How do you prove I2 =- 1?

Answers

Answer 1

We check the validity that is equal to -1

The first thing we will do is define numerical sets and complex numbers.

Numerical sets are groupings of numerical values that have a particularity in common, they can be integers, decimals, fractions, among others.

What are Complex Numbers?

Among the numerical sets there is one that we call complex numbers, which include values that are not real, such as "i" a letter that denotes that it is an imaginary number.

The definition of a letter value that identifies a type of complex number is the "i" which is the result of the square root of -1, then we have:

√(-1) = i

√(-1) x √(-1) = i²

[√(-1)]² = i²

(-1) = i²

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Related Questions

jksjsisks 78i2o
[tex]32. \frac{33}{31?} [/tex]

Answers

Answer:

34.064516129

Step-by-step explanation:

[tex]32 \times \frac{33}{31} = \frac{1056}{31} [/tex]

[tex] = 34.064516129[/tex]

i hope this helps

How do you tell if a function is positive or negative on a graph?

Answers

Answer:

You can tell if a function is positive or negative by checking the Y values. If all the Y values are above the x-axis it should be positive, and if the all y values are below the x-axis the function should be negative.

Good luck!

How do you find the Y intercept x intercepts vertical asymptotes and horizontal asymptotes in a rational function?

Answers

To find the x-intercept of a rational function we put y=0 in the given and find the corresponding value of x.To find the y-intercept of a  rational function we put x=0 in the function and the value of y.

what are intercepts?

The x-intercept is the point where a line crosses the x-axis.At this point y=0 and the y-intercepts is the point where a line crosses the y-axis.At this point x=0

It is point where the graph of the rational function intersects the x-axis or y-axis.

How do we find vertical and horizontal asymptotes of rational function?

For Horzontal asymptotes

The horizontal asmptotes of a rational function can be determined by looking at the degree of the numerator and denominator.if Nis the degree of numerator and Dis the degree of denominator.Then N<D

So horizontal asymtote is y=0

To finding horizontal asymptotes we can just focus on degree of numerator and denominator.

For vertical asymptotes

vertical asymptotes occur where the denominator of a rational function approaches zero.A rational function cannot cross a vertical asymptotes because it would be dividing by zero. we set denomintor to zero and solve value of x.The values of x are vertical asymptotes.

Hence we can find easily horizontal and vertical asymptotes of rational function.

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What is the coefficient of y2 in the expression 3y2 4x?

Answers

The coeficient of in the expression is the number 3

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

In the given expression we have the following:

3y² + 4x

 As we are asked for the coefficient of the variable "y" then we must take the number that is just before the letter which in this case is the number 3.

3 is the coefficient of

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What are the mean and standard deviation of the distribution of rs?

Answers

The mean and standard deviation of the distribution of R-S is

B Mean 3 and standard deviation 5

How to find the mean and the standard deviation

The mean is calculated by simply substracting the values

= mean R - means S

= 10 - 7

= 3

standard deviation, SD

standard deviation is solved by the use of radicals and this affects the solution hence it will not be simple subtraction, rather we solve back to remove the radical and hence we get the variance

= (SD, R)² + (SD, S)²

= 4² + 3²

= 16 + 9

= 25

the variance is 25

SD = √variance = √25 = 5

complete question

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S

has mean 7 and standard deviation 3. If Rand S are independent, what are the mean and standard deviation of the

distribution of R-S?

A Mean 3 and standard deviation 1

B Mean 3 and standard deviation 5

C Mean 3 and standard deviation 7

D Mean 17 and standard deviation 1

E Mean 17 and standard deviation 5

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What are the roots of 3x² 5x 2 0?

Answers

The equation 3x² + 5x + 2 = 0 has two solutions, x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.

