What are the polar coordinates of the rectangular coordinates (2, -2√3)?

A. (4, 11π/6)
B. (4, 5π/3)
C. (2, 5π/3)
D. (2, 11π/6)
​

Common logarithm is the logarithm with the base 10, it is written as:

Natural logarithm is the logarithm with the base of e and is written as ln a.

How to rewrite a logarithm [tex]log_a\ b[/tex] as a ratio of logarithms with a different base c:

Apply this to the given logarithm:

a. Common logarithms:

b. Natural logarithms:

Answer:

[tex]\textsf{a)} \quad \dfrac{\log_{10}4}{\log_{10}\dfrac{1}{3}}=-\dfrac{\log_{10}4}{\log_{10}3}[/tex]

[tex]\textsf{b)} \quad \dfrac{\ln 4}{\ln \dfrac{1}{3}}=-\dfrac{\ln 4}{\ln 3}[/tex]

Step-by-step explanation:

Given logarithm:

[tex]\log_{\frac{1}{3}}(4)[/tex]

The common logarithm is the logarithm with base 10.

[tex]\boxed{\textsf{Change of base}: \quad \log_ba=\dfrac{\log_xa}{\log_xb}}[/tex]

Use the change of base formula to rewrite the given logarithm as a ratio of common logarithms:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{\log_{10}\dfrac{1}{3}}[/tex]

[tex]\boxed{\begin{minipage}{5cm} \underline{Log quotient law}\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\end{minipage}}[/tex]

This can be simplified using the log quotient rule:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{\log_{10}\dfrac{1}{3}}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{\log_{10}1-\log_{10}3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{10}4}{0-\log_{10}3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=-\dfrac{\log_{10}4}{\log_{10}3}[/tex]

The natural logarithm is the logarithm with base e.

[tex]\textsf{Also} \; \log_ex=\ln x[/tex]

Use the change of base formula to rewrite the given logarithm as a ratio of natural logarithms:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\log_{e}4}{\log_{e}\dfrac{1}{3}}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{\ln \dfrac{1}{3}}[/tex]

[tex]\boxed{\begin{minipage}{5cm} \underline{Log quotient law}\\\\$\ln \left(\dfrac{x}{y}\right)=\ln x - \ln y$\\\end{minipage}}[/tex]

This can be simplified using the log quotient rule:

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{\ln \dfrac{1}{3}}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{\ln1 - \ln 3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=\dfrac{\ln 4}{0 - \ln 3}[/tex]

[tex]\implies \log_{\frac{1}{3}}(4)=-\dfrac{\ln 4}{\ln 3}[/tex]

The Fourier transform of this sequence does not exist

What is Fourier Transform?

The output of a Fourier transform is a function of frequency and is a mathematical transformation that breaks down functions into frequency components.

To determine the z-transform of a given sequence, we need to find the sum of the sequence's terms multiplied by z raised to the negative of the term's position. For example, given a sequence x[n], the z-transform X(z) is given by:

[tex]X(z) = sum_{n=-infinity}^{infinity} x[n] * z^{-n}[/tex]

To sketch the pole-zero plot of a z-transform, we need to plot the poles (values of z where the z-transform is infinite) and zeros (values of z where the z-transform is zero) in the complex plane. The region of convergence (ROC) is the set of values of z for which the sum defining the z-transform converges.

[tex]x[n] = a^n u[n][/tex], where a is a constant and u[n] is the unit step function[tex](u[n] = 1 for n > = 0[/tex] and [tex]u[n] = 0 for n < 0)[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} a^n * z^{-n}= 1 / (1 - a*z^{-1})[/tex]

This z-transform has a pole at z = 1/a and a zero at z = 0. The pole-zero plot consists of a single pole at 1/a in the complex plane. The ROC is the set of values of z such that [tex]|a*z^{-1}| < 1[/tex], which is the region inside the unit circle centered at the origin. The Fourier transform of this sequence exists.

[tex]x[n] = (-1)^n u[n].[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} (-1)^n * z^{-n}= 1 / (1 + z^{-1})[/tex]

This z-transform has a pole at z = -1 and a zero at z = 0. The pole-zero plot consists of a single pole at -1 in the complex plane. The ROC is the set of values of z such that [tex]|z^{-1}| < 1[/tex], which is the region inside the unit circle centered at the origin. The Fourier transform of this sequence exists.

