For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.

For The Following Graph, State The Polar Coordinate With A Positive R And Positive Q (in Radians). Explain

Answers

Answer 1

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )


Related Questions

Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0

Answers

Answer:

x=0 or x=2 or x=−4 or x= (7)(2)

Step-by-step explanation:

plz someone help me with this question

Answers

Answer:

(x+3)^2=-4(y-3)

Step-by-step explanation:

(x-h)^2 = 4p(y-k)

P is the distance between the focus and vertex

P = 1 --> used distance formula for the points of -3,2 -3,3

Vertex is -3,3 --> according to picture

(x+3)^2=-4(y-3)

P is negative since it goes downwards in the picture.

The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.

Answers

Answer:

d. 25.25.

Step-by-step explanation:

A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.

Complete each ordered pair so that it is a solution of the given linear equation.

x - 4y = 4; (_,3), (4,_)

Answers

Answer: (16,3)  and (4,0)

Step-by-step explanation:

Using the equation x-4y=4  is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.

x-4(3)=4  multiply the left side

x - 12 = 4   add  12 to both sides

x= 16

You will now have the coordinates (16,3)  

In the second pair it gives the x coordinate which is 4 but we need to solve for y.  

4 - 4y=4  subtract 4 from both sides

-4        -4

 -4y = 0  Divide both sides by 4

    y = 0

The ordered pair will be (4,0)

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.

Answers

Answer:

[tex]\large \boxed{\$10000.00}[/tex]

Step-by-step explanation:

We can use the formula for continuously compounded interest.

[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]

6. A car dealership would like to estimate the mean mpg of its new model car with 90% confidence. The population is normally distributed; however we are taking a sample of 25 cars with a sample mean of 96.52 and a sample standard deviation of 10.70. Calculate a 90% confidence interval for the population mean using this sample data.

Answers

Answer:

92.9997<[tex]\mu[/tex]<99.5203

Step-by-step explanation:

Using the formula for calculating the confidence interval expressed as:

CI = xbar ± Z * S/√n where;

xbar is the sample mean

Z is the z-score at 90% confidence interval

S is the sample standard deviation

n is the sample size

Given parameters

xbar = 96.52

Z at 90% CI = 1.645

S = 10.70.

n = 25

Required

90% confidence interval for the population mean using the sample data.

Substituting the given parameters into the formula, we will have;

CI = 96.52 ± (1.645 * 10.70/√25)

CI = 96.52 ± (1.645 * 10.70/5)

CI = 96.52 ± (1.645 * 2.14)

CI = 96.52 ± (3.5203)

CI = (96.52-3.5203, 96.52+3.5203)

CI = (92.9997, 99.5203)

Hence a 90% confidence interval for the population mean using this sample data is 92.9997<[tex]\mu[/tex]<99.5203

Figure ABCD is a square find the value of x

Answers

Answer:

x=3

Step-by-step explanation:

since its a square all sides equal each other

5x-2=x+10

4x -2 =10

4x=12

x = 3

Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7

Answers

Rewrite 3 3/4 as an improper fraction

3 3/4 = 15/4

Now you have

15/5 / 5/7

When you divide fractions, change the division to multiplication and flip the second fraction over:

15/4 x 7/5

Now multiply the top numbers together and the bottom numbers together:

( 15 x 7) / (4 x 5) = 105/20

Write as a proper fraction:

105/20 = 5 1/4

Answer: 21/4 or 5 1/4

Explanation:
3 3/4 divide by 5/7
= 15/4 x 7/5
= 105/20
= 21/4 or 5 1/4

12) A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state

Answers

Answer:

0.8343

Step-by-step explanation:

From the question, we have the following values:

Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75

Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25

P = 0.25

n = number of random variables = 9

The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:

P < 4 = P ≤ 3

n = 9

P(x) = n!/(n - x)! x! × p^x × q^(n - x)

x = 3

p = 0.25

q = 0.75

P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)

P(x) =0.8343

The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.

Given information:

75% of the vehicles passing through a checkpoint are from within the state.

So, the probability that the vehicle is from within the state is 0.75.

The probability that the vehicle is from outside the state will be 1-0.75=0.25.

Now, let x be the random variable. So, the value of n=9. and x<4

It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.

So, [tex]x< 4[/tex], p=0.25 and q=0.75.

So, the required probability can be calculated as,

[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]

Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.