To solve 3x² + 5x + 2 = 0, we must first find the roots of the equation. To do this, we can use the quadratic formula to solve for the two roots. The quadratic formula is x = [-b ± √(b² - 4ac)]/2a, where a, b, and c are the coefficients of the equation. To apply this to our equation, we have a = 3, b = 5, and c = 2, so the formula becomes x = [-5 ± √(5² - 4(3)(2))]/2(3). Simplifying this equation gives us x = [-5 ± √29]/6. The two solutions of this equation are x = -2 and x = -1/3. This means that when the equation is set equal to zero and then solved, the two values of x that will make the equation true are -2 and -1/3.

x = [-5 ± √29]/6

x = [-5 + √29]/6 = -2

x = [-5 - √29]/6 = -1/3

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Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate.) / e4x dx 19 e8x e4x C 8 19 e4x 19 4x 19 + C 19 19 19 C 19 + C 19 19 + C 8 19 4x 19 0/1 points | Previous Answers SCalcET8 7.6.023. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 33 sec5(x) dx X Use the Table of Integrals to evaluate the integral. 6х4е-x dx

Answers

The integration is as follow

[tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex] = 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C[tex]\int\limits {33 sec^5 (x)} \, dx[/tex] =  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

What is Integration?

Finding an antiderivative of a function is the process of integration. If a function can be integrated and its integral across the domain is finite with the given bounds, then the integration is definite.

Given:

first, [tex]\int\limits {e^{4x} / 19 - e^{8x}} \, dx[/tex]

= [tex]\int\limits {e^{4x} / 19 - e^{(4x)}^2} \, dx[/tex]

let [tex]e^{4x}[/tex] = z

4[tex]e^{4x}[/tex] dx = dz

= 1/4 [tex]\int\limits {dz / \sqrt{19} ^2 -z^2} \,[/tex]

= 1/4 x 1/2√19 log|(z+ √19)/(z-√19)| + C

= 1/8√19 log|([tex]e^{4x}[/tex] + √19)/ ([tex]e^{4x}[/tex] - √19)| + C

Second,

[tex]\int\limits {33 sec^5 (x)} \, dx[/tex]

= 33 [ 1/4 tan x sec³x + 3/4 ∫sec³x dx]

= 33/4  tan x sec³x + 99/4[ 1/2 tan x sec x +1/2 ∫sec x dx]

=  33/4  tan x sec³x + 99/8 tan x sec x +99/8 log (sec x+ tan x) + C

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6 less than a number​

Answers

Answer:

n - 6

Step-by-step explanation:

Number n is A less than B: n = B - A.

Hey people can you guess NFL player with seven Super Bowl

Answers

Maybe Derrick Henry?

Which quadratic function has one real solution
0=2(x+7)(x-5)
0=2/3(x-3)(x-3)
0=2.4(x-2)(x+2)
0=1/2(x-2)(x-1)

Answers

Answer: [tex]0=\frac{2}{3}(x-3)(x-3)[/tex]

Step-by-step explanation:

The roots are [tex]-7[/tex] and [tex]5[/tex].There is one only distinct root, which is [tex]3[/tex].The roots are [tex]\pm 2[/tex].The roots are [tex]1[/tex] and [tex]2[/tex].

The population of a city has decreased by 35% since it was last measured. If the current population is 20,800, what was the previous population?


help pls

Answers

The previous population of the city was 32,000.

What is percentage?

Percentage is a measurement to find value of given number out of hundred.

Given that,

The current population of the city = 20,800.

Let the previous population was 100%.

Since, The population of the city decreased by 35%,

So, the current population of the city = 100 - 35 = 65%

According to given condition,

65 % = 20800

1 % = 20800 / 65

1 % = 320

100% = 320 x 100

         = 32,000

Hence, the initial population was 32,000.

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What doe the expreion 3x4y repreent?
A. The total number of baket of tomatoe and bag of onion the cutomer purchaed
B. The cot per baket for the tomatoe plu the cot per bag for the onion
C. The total cot, in dollar, for the cutomer’ purchae
D. The number of baket of tomatoe and the number of bag of onion that can be purchaed for $7

Answers

The expression 3x+4y represents 3 bags of $3 tomatoes and 4 bags of $4 onions.

What is an expression?

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of logical grammar, such as the operation order.

Given that a basket of tomatoes costs $3, whereas an onion package costs $4. A customer buys y sacks of onions and x baskets of tomatoes.

Three bags of $3 tomatoes and four bags of $4 onions are denoted by the equation 3x+4y.

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Find the product:
[2 1 0] x [1 -1 2] = [a b c]
[-1 -2 1]
[0 1 1]

Answers

Step-by-step explanation:

the multiplication result is found by row×column multiplications.

1st row × 1st column = a

2×1 + 1×-1 + 0×0 = 2 - 1 = 1 = a

1st row × 2nd column = b

2×-1 + 1×-2 + 0×1 = -2 + -2 = -4 = b

1st row × 3rd column = c

2×2 + 1×1 + 0×1 = 4 + 1 = 5 = c

Need help (100 easy points)

Answers

Answer:

Step-by-step explanation:

Please help !!!!!???