[tex]x[n] = n^2 u[n].[/tex]

The z-transform of this sequence is given by:

[tex]X(z) = sum_{n=0}^{infinity} n^2 * z^{-n}= z^{-2} / (1 - z^{-1})^3[/tex]

This z-transform has poles at z = 1, z = 1, and z = 1. The pole-zero plot consists of three poles at the origin in the complex plane. The ROC is the set of values of z such that [tex]|z^{-1}| > 1[/tex], which is the region outside the unit circle centered at the origin.

Hence, The Fourier transform of this sequence does not exist.

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Answer:

A.-7-100. [Since it is -107]

answer: yes.

since y = 6 and x = -1 are parallel to the y and x axis, respectively, they hit each other at a 90° angle when graphed, making a plus sign. they are perpendicular lines.

The sum of the interior angles of a regular polygon with 9 sides will be 1260°. The correct option is A.

An angle is defined in mathematics as the figure formed by joining two rays at their common endpoint. An interior angle is an angle that exists within a shape. Polygons are closed shapes with sides and vertices. All of the interior angles of a regular polygon are equal.

Given that the number of the sides of the polygon is 9. The sum of the interior angles of the polygons will be calculated as,

Sum = ( n - 2 ) 180°

Sum = ( 9 - 2 ) 180

Sum = 7 x 180

Sum = 1260°

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The value of k is 1 and -5.

What is factorization?

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, typically smaller or simpler things of the same kind.

Here, we have

Given function: 5k²+20k-25 = 0

Now, we factorize the given function and we get

5k²+20k-25 = 0

5(k²+4k-5) = 0

k² + 4k - 5 = 0

k² + 5k - k -5 = 0

k(k+5) -1(k+5) = 0

(k+5)(k-1) = 0

k+5 = 0, k-1 = 0

k = -5, k = 1

Hence, The value of k is 1 and -5.

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The angles whose measure are greater than the measure of ∠1 are ∠2, ∠3, ∠7, ∠5 .

The general equation of a straight line is -

    where -

Given is a graph as shown in the image.

The ratio of {y/x} is called the slope of a line. So, we can write -

m = 3/2

m = 1.5

Therefore, the ratio of [y] by [x] is equivalent to 1.5.

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The cotangent of the angle is -√570/30

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

(√30/7,-√19/7)

This means that

(x, y) = (√30/7,-√19/7)

The cot(θ) is calculated as

cot(θ) = y/x

Substitute the known values in the above equation, so, we have the following representation

cot(θ) = (-√19/7)/(√30/7)

Evaluate

cot(θ) = -√19/√30

Rationalize

cot(θ) = -√570/30

Hence, the value of cot(θ) is -√570/30

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The number of the tickets purchased for upper reserve is 146 and lower is 470.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that  there were 616 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $6543.50.

The equations will be formed as,

L + U = 616

12.5L + 8U = 6543.5

Solve the above equations,

12.50L + 8 (616-L) = 6543.5

12.5L + 4928 - 8L = 6543.5

12.50L - 8L = 6543.5 - 4428

4.50L = 2118.5

L = 470

U = 616 - 470

U = 146

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An combined area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!

Z = ( x - μ)/σ

if the random variable X has a mean μ and standard deviation σ,

then transforming X using the z-score creates a random variable with mean 0 and standard deviation 1!

With that in mind, we just need to learn how to find areas under the standard normal curve, which can then be applied to any normally distributed random variable.

An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

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Every normally distributed random variable has a slightly different distribution shape, the only way to find areas using a table is to standardize the variable - transform our variable so it has a mean of 0 and a standard deviation of 1. How do we do that? Use the z-score!

Z = ( x - μ)/σ

if the random variable X has a mean μ and standard deviation σ,

An area of 0.10416 to the right means that it must have an area of 0.90 to the left, so the answer is again 1.28.

Answer:

It is an integer.

It is rational.

Step-by-step explanation:

A whole number is in the set

0, 1, 2, 3...

This set starts at zero and only includes zero and the positive numbers. So the given number is NOT a whole number.

It IS an integer. Integers include positive and negative numbers. That is, whole numbers and their opposites.

The number IS rational. That is, it can be written as a ratio:

-560114/1

Since it is rational, it is not irrational.

Answer:

$1 per movie

$5.50 per video game

Step-by-step explanation:

We know 5 movies and 2 video games cost $16 and 3 movies and 8 video games cost $47.

Let x be the cost of 1 movie and y be the cost of a video game.