For more details, refer to the link:

https://brainly.com/question/14282621

Find the value of NT
A. 4
B. 14
C. 12
D. 16

Answers

Answer:

14

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

12*x = 8 * (x+2)

Distribute

12x = 8x+16

Subtract 8x

12x-8x = 8x+16-8x

4x = 16

Divide by 4

4x/4 = 16/4

x = 4

We want NT

NT = 8+x+2

     = 10 +x

    = 10 +4

    = 14

Which expression is equivaleny to 0.7 + p + 0.86p?

A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p

Answers

Answer:

None of the above.

1.86p + 0.7

Step-by-step explanation:

Step 1: Write expression

0.7 + p + 0.86p

Step 2: Combine like terms

0.7 + 1.86p

None of those answer choices are correct unless you wrote the problem incorrectly.

I NEED HELP ASAP

191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students. Calculate the Margin of Error, rounded to the nearest tenth of a percent. Is it reasonable that the state education department claims the percentage for the entire state is 73%? Justify your answer.

Answers

Answer:

It is not reasonable that the state education department claims the percentage for the entire state is 73%.

Step-by-step explanation:

We are given that 191 of the 288 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                         P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of high school students who went outside more during school hours as elementary school students than they do now as high school students =  [tex]\frac{191}{288}[/tex] = 0.66

           n = sample of high school students = 288

            p = population percentage for the entire state

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

The margin of error is given by;

       M.E.  =  [tex]2 \times \sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]

                =  [tex]2 \times \sqrt{\frac{0.66(1-0.66)}{288} }[/tex]

      M.E.  =  0.056 or 5.6%

So, the confidence interval so formed = [tex]\hat p \pm \text{Margin of error}[/tex]

                                                                = [[tex]0.66 - 0.056 , 0.66 + 0.056[/tex]]

                                                                = [0.604, 0.716]

Since the above interval does not include 0.73 or the population proportion of 73% falls outside the above interval. So, it is not reasonable that the state education department claims the percentage for the entire state is 73%.

Select the best estimate of the capacity of a bath tub. A. 5 ml B. 500 ml C. 50 cl D. 500 L.

Answers

Answer:

D. 500 L

because ml cl is smaller than L

Answer:

D. 500 L

Step-by-step explanation:

Choice A (5 ml) is basically a teaspoon. A bathtub can most definitely hold much more then one teaspoon of water.

Choice B (500 ml) is about 17 ounces. Which is basically the amount of water in a normal water bottle. A bathtub can hold more then the amount of water in one water bottle.

Choice C (50 cl) is a little bit more then 2 cups of water. I believe a normal bathtub can hold about 1280 cups of water.

That rules out choices A, B, and C. By process of elimination, we can tell choice D is the answer. But let's just take a look at D.

Choice D (500 L) is about 132 gallons. This is the most plausible one, although some bathtubs don't hold as much water as that, it still is the best estimate of the capacity of a bath tub. \

Hope that helped!

Please help me on question 4 and 5 I am really stuck thank you I would really appreciate it

Answers

Answer:

1. 5/4

2. 7

Step-by-step explanation:

1) Lets call the width as w

Therefore length would be:

w+4

To find the perimeter you use the formula:

2 (l+w)

Now substitute our values into this formula:

2 (w+4+w)

2( 2w+4)

4w+8

Now make this equal to 13:

4w +8 = 13

4w = 5

w = 5/4

2. In this question we will call length l

Therefore width would be:

l-5

Now we will do the steps we did above:

2 (l+l-5)

2 (2l-5)

4l -10

4l - 10 = 18

4l = 28

l = 7

Which choice is equivalent to the expression below? √-12

A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i

PLEASE DON’T GUESS

Answers

Answer:

D.  2i√3

Step-by-step explanation:

You have the expression √-12.  You can divide the number in the radical sign into the numbers that make up the expression.  After you do this, you will be able to take numbers out of the radical sign

√(-12)

√(-1 × 4 × 3)

√-1 = i

√4 = 2

√3 = √3

2i√3

The answer is D.

Complete the point-slope equation of the line through (2,3)(7,4). Use exact numbers. y-4=


Please help me, I would really appreciate it!

Answers

Answer:

The answer is

[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]

Step-by-step explanation:

To find the equation of a line given two points first find the slope and use the formula

[tex] y - y_{1} = m(x - x_{1})[/tex]

Where m is the slope

To find the slope we use the formula

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

The slope of the line using points

(2,3)(7,4) is

[tex]m = \frac{4 - 3}{7 - 2} = \frac{1}{5} [/tex]

Equation of the line using point (7,4) and slope 1/5 is

[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]

Hope this helps you

Answer:

y-4=1/5(x-3)

Step-by-step explanation:

We plug in the x's and the y's and find the slope with:

[tex](y-y_{1} )/ x-x_{1})=m[/tex]

The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in

Answers

Answer:

396 in^2

Step-by-step explanation:

The perimeter of a triangle is given by the formula:

● P = 2w+2L

L is the length and w is the width

■■■■■■■■■■■■■■■■■■■■■■■■■■

The width hereis 18 inches and the perimeter is 80 inches.

