Show that the Euler's equation, eiθ=cosθ+isinθ, leads to the following representations of the trigonometric functions cosθ=Re(eiθ)=2eiθ+e−iθ​sinθ=Im(eiθ)=2ieiθ−e−iθ​​ Bonus: use these equations to show that sin2θ+cos2θ=1 and cos(θ1​+θ2​)= cosθ1​cosθ2​−sinθ1​sinθ2​.

[1] H 2.4

    Let us turn the pictures into equations, using the key given. Then, we will solve.

x + x + \(\frac{1}{4}\)x + 1 + 1 + 1 = x + x + x + \(\frac{1}{2}\)x

2x + \(\frac{1}{4}\)x + 3 = 3x + \(\frac{1}{2}\)x

\(\frac{9}{4}\)x + 3 =  \(\frac{7}{2}\)x

3 = \(\frac{5}{4}\)x

x = 2.4

[2] J

    We can tell the first two options are incorrect because there was a change in size, not position.

    Option H would make the shape bigger, but it becomes larger. This means the answer is option J.

Answer:

300 gallons per hour.

Step-by-step explanation:

It takes 4 of 1/4 hours to make 1 hour. Now multiply gallons per quarter hour by four.

75 x 4 = 300

Answer:

A (Only A)

Step-by-step explanation:

the X position can NOT repeat itself at all. In A it does not do that but in the rest it does
in B there is a 2,5 and a 2,2 (Repeating X)

in C there is a -1,4 and a -1, 7 (Repeating X)

in D there is a 3,1 and a 3,2 (Repeating X)

Answer:

A

Step-by-step explanation:

A function is a set of coordinate points that has a separate point for the x axis in every pair.

In order to find a function, just look at the first number in every parentheses and see if there are any multiples

Answer A has -2, 2, -3, and 3

Answer B has 2, 3, 4, and 2

Answer C has 0, -1, 1, and -1

Answer D has 1, 2, 3, and 3

Answer A is the only one that doesn't have repeating x points

Please give brainliest if I helped! :)

We know that 1 gallon = 3.785 L,Therefore, 24.1364 L = 24.1364/3.785 gallons= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

The car travels for 3.0 hours at a velocity of 55 miles per hour. The gas mileage of the car is 11 km/L. We have to find how many gallons of gas will be used on this trip. We can solve this problem by using the following steps:Step 1: Convert the velocity from miles per hour to km/hourWe know that 1 mile

= 1.609 km Therefore, 55 miles per hour

= 55 × 1.609 km per hour

= 88.5 km per hour Step 2: Calculate the distance traveled by the car We know that distance = velocity × time Therefore, distance traveled by the car

= 88.5 km/hour × 3.0 hours

= 265.5 km

Step 3: Convert the distance from kilometers to miles We know that 1 mile

= 1.609 km Therefore, 265.5 km

= 265.5/1.609 miles

= 165.1287 miles (rounded to four decimal places)Step 4: Calculate the fuel consumption in liters We know that fuel consumption

= distance traveled/gas mileage Therefore, fuel consumption

= 265.5 km/11 km/L

= 24.1364 L (rounded to four decimal places)Step 5: Convert the fuel consumption from liters to gallons.We know that 1 gallon

= 3.785 L,Therefore, 24.1364 L

= 24.1364/3.785 gallon

s= 6.3781 gallons (rounded to four decimal places)Therefore, the car will use approximately 6.3781 gallons of gas on this trip.

To know more about gallons visit:

https://brainly.com/question/31702678?

#SPJ11

Answer:

i think

the answer is A. 4.9

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

Read more about Unit Circle at: https://brainly.com/question/26284611

#SPJ1

Answer:

87 people

Step-by-step explanation:

3500-100(cleanup)

3400÷39=87

Answer:

Undefined

Step-by-step explanation:

in order to find the slope we can plug it into the slope formula:

k=(y1-y2)/(x1-x2) where the line contains points (x1,x2) and (y1,y2)

So we plug in

it's equal to -6-4/3-3 which is -10/0 which is undefined because we can't divide by 0

To meet her daily goal, Ling need to pedal approximately 1,008 revolutions each day.

To find the number of revolutions Ling will need to pedal each day to meet her daily goal, we need to first find the circumference of her unicycle tire.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Since the diameter of Ling's unicycle tire is 20 inches, the radius is 10 inches. Therefore, the circumference of her unicycle tire:

C = 2π(10) = 20π inches.

Next, we need to convert Ling's daily goal of one mile, or 5280 feet, to inches. There are 12 inches in a foot, so 5280 feet is equal to 5280 * 12 = 63360 inches.