5x + 2y = 16

3x + 8y = 47

In the first equation, lets solve for y

2y = 16 - 5x

y = 8 - 2.5x

Now, we can substitute this into the other equation.

3x + 8(8 - 2.5x) = 47

3x + 64 - 20x = 47

-17 x = - 17

x = 1

So a movie costs $1 to rent.

2y = 16 - 5(1)

2y = 11

y = 5.5

A video game costs $5.50 to rent.

Answer:

  0.5 oz

Step-by-step explanation:

You want the greatest possible error associated with the measurement 19 oz.

The possible error is generally considered to be half the place value of least-significant digit. Here, the least significant digit has a place value of units, so the greatest error is 1/2 unit, or 0.5 ounces.

__

Additional comment

We know that values of 18.5 oz up to 19.4999... oz will round to 19 oz. That is why the greatest error is considered to be 0.5 oz.

In practice, there can be some difficulty associated with knowing that a value is 18.5 instead of 18.49. Hence real-world error may actually be slightly larger than 0.5 oz. In math, we ignore that case.

Answer: $45.3

Step-by-step explanation:

1 hour of mowing: $8.80

5 hours of babysitting: $7.30 x 5 = $36.5

$36.5 + 8.80 = $45.3

$45.3 is your answer.

Answer:

45.30

Step-by-step explanation:

its simple math bro lol

The value of MW in the given figure is 5.

In Euclidean geometry, an angle is a figure made up of two rays that have a shared vertex, also known as a common terminus, and are referred to as the angle's sides. The angles of two rays are situated in the plane containing the rays. An angle is also created when two planes intersect at an angle. These are referred to as dihedral angles. Another technique to define two curves is to specify the angle generated by rays that are tangent to the intersection of two curves. Angle is another word for how long a rotation or angle is.

Given,

In the figure,

PM=MW

It means PM is similar to MW

As given in the figure,

PM=5

Since PM is similar to MW

Then,

MW=5

Therefore, the value of MW in the given figure is 5.

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Answer: x + 8 - 8 = 10 - 8

Simplifying the left side of the equation gives us:

x = 2

Therefore, the value of x in this equation is 2.

The equation in standard form of the line that has a slope of 1/4 and passes through the point (4, −8) is written as: -x + 4y = -36.

The equation of a line can be written in standard form as Ax + By = C.

Given the following:

A point (4, -8) = (a, b).

Slope (m) = 1/4.

Substitute m = 1/4 and (a, b) = (4, -8) into y - b = m(x - a):

y - (-8) = 1/4(x - 4)

y + 8 = 1/4(x - 4)

Rewrite the equation in standard form:

4(y + 8) = x - 4

4y + 32 = x - 4

4y = x - 4 - 32

4y = x - 36

-x + 4y = -36

The equation is: -x + 4y = -36.

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The maximum speed of the linear function is y = -7x + 90

a. we have two points connecting (speed, degree) are (+5,55) and (-2,104) representing (x₁ , y₁) and (x₂, y₂)

Slope = (y₂ - y₁) / (x₂ - x₁)

slope = (104-55) / (-2-5) = 49/-7 = -7 mph/1°

speed = slope x (degree) + b

Solve 'b':

55 = -7 x (5) + b

55 = -35 + b

b = 55 + 35

b = 90

y₁ = -7x₁ + 90

b) What does the speed-intercept equal and what does it represent?  

The speed is 90 mph when there is no hill.

c ) What does the degree of steepness-intercept and what does it represent?

Up the hill, the steepness is roughly 12.9 degrees at its maximum. Whenever there is a slope, the car will not move.

d) Interpret the slope in words.

The speed drops by 7 mph for every 1 degree that the hill's steepness increases.

e) If your top speed is 83 mph, how steep is the hill?  Be sure to include whether the direction is up or down.

83 = -7 x + 90

83 -90 = -7x

-7 = -7x

x = 1° up the hill

f) How fast could you go down a 7º hill?

y = -7 (-7) + 90

y = 139 mph

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Answer:

0.27563735723563.

Step-by-step explanation:

74 is an acute angle since it is less than 90° cos (74) = 0.27563735723563. Write cos (74) in terms of sin Since 74° is less than 90, we can express this in terms of a cofunction.