Answers

The height of Dubai fountain is 500 feet tall.

Define basic arithmetic.

The foundational subject in mathematics is arithmetic, which covers operations with numbers. These include multiplication, division, addition, and subtraction. One of the key areas of mathematics, arithmetic serves as the cornerstone for students studying the topic of mathematics. The Greek term "arithmos," which means "numbers," is where the word "arithmetic" originates. Arithmetic is one of the oldest and most basic concepts in mathematics. It deals with numbers and the basic operations (addition, subtraction, multiplication, and division) that can be carried out on them.

Given

The Burj Khalifa in Dubai is the tallest building in the world, at 2,717 feet.

Burj Khalifa is 217 feet taller

Height of Dubai fountain

Subtracting

2717 - 217

2500

5 times the height

Divide by 5,

2500/5

500

The height of Dubai fountain is 500 feet tall.

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What is the answer for 2x 3y 12?

Answers

Linear equations are one-degree equations. So, the two solutions of the equation is (0,-4)(6,0).

How do one express the standard form of a linear equation?

It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0. A linear equation has the following standard form: ax + by + c = 0.

Here, variables are x and y and constants a, b, and c are used. Also, a ≠ 0, and b ≠ 0.

We can find the solution of the linear equation by putting x = 0 and y = 0 so that two points form which are the solution of the linear equation,

Put x = 0 in the linear equation 2x - 3y = 12,

2 × (0) - 3y = 12

or, - 3y = 12

or, y = -4

The points is (0,-4)

Put y = 0 in the linear equation 2x - 3y = 12,

2x - 3 × (0) = 12

or, 2x = 12

or, x = 6

The points is (6,0)

Therefore, the two solutions of the equation is (0,-4)(6,0)

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The complete question is as follows:

What is the answer for 2x - 3y = 12?

pls help me I’m confused i’ll give brainliest

Answers

Answer:

I would say the length  is near 8

Answer:

In the given right angled triangle,

base(b)=2 mm and perpendicular(p)=7mm

hypotenuse (h)=?

By using Pythagoras theorem,

h²=p²+b²

or,h²=(7)²+(2)²

or,h²=49+4

or,h²=53

or,h=√53

or,h=7.28

The length of unknown side is 7.28 mm and it is not determined exactly.

The length 7.28 mm is between integers 7 and 8 and it is more closer to 7.

Solve pls brainliest

Answers

Answer:

Your answer is 2,600.019

Step-by-step explanation:

Very simply to answer it with or without a calculator.

2.6 * 10^3 + 0.19 * 10^-2

Without calculator
First move the decimal points before adding.

Positive exponential moves the decimal to the right.

2.6 * 10^3 = 2,600.

Negative exponential moves the decimal to the left.

0.19 * 10^-2 = 0.0019

This equation 2.6 * 10^3 + 0.19 * 10^-2 becomes

2,600 + 0.0019

Then add.

2,600.0019

Given the system: 2x + 3y = 12 2x - y = 4 What is the value of x + y?

Answers

The value of x + y is 5.

What is linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given linear equations are

2x + 3y = 12  ....(i)

2x - y = 4    ......(ii)

To solve the give linear equation, using elimination method.

Subtract equation (ii) from equation (i)

2x + 3y = 12

2x - y = 4

(-)  (+)   (-)

________

   4y = 8

Divide both sides by 4:

y = 2

Putting y = 2 in equation (ii)

2x - 2 = 4

Add 2 with both sides:

2x = 6

Divide both sides by 2

x = 3

Putting x = 3 and y =2 in x + y:

x + y = 3 + 2 =5

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Is Root 3x² 2x a polynomial?

Answers

Yes, √3x² - 2x is a polynomial.

What is a polynomial?

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

√3x² - 2x

This is in the form of ax² - bx

This is a polynomial with degree 2.

Thus,

√3x² - 2x is a polynomial.

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What is dependent and dependent variable?

Answers

Independent and dependent variables are interdependent.

Dependent Variable: The term "dependent variable" refers to the variable that is being measured or tested in an experiment.

The results of the participants' tests, for instance, would be the dependent variable in a study looking at how tutoring affects test scores because that is what is being measured.