Finally, we can find the number of revolutions Ling will need to pedal each day by dividing her daily goal in inches by the circumference of her unicycle tire in inches:

Number of revolutions = 63360 inches / 20π inches = 20,160π / 20π = 1,008

Therefore, Ling will need to pedal approximately 1,008 revolutions each day to meet her daily goal.

Learn mroe about Circumference here: brainly.com/question/28758341

#SPJ11

Answer:

D) (8,-22)

Step-by-step explanation:

I used my graphing calculator.

Answer:

D

Step-by-step explanation:

A graphical plot with sales on the Y axis and time on the X axis is a:

a. Scatter diagram.

Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.

Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

Thus, correct option: a

To know more about Scatter diagram refer to:

https://brainly.com/question/6592115

#SPJ4

A continuous time system can behave roughly throughout a variety of periods using a discretized state matrix. A continuous time condition matrix should be used in its place if these requirements are not satisfied since a discretized state matrix might not adequately depict the performance of a continuous time system.

A continuous time condition matrix is a matrix that is used to indicate the state of a system at any moment, as opposed to a discretized state matrix, which is used to describe the status of a system at discrete time intervals. Under the following conditions, a discrete-time state matrix is identical to a time series state matrix:

The system may be regarded as being in stable equilibrium at each time point since the time gaps between every discretization are short enough. This indicates that the behavior of the system does not drastically vary from one-time point to the next.

Over the time frames between each discretization, a linear model accurately predicts the behavior of the system. This means that the behavior of the system can be precisely predicted by a linear equation of the type "Ax = Bu," where A as well as B are matrices and x as well as u are vectors that, respectively, represent the system's state and input.

Over the intervals between each discretization, the system's input remains constant. This indicates that the system's input does not drastically vary from one-time point to the next.

Learn more about the matrix at

https://brainly.com/question/14667821?referrer=searchResults

#SPJ4

Answer:

b) The average speed at which he travelled for the whole journey

Step-by-step explanation:

If he had travel 200- km/h and had broke down by which was at 10:30 a.m  you would have to subtract 200 km/h to 10:30  your answer would be 189.7 when they back on the road also the speed slowed down a bit about 50 km/h so you would add 50 km/h to 20 mins you would get 70km/h they were traveling by, then you add all of the numbers up by 100 you would get 640 so your answer would be 640

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Let us remember that in a 6-sided dice, the numbers it contains are (1,2,3,4,5,6), and of those 3 are odd, then we are going to substitute in the following formula of the simple probability of an event :

Probability of an event=Favorable Cases/Possible Cases

Probability of tossing an odd number with 6 sided number cube =3/6

Probability of tossing an odd number with 6 sided number cube =1/2

Finally we obtain that the probability of tossing an odd number with 6 sided number cube is 1/2.

The statement that Account W will have a balance of approximately $207.19 after 3 years is  true.

Account Y will have earned approximately $368.50 in interest after 5 years is true.

After 10 years, Account Y will earn approximately $110.30 more in interest than Account W will earn is false.

In terms of Account W:

After 3 years, the simple interest earned on the deposit of $2,125 will be:

P x r x t

Where:

P= Principal

r= rate

t = time

$2,125 x 0.0325 x 3

= $2067.19

For Account Y:

The left over after 5 years along with annual compounding will be calculated as:

$2,125 x (1 + 0.0325)⁵

= $2,493.50

The interest earned will be:

$2, 493.50 - $2,125

= $368.50

For the comparison between Account W and Account Y after 10 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

To comparison between Account W and Account Y after 10 years, the formula for compound interest to use will be:

A = P(1 + r/n)^(nt)

For Account W, the interest after 10 years will be:

$2,125 x 0.0325 x 10

= $690.63

The balance after 10 years will be:

$2,125 + $690.63

= $2,815.63

For Account Y, the balance after 10 years along with that of the annual compounding will be:

$2,125 x (1 + 0.0325)¹⁰

=$2925.90

The interest earned will be:

$2925.90 - $2,125

= $800.9

Learn more about interest from

https://brainly.com/question/24274034

#SPJ1

See text below



Trent deposits $2,125 into each of two savings accounts.

• Account W earns 3.25% annual simple interest.

• Account Y earns 3.25% interest compounded annually.

Trent does not make any additional deposits or withdrawals.

Determine whether each statement is true or false based on the given account information. Select the correct answer in each row.

Statement: True or False

Account W will have a balance of approximately $207.19 after 3 years.

Account Y will have earned approximately $368.50 in interest after 5 years.

After 10 years, Account Y will earn approximately $110.30 more in interest than Account W will earn.