Answer:

116.7m/s

Step-by-step explanation:

distance(s) = 1km = 1 × 1000m = 1000m

Time(t) = 60– 30 = 30s

initial velocity = u

acceleration (a) = 10m/s

using the formula

S = ut + ½at²

1000 = 30u + ½ × 10 × 30²

1000 = 30u + 5 × 900

1000 = 30u + 4500

30u = 4500 – 1000

30u = 3500

divide both sides by 30

u = 116.7m/s

i hope i helped

The equation variation for the electric circuit is  V = 25R.

In each electric circuit, the voltage in a battery is measured in volt and the resistance in the circuit is measured in ohms.

The voltage, V is directly proportional to the resistance, R. In a given circuit the voltage is 200 volts, when the resistance is 8 ohms.

The equation variation for the circuit can be represented as follows:

V α R

V = kR

where

Therefore,

voltage = 200 volts

resistance = 8 ohms

200 = 8k

k = 200 / 8

k = 25

Therefore, the equation is V = 25R

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To find the time it took the cruise ship to travel to Madagascar, we need to use the formula for distance, which is distance = speed x time. We are given the distance and the speed of the ship on the trip there, so we can solve for the time by dividing the distance by the speed:

time = distance / speed

We are told that the distance of the trip there was the same as the distance of the return trip, which took 6 hours. We are also told that the ship traveled 12 km/h on the trip there, so the distance of the trip there was 12 km/h x 6 h = 72 km.

Now we can plug this information into the formula to solve for the time:

time = 72 km / 12 km/h = <<72/12=6>>6 hours

Therefore, it took the cruise ship 6 hours to travel to Madagascar. The correct answer is therefore (A) 12 hours.

The actual annual value of this job to Karla is 33000.

What are arithmetic operations?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

the job will pay 2400 per month,

if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,

the actual annual value of this job to Karla is:

2400 per month

annual value  = 2400 * 12 = 28,800

the medical insurance is 450 a month

half the cost of medical insurance is  225 a month

annual value  = 225  * 12 = 2700

the full 1500 every year tpa retirement plan,

So, the total value is:

= 28,800 + 2700 + 1500

= 33000

Hence,  the actual annual value of this job to Karla is 33000.

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The prevalence of asthma on January 1, 2019 is 0.055, the prevalence of asthma on September 1, 2019 is 0.080, the incidence of asthma between January 1 and September 1 is 0.025, there is not possible to calculate asthma incidence rate for the year 2018.

Prevalence is the formula to determine the rate of some case based on population. This can be calculated by divide the case by the population.

Incidence rate is same as prevalence in some factor except it only calculate time range and for this case it have same formula which is we can calculate incidence rate by divide the case by the population.

So, for January 1, 2019 is

Prevalence = 1,098 / 19,800

= 0.055

For September 1, 2019 is

Prevalence = (1,098 +  new 495) / 19,800

= 1,593 / 19,800

= 0.080

For incidence of asthma between January 1 and September 1 is

Incidence = 495 / 19,800

= 0.025

For 2018 because we are not provided with data for that year so it is impossible to calculate it.

Thus, the prevalence in January 1 is 0.055, September 1 is 0.080, and incidence between January 1 and September 1 is 0.025, and also there is not possible to calculate asthma incidence rat for the year 2018.

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Answer:

Step-by-step explanation:

c 0,4 .01

The green grapes weigh 0.125 pounds more than the red grapes.

1/4 of a pound = 0.25 pounds

1/8 of a pound = 0.125 pounds

0.25 - 0.125 = 0.125 pounds

Hope this helps :)

The y-intercept of Function A is greater than the y-intercept of Function B.

What is y-intercept ?

The y intercept of a graph is the point where the graph intersects the y-axis. We know that the x-coordinate of any point on the y-axis is 0. So the x-coordinate of a y-intercept is 0.

Here are the steps to find the y intercept of a function y = f(x),

Given:

Function A : y=x-1

y-intercept of Function A (x=0) is y = -1

y-intercept of Function B are  -6 , -4 and -3.

Since , -1 > -6  , -1 > -4 and -1 > -3

Hence , the y-intercept of Function A is greater than the y-intercept of Function B.

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Answer:

Harry made 9 resolutions.

Step-by-step explanation:

Tim made x resolutions.

Harry made five more, x + 5.

Harry and Tim's together was 13.

x + x + 5 = 13

combine like terms.

2x + 5 = 13

subtract 5

2x = 8

divide by 2

x = 4

Tim made 4 resolutions.

Harry made 4 + 5, that is, 9 resolutions.

Check:

Harry and Tim together is 13.

4 + 9 = 13

Harry made 9 resolutions.