x^2y^-3
will give brainliest to best answer

Answers

Answer:

x=3 and y=6

Step-by-step explanation:

define the semantics (inference rule) of the if statement: {p} if (e) s1 else s2 {q}. hint: one way to prove it is to do a case analysis. if e is true, the whole statement is equivalent to what? if e is false, the whole statement is what? formulate it as an inference rule.

Answers

The inference rule is ({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q}).

In the given question, we have to define the semantics (inference rule) of the if statement: {P} if (E) S1 else S2 {Q}.

A way of inferring the veracity of one assertion based on the significance of other assertions is known as an inference rule.

(S1, S2, ........, Sn)/S

According to the rule, if S1, S2,..., and Sn are real, then S's validity can be derived.

Given,

{P} if (E) S1 else S2 {Q}

The inference rule is

We know that if if E and P are true then it is S1 with postcondition {Q} or if E and P is false then it is else part that is S2 with postcondition {Q}

i.e. {E and P} S1 {Q},{not E and P} S2 {Q}

So the inference rule is:

({E and P} S1 {Q},{ not E and P} S2 {Q})/({P}if E then S1 else S2{Q})

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define the semantics (inference rule) of the if statement: {p} if (e) s1 else s2 {q}. hint: one way to

Find all numbers such that 85 minus three times the number is at least 250.

Answers

Answer:

x < -55

Step-by-step explanation:

Step 1: Convert word to math

85 - 3x > 250

Step 2: Solve for x

Subtract 85 on both sides: -3x > 165Divide both sides by -3: x < -55

Here we see that any value smaller than -55 will work.

a professional golfer wants help with their putting game. an experiment was conducted to study the effects of four factors on putting accuracy. these factors are length of putt (10 vs 30 ft), type of putter (cavity back vs. mallet), break of putt (breaking vs. straight), and slope of putt (downhill vs. level). the dependent variable is the measured distance from the center of the cup after the ball comes to rest. the golfer wishes to minimize the dependent variable. a 2^4 factorial design with 7 replicates is used and the putts are made in random order. the results are as recoded as follows: a. analyze the data and determine if this is a valid model. b. if the model is not valid, suggest a transformation to improve the model. c. reanalyze the data to determine if this is now a valid model. d. determine which factors significantly affect putting performance. e. make your recommendations to the golfer in order to improve putting.

Answers

A factorial design with 2^4 levels and 7 replicates was used to study the effects of factors on putting accuracy. ANOVA revealed a significant model. The factors that significantly affect putting performance were determined, and recommendations were made to the golfer to improve their putting.

To determine if this is a valid model, we need to perform an analysis of variance (ANOVA) on the data. This will allow us to determine if the means of the groups are significantly different from each other, and if the factors have a significant effect on the dependent variable.

Before performing the ANOVA, we can check for normality of the data using a normal probability plot or a histogram. If the data is not normally distributed, we can consider a transformation, such as a logarithmic or square root transformation, to improve the model.

Assuming that the data is normally distributed, we can perform an ANOVA to determine if the model is valid.

To determine which factors significantly affect putting performance, we need to look at the main effects and interaction effects of the factors. The main effects are the effects of each factor on the dependent variable, while the interaction effects are the effects of combinations of factors on the dependent variable.

We can use a statistical software package, such as SPSS or R, to perform the ANOVA and calculate the main effects and interaction effects.

Based on the results of the ANOVA, we can make recommendations to the golfer to improve their putting. For example, if we find that the length of putt significantly affects putting performance, we can recommend that the golfer focus on practicing putts of a certain length.

Similarly, if we find that the type of putter significantly affects putting performance, we can recommend that the golfer try different putters to find one that works best for them.

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Which is larger:8/10 or 73/100

Answers

Answer:

8/10 is larger

Step-by-step explanation:

8/10 can be also written as  80/100

So comparing 80/100 and 73/100

80/100 is larger thus 8/10 is larger

Hope this helps!

Answer:

8/10

Step-by-step explanation:

Step 1: Convert to Common Denominator (100)

8/10 = 80/100

Step 3: Which is bigger???

80/100 (8/10) is bigger than 73/100

What does this mean and how do I do it

What does this mean and how do I do it

Answers

Answer:

Step-by-step explanation:

The degree of f(x) is 0.

Its leading coefficient is 13 and the type is constant. Because the function is constant,

f(x = 13 when x --> -∞ and

f(x) = 13  when x --> ∞ .

(How? Because I'm smart like that!! :D)

if the observed t value exceeds the critical t value, then the difference between the sample means is most likely ____.

Answers

If the observed t-value exceeds the critical t-value, then the difference between the sample means is most likely statistically significant.

In other words, the difference between the sample means is unlikely to have occurred by chance and is likely due to a real difference in the population means. The direction and magnitude of the difference must be further examined using effect size measures and confidence intervals.

Therefore, the most suitable value to be fit in the blank space of the given incomplete statement is, statistically significant.

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Let T=




−3
2
1


3
1
14





The range of T is (x,y,z), where x,y,z must satisfy the equation Question Help: 囷 Written Example

Answers

The range of the matrix T is the set of all vectors that can be obtained by multiplying T by a vector. In this case, the range of T is the set of all vectors of the form (x, y, z) where x, y, and z satisfy the equation 3x + y + 14z = 0.

The range of a matrix is the set of all vectors that can be obtained by multiplying the matrix by a vector. In this case, the matrix T is a 2 × 3 matrix, so the range of T is a 3-dimensional space.