If you keep in mind that the dependent variable depends on the independent variable, finding it can be simpler.

The dependent variable's variable is being measured.It might change based on additional circumstances.It is reliant on other elements.A separate variable

This isn't the same as an experiment's independent variable, which is a variable that can stand on its own. The dependent variable (test results), however, may alter depending on the independent variable (tutoring).

The unrelated factor

Because the experimenters are allowed to change the independent variable as necessary, it is called a "independent" variable.

Changing variable in an independent variable.It doesn't alter in response to other factors.It can stand alone.

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Please someone help me with this!
A projectile is fired from the ground at an angle of 30 degrees above the horizon with an initial velocity of 960 ft/sec. If the height as a function of time t is given by h(t)=480t-16t^2, find,
The time when the projectile hits the ground
The maximum height

Answers

I think

h(t)=480t–16t^2

Max height is the vertex of the parabola at t = -b/2a

t = -480/-32 = 15 seconds

--> h(15)

Choose if each statement is True or False. {(2, 2), (3, 2), (4, 2), (6, 2)} is a function: {(-1, 5), (0, 8), (3, 12), (6, 21)} is a function: 5 -10 0 -5 15 -10- 5 0 -5 -10+ 5 5 10 is a function: 10 15 is a function:​

Answers

Answer:

True False True False

Step-by-step explanation:

How do you do 3 terms in binomial expansion?

Answers

The solution of the expression with three terms using binomial theorem can be solved by supposition and resubstituting the value.

Let us consider an example of three terms :

( 1 + x + x² ) ³

Use binomial theorem and expand the given expression:

Standard form of binomial expansion is :

( a + b )ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +..............+  ⁿCₙa⁰bⁿ

Let us consider x + x² = y

( 1 + y )³

=³C₀1³y⁰ +  ³C₁1³⁻¹y¹ + ³C₂1³⁻²y² +  ³C₃1⁰y³

= 1 + 3y + 3y² + y³

Resubstitute the value of y = x + x² we get,

= 1 + 3(x + x²) + 3(x + x²)² + (x + x²)³

= 1 + 3x + 3x² + 3( x² + 2x³ + x⁴) + ³C₀x³(x²)⁰ +  ³C₁x³⁻¹(x²)¹ + ³C₂(x)³⁻²(x²)² +  ³C₃x⁰(x²)³

= 1 + 3x + 3x² + 3x² + 6x³ + 3x⁴ + x³ + 3x⁴ + 3x⁵ + x⁶

= 1 + 3x + 6x² + 7x³ + 6x⁴ + 3x⁵ + x⁶

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Consider the function. f(x)=−8x+4 What is the value of f(−14)?

Answers

The value of polynomial for x = 2 that is f(2) will be 32.  

What is polynomial?

In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science.

They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions. Polynomial rings and algebraic varieties, two fundamental ideas in algebra and algebraic geometry, are constructed in advanced mathematics using polynomials.

We have given polynomial f(x)=3x²8x+4

We have to find the value of f(2

We have to find the value of polynomial for x = 2

So for finding this value we have to just put x = 2 in polynomial

So f(2) will be

So the value of polynomial for x = 2 will be 32

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Grandpa Ernie is shrinking! Over the past 4 years, his height decreased by a total of 2.4 cm 2.4. It decreased by the same amount each year.
What was the change in Grandpa Ernie's height each year?

Answers

Answer:

Step-by-step explanation:

Grandpa Ernie has been shrinking for the past four years. His height decreased by a total of 2.4 cm during this period, which means that it went down by 0.6 cm each year. This gradual decrease in his height is quite remarkable given his age and overall health condition; however, it is not an entirely unexpected phenomenon due to aging and the natural decline of muscle mass with age as well as other factors such as poor nutrition or lack of exercise can contribute to this process too.

a number m is either less than 2 or greater than 9

Answers

it would be a big mistake to have a number like that

A covered Bridge is 8 yards long. In a photograph for sale at a gallery The Bridge is 5/12 foot-long which statements are true?

1. One yard of the covered Bridge is represented by 1.6 inches in the photograph
2. One inch on the photograph represents 1.6 yards of the real bridge.
3. A tree that is 3 inches tall in the photograph is 4.8 yards tall.
4. The people walking over the bridge are about 2.5 inches tall in the photograph.
5. A river that is 12 yards wide is 7.5 inches wide in the photograph.
(PLEASE EXPLAIN)

Answers

Answer:

2. One inch on the photograph represents 1.6 yards of the real bridge.

Step-by-step explanation:

1 yd = 36 in.