Because r must be between -1.00 and +1.00 and the closer to either indicates a stronger relationship, the strongest must be -0.74. It is a strong negative correlation.

Any statistical association, whether causal or not, between two random variables or bivariate data is referred to in statistics as correlation or dependency. A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

A relationship between two variables is said to have a positive correlation when both variables move in the same direction. Consequently, when one variable rises as the other rises, or when one variable falls while the other falls. The link between height and weight is a good example.

Learn more about correlation here

https://brainly.com/question/4219149

#SPJ4

The required quadratic equation is x² - 12x + 36 Or (x - 6)².

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know (a - b) = a² - 2ab + b².

Given, An expression 36 - 12x + __

now, here b² = 36 ⇒ b = 6,

∴ - 2ab = - 2(a)(6).

So, a = 1.

∴ The required quadratic equation is x² - 12x + 36 Or (x - 6)².

learn more about quadratic equations here :

https://brainly.com/question/17177510

#SPJ1

The given statement "a rational expression is undefined if the numerator is zero" is false because a rational expression is undefined if the denominator is zero, not the numerator.

When the denominator of a rational expression becomes zero, the expression becomes undefined because division by zero is not defined in mathematics.

If the numerator of a rational expression is zero, it does not make the expression undefined. Instead, it results in the value of the expression being zero, regardless of the value of the denominator.

To know more about rational expression:

https://brainly.com/question/30488168

#SPJ4

Answer:

x=2

Step-by-step explanation:

Answer:

C. 140

Step-by-step explanation:

C = 1/2 ( 360° - 80°)

c = 1/2 * 280°

c = 140°

A completely random guess for each answer is more likely to earn a perfect score on exam B, which consists of fourteen true-or-false questions, compared to exam A.

Exam A has six multiple-choice questions, and for each question, there are five choices. To earn a perfect score on this exam by random guessing, a student would have to correctly guess the correct option out of five for all six questions.

The probability of guessing one question correctly is 1/5, so the probability of guessing all six questions correctly would be (1/5)^6, which is approximately 0.000064 or 0.0064%.

On the other hand, exam B consists of fourteen true-or-false questions. For each question, there are only two possible choices. Therefore, the probability of guessing one question correctly is 1/2.

To earn a perfect score on exam B, a student would have to guess all fourteen questions correctly, with a probability of (1/2)^14, which is approximately 0.000061 or 0.0061%.

Comparing the probabilities, we can see that the probability of earning a perfect score by random guessing is slightly higher for exam B (0.0061%) than for exam A (0.0064%).

Learn more about exam here:

https://brainly.com/question/29657389

#SPJ11

\((\stackrel{x_1}{0}~,~\stackrel{y_1}{-\frac{3}{5}})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-\frac{3}{5})}=\stackrel{m}{- 1}(x-\stackrel{x_1}{0}) \implies y +\cfrac{3}{5} = - 1 ( x -0) \\\\\\ y+\cfrac{3}{5}=-x\implies y=-x-\cfrac{3}{5}\)

Answer:

y = -x-3/5

Step-by-step explanation:

We are given that a line goes through the point (0, -3/5) and has a slope (m) of -1.

We want to find the equation of this line.

Notice how the answers are written in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y-intercept.

As we are given the slope, we can immediately plug that into the equation.

Substitute m as -1.

y = -1x + b

We can rewrite it to become:

y = -x + b

Now, notice that (0, -3/5), the point we are given is the y-intercept of the line (as the value of x is 0).

So, substitute -3/5 as b in the equation.

y = -x-3/5

The answer is the first one :).

The constant of variation (spring constant) is 7.33 newtons per inch.

What is force ?

Force can be defined as a push or pull that can cause an object to accelerate or deform. In physics, force is a vector quantity that has both magnitude and direction. It is typically measured in units of newtons (N) and is denoted by the symbol "F".

To find the constant of variation, we can use Hooke's Law, which states that the force required to stretch or compress a spring is proportional to the distance the spring is stretched or compressed. Mathematically, this can be written as:

F = kx

where F is the force applied to the spring, x is the distance the spring is stretched or compressed, and k is the constant of variation, also known as the spring constant.

In this problem, we are given that a force of 110 newtons stretches a spring 15 inches. So we can write:

110 = k(15)

To solve for k, we can divide both sides of the equation by 15:

110/15 = k

This simplifies to:

k = 7.33

Therefore, the constant of variation (spring constant) is 7.33 newtons per inch.

To learn more about Force from given link.

https://brainly.com/question/13191643

#SPJ1

Answer:

The estimated total profit of producing 100 units using the trapezoid rule is $6,300.