To find the range of T, we can write T as a linear transformation. The linear transformation that T represents takes a 2-dimensional vector (x, y) and maps it to a 3-dimensional vector (3x + y + 14z, x + y + 14z, y + 14z).

The equation 3x + y + 14z = 0 represents the set of all vectors that are mapped to the origin by the linear transformation that T represents. Therefore, the range of T is the set of all vectors that are not mapped to the origin by the linear transformation that T represents. This is the set of all vectors of the form (x, y, z) where x, y, and z satisfy the equation 3x + y + 14z = 0.

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b. You have a recipe that indicates to use 7
parts of sugar for every 5 parts of flour. You
use 28 cups of sugar. How much flour do you
need?

Answers

Answer:

20 parts

Step-by-step explanation:

7:5

28:x

7*4=28, 5*4=20; x=20

28:20

in general, the strictest standards with the lowest acceptable levels are the

Answers

Answer:

Step-by-step explanation:

are the what???

maximum contaminant levels

what is the slope of the line passing through the points (0,-5) and (4,2)

Answers

Answer: 7/4.

Step-by-step explanation: To find the slope of a line, one must use the formula (y2-y1)/(x2-x1). In this case y2 is 2, y1 is -5, x2 is 4, and x1 is 0. We can plug this into the equation to get 7/4.

Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180. She draws a triangle and extends one of the sides through a vertex. She then draws a line through this vertex that is parallel to the opposite side

Answers

Answer:

As we know, if we add up the interior and exterior angles of one corner of a triangle, we always get 180. the exterior angle in question is equal to the sum of the other two angles in the triangle

Which equation represents a line of best fit for the set of ordered pairs?
{(1, 16), (2, 20), (3, 24), (4, 30), (5, 36)}
A. y = 5x + 10
B. y = 10x + 5
C. y = -5x + 10
D. y = -10x +5

Answers

Answer:

Here’s the answer! Best of luck.

Step-by-step explanation:

Which equation represents a line of best fit for the set of ordered pairs?{(1, 16), (2, 20), (3, 24),

2(4+6) = 2 (

I NEED HELP BADDDDDDDDDDDDD

Answers

Answer:

Need the other part of the problem

Step-by-step explanation:

Maybe...2(4+6)=2(10)

What is an angle that is adjacent to IDH ?

What is an angle that is adjacent to IDH ?

Answers

Answer:

Angle EDC

Step-by-step explanation:

Since angle IDH is perpendicular, that should mean that the other angle should be the same as angle IDH.

If this did not help, let me know.

If it did, your welcome! :)

Could someone help me real quick.
n-6-1=5
what is n? If you can, please also explain how you did it. Thank you a ton!!

Answers

12 is the correct answer. When you have problems like this just add over the equal sign. So 5 plus 6 plus 1 is 12. 12 minus 6 minus 1 is 5!

Answer question with correct answer, if correct i give brainliest. i

Answer question with correct answer, if correct i give brainliest. i

Answers

Answer:

y = 95x (or: miles = 95 x hours)

Step-by-step explanation:

I) Analyze the data:

We can see that for every hour, the train travels 95 miles.

II) Construct the equation:

Let's represent the miles as y and the hours as x.

y = 95x

Let A and B by 3 x 3 matrices with det(A) = –2 and det(B) = 3. Use properties of determinants to compute: (a) det(A³) (b) det(2B) (c) det(ABᵀ) (d) det(B⁻¹)

Answers

Using the properties of determinants, we can compute the following:

(a) det(A³) = (det(A))^3 = (-2)^3 = -8.

(b) det(2B) = 2^3 * det(B) = 8 * 3 = 24.

(c) det(ABᵀ) = det(A) * det(Bᵀ) = det(A) * det(B) = -2 * 3 = -6.

(d) det(B⁻¹) = 1/det(B) = 1/3.

(a) To compute det(A³), we can use the property that the determinant of a matrix raised to a power is equal to the determinant of the matrix raised to that power. Therefore, det(A³) = (det(A))^3 = (-2)^3 = -8.

(b) For det(2B), we can use the property that the determinant of a scalar multiple of a matrix is equal to the determinant of the matrix multiplied by that scalar. Hence, det(2B) = 2^3 * det(B) = 8 * 3 = 24.

(c) To find det(ABᵀ), we can use the property that the determinant of a product of matrices is equal to the product of their determinants. Therefore, det(ABᵀ) = det(A) * det(Bᵀ). Since the determinant of a matrix and its transpose are equal, det(Bᵀ) = det(B). Thus, det(ABᵀ) = det(A) * det(B) = -2 * 3 = -6.

(d) To compute det(B⁻¹), we can use the property that the determinant of the inverse of a matrix is equal to the reciprocal of the determinant of the original matrix. Hence, det(B⁻¹) = 1/det(B) = 1/3.

In summary, (a) det(A³) = -8, (b) det(2B) = 24, (c) det(ABᵀ) = -6, and (d) det(B⁻¹) = 1/3.

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Give the rate in miles per hour.


28 miles in 3/4 hour


28 miles 3/4 hour=

Answers

Answer:

37.33 mph

Step-by-step explanation:

calculator soup app is good for this type of problem.

The rate when expressed in miles per hour gives us;

37.33 miles per hour

We are given;

28 miles in 3/4 hour

This means that a distance of 28 miles is covered in every 3/4 hour.

Now, we want to express it as a rate in miles per hour

Miles per hour simply means speed.

We know that formula for speed is;

Speed = distance/time

Speed = 28 miles/(3/4 hour)

Speed = (28 × 4)/3

Speed = 37.33 miles per hour

Thus, the rate when expressed in miles per hour is 37.33 miles per hour

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