8 yd = 36 in./yd × 8 yd = 288 in

1 ft = 12 in.

5/12 ft × 12 in./ft = 5 in.

5 in. in the picture equals 288 inches real.

1 in. in the picture equals 57.6 inches real.

57.6 in. × (1 yd)/(36 in.) = 1.6 yd

1 in. in the picture equals 1.6 yd real

Answer:

2. One inch on the photograph represents 1.6 yards of the real bridge.

Factorize:
(2a^3-8a)÷ 2a (a-2)

Answers

The factorized expression of (2a³ - 8a) ÷ 2a (a - 2) is (a - 4) ÷ (a - 2)

How to factorize the expression?

From the question, we have the following parameters that can be used in our computation:

(2a^3-8a)÷ 2a (a-2)

Rewrite the above expression properly

So, we have the following representation

(2a³ - 8a) ÷ 2a (a - 2)

Divide the fraction by 21

This gives

(a - 4) ÷ (a - 2)

The above expression cannot be solved further

Hence, the solution is (a - 4) ÷ (a - 2)

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5 ≤ y + 2 ≤ 11 find the compound inequality

Answers

Answer:jkd

Step-by-step explanation:

d

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Is coding strand 5 to 3? 2. A swimming pool has a volume of 32,700 cubic feet. How many gallons of water doesthe pool hold?A. 4,371.66 galB. 239,360 galC. 244,596 galD. 4,278.07 gal Name the compound Al2O3.A) Aluminum oxideB) Aluminum (II) oxideC) Dialuminum trioxideD) Aluminum trioxideE) Aluminum (I) oxide If this net were to be folded into a cube, which number would be opposite of the number 1 Marvin is playing a solitaire game with marbles. There are n bowls (for some positive integer n), and initially each bowl contains one marble. Each turn, Marvin may eitherremove a marble from a bowl, orchoose a bowl A with at least one marble and a different bowl B with at least as many marbles as bowl A, and move one marble from bowl A to bowl B.The game ends when there are no marbles left, but Marvin wants to make it last as long as possible.Prove that the game must end after at most n(n+1)/2 turns.Prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns.Marisa comes along and asks to join the game. Marvin and Marisa revise the rules: they will alternate taking turns, starting with Marisa. When the game ends, whoever took the last turn is the winner.Prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy. during a transamination reaction glutamate present in skeletal muscle tissue transfers its amino group to another compound. thus a new compound is produced within the muscle tissue. this newly formed compound is then transported into the blood circulation, and finally enters into the liver tissue. identify the compound to which glutamate would trasfer its amino group during this transamination reaction in muscle tissue. How do you say In order to win a game you have to cheat in french? what type of food provides large amounts of vitamins and minerals with relatively few calories? What are examples of causal relationships? Is 1 the biggest prime number? Collin states that 8+(16+9)=(8+16)+9 is always true. which of the following properties would prove Collin is correct?Transitive PropertyAssociative Property of MultiplicationAssociative Property of AdditionCommutative Property of Addition What is the main role of an external auditor? What is the ordered pair for Point N?Enter the coordinates in the boxes. provide the missing reagents and aromatic compounds in the reaction scheme. show formal charges if applicable. the nitro group can be found in the groups menu. note that this question provides no targeted feedback. What happens to the federal funds rate when there is a recession? while analyzing the advantages of orientation programs for new employees, carson learns that these programs can make new employees more comfortable in their jobs and thus help them focus on their work. this, in turn, increases employee efficiency and reduces the likelihood that they will quit their jobs. which statement should carson avoid making to ensure he doesn't lower his credibility? melissa and brian are going to marriage counseling, as they have had a difficult time getting along and supporting each other since their daughter was born. which therapeutic method is likely used for their treatment? Yesterday the temperature at noon was 26.4F. By midnight, it had decreased by32.4F. What was the temperature at midnight? ANIMAL QUESTION The video discusses giving animals human medications like anti-anxiety or anti-depression drugs. Do you think animals should be treated with drugs used for mental illness? Why or why not? How did the enlightment affect peoples attitudes towards political authority