Explanation:

To estimate the total profit of producing 100 units using the trapezoid rule, we need to calculate the total cost and total revenue first.

Given:

Total fixed cost (TFC) = $2000

Units: 0, 20, 40, 60, 80, 100

Marginal Cost (MC): 260, 250, 240, 200, 240, 250

Marginal Revenue (MR): 410, 350, 300, 250, 270, 250

To calculate the total cost (TC), we'll use the trapezoid rule by averaging the marginal costs at each interval and multiplying them by the corresponding change in units.

Interval 1: 0 to 20 units

Average MC = (260 + 250) / 2 = 255

Change in units = 20 - 0 = 20

TC1 = Average MC * Change in units = 255 * 20 = $5100

Interval 2: 20 to 40 units

Average MC = (250 + 240) / 2 = 245

Change in units = 40 - 20 = 20

TC2 = Average MC * Change in units = 245 * 20 = $4900

Interval 3: 40 to 60 units

Average MC = (240 + 200) / 2 = 220

Change in units = 60 - 40 = 20

TC3 = Average MC * Change in units = 220 * 20 = $4400

Interval 4: 60 to 80 units

Average MC = (200 + 240) / 2 = 220

Change in units = 80 - 60 = 20

TC4 = Average MC * Change in units = 220 * 20 = $4400

Interval 5: 80 to 100 units

Average MC = (240 + 250) / 2 = 245

Change in units = 100 - 80 = 20

TC5 = Average MC * Change in units = 245 * 20 = $4900

Total Cost (TC) = TC1 + TC2 + TC3 + TC4 + TC5 = $5100 + $4900 + $4400 + $4400 + $4900 = $23,700

To calculate the total revenue (TR), we'll use the trapezoid rule by averaging the marginal revenues at each interval and multiplying by the corresponding change in units.

Interval 1: 0 to 20 units

Average MR = (410 + 350) / 2 = 380

Change in units = 20 - 0 = 20

TR1 = Average MR * Change in units = 380 * 20 = $7600

Interval 2: 20 to 40 units

Average MR = (350 + 300) / 2 = 325

Change in units = 40 - 20 = 20

TR2 = Average MR * Change in units = 325 * 20 = $6500

Interval 3: 40 to 60 units

Average MR = (300 + 250) / 2 = 275

Change in units = 60 - 40 = 20

TR3 = Average MR * Change in units = 275 * 20 = $5500

Interval 4: 60 to 80 units

Average MR = (250 + 270) / 2 = 260

Change in units = 80 - 60 = 20

TR4 = Average MR * Change in units = 260 * 20 = $5200

Interval

5: 80 to 100 units

Average MR = (270 + 250) / 2 = 260

Change in units = 100 - 80 = 20

TR5 = Average MR * Change in units = 260 * 20 = $5200

Total Revenue (TR) = TR1 + TR2 + TR3 + TR4 + TR5 = $7600 + $6500 + $5500 + $5200 + $5200 = $30,000

To calculate the total profit (TP), we subtract the total cost from the total revenue.

TP = TR - TC = $30,000 - $23,700 = $6,300

Therefore, the estimated total profit of producing 100 units using the trapezoid rule is $6,300.

Learn more about the trapezoid rule: https://brainly.com/question/30401353

#SPJ11

Answer:

Value of F(2) = 12

Step-by-step explanation:

Given:

F(x) = 7x - 2

Find:

Value of F(2)

Computation:

F(x) = 7x - 2

putting x = 2

f(2) = 7(2) -2

f(2) = 14 - 2

f(2) = 12

So, Value of F(2) = 12

Answer:

For question y=x+3

Your answer is y=(2x+1)+3

Step-by-step explanation:

Answer:

it should be B. welcome!!

Step-by-step explanation:

Answer:

The answer is B) 432

Step-by-step explanation:

The 4 in 432 becomes a 3, because we can't subtract 6 from 3. The 3 becomes 13 and if we subtract 13 with 6... We get 7.

I got 0 with option B... With A I got 2 which is a remainder. With C I got 6.5 (repeating). And with D I got 7.77777777778.

Hence, B) 432 is the correct option.

Check screenshot of my work below.

(I forgot to include 48 on top of the division I just did. Don't mind that too much..)

A) 326

\( \frac{326}{9} \)

\( = 36.2222222222 \)

B) 432

\( \frac{432}{9} \)

\( = 48\)

C) 531

\( \frac{531}{9} \)

\( = 59\)

D) 630

\( \frac{630}{9} \)

\( = 70\)

so, the correct answer is option A.