Replace w by 18 and P by 80 to find L.

● P= 2L+2w

● 80 = 2L + 2×18

● 80 = 2L + 36

Substrat 36 from both sides

● 80-36 = 2L+36-36

●44 = 2L

Divide both sides by 2

● 44/2 = 2L/2

● 22 = L

So the length is 22 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

The area of a rectangle is given by the formula:

● A= L×w

● A = 22×18

● A = 396 in^2

PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.

Answers

Answer:

The answer is

15x - y = - 126

Step-by-step explanation:

To find the equation of the line we must first find the slope (m)

[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]

So the slope of the line using points

(-8,6) (-9,-9) is

[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]

So the equation of the line using point (-8,6) and slope 15 is

y - 6 = 15( x + 8)

y - 6 = 15x + 120

Writing the equation in the form

Ax+By=C

We have

15x - y = -120-6

The final answer is

15x - y = - 126

Hope this helps you

NEED HELP ASAP trig question!! Need to find y!!

Answers

Answer:

Hey there!

Tangent 70=12/y

Tangent 70y=12

y=12/Tangent 70

y=4.37 cm

Let me know if this helps :)

What fraction of a ton is a pound?

Answers

Answer:

There are 2000 pounds in a short ton. To convert short tons to pounds, multiply the ton value by 2000.

Answer:

5/100000 tons

Step-by-step explanation:

find the derivative of f(x)=3x^2✓x​

Answers

Answer:

  [tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]

Step-by-step explanation:

The power rule applies.

  d(x^n)/dx = nx^(n-1)

__

  [tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]

Four members from a ​"55"person committee are to be selected randomly to serve as​ chairperson, vice-chairperson,​ secretary, and treasurer. The first person selected is the​ chairperson; the​ second, the​ vice-chairperson; the​ third, the​ secretary; and the​ fourth, the treasurer. How many different leadership structures are​ possible?

Answers

Answer:

8,185,320 different leadership structures

Step-by-step explanation:

Since the order at which the members of the committee are chosen matters, this is a permutation of 4 out 55 people and it is given by:

[tex]n=\frac{55!}{(55-4)!}=55*54*53*52 \\\\n=8,185,320[/tex]

8,185,320 different leadership structures are​ possible.

A teacher shares sweets among 8 students so they get 6 each. How many sweets would they each have got if there had been 12 students? ​

Answers

Answer:

4 sweets

Step-by-step explanation:

we know that there is a total of 48 sweets being handed out, and we can tell that this is an example of inverse proportion:

when one increases the other decreases

So, we multiply 8 * 6 to get 48, and then divide that by 12 to get 4 which is how many each student gets

for some constant k -> xy/z=k

∠3 and ∠6 can be classified as:

Answers

Answer:

Alternate Interior Angles

Step-by-step explanation:

Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.

Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.

Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.

Therefore, we are left with Alternate Interior Angles.

Answer:

angle 3 and angle 6 are

1) Alternate Angles

2) Interior Angles

Step-by-step explanation:

(see attached for reference)

|5x|=3 please help me

Answers

Answer: see below

Explanation:

|5x| = 3

5x = 3
x = 3/5

5x = -3
x = -3/5

What is the x-intercept?

Answers

Answer: x-intercept = -94, -74, and -54

A flagpole is 50 feet high. You are standing a distance from the flag pole. The angle of elevation from where you are standing to the top of the flagpole is 23°. How far away from the flagpole are you standing? Note that the angle of elevation is the angle formed by the ground and the line of sight to the top of the flagpole.

Answers

Answer:

x = 21.2 ft

Step-by-step explanation:

x = tanФ h

h = 50

Ф = 23°

x = tan(23°) * 50

x = 21.2 ft

How much work is done in lifting a 1.4-kg book off the floor to put it on a desk that is 0.7 m high?

Use the fact that the acceleration due to gravity is g = 9.8 m/s^2. How much work is done in lifting a 21-lb weight 6 ft off the ground?

Answers

Answer:

Step-by-step explanation:

Work is said to be done when a force applied to an object cause the body to move in a specified direction.

Work-done = Force * Distance

Since Force = mass * acceleration due to gravity

Work-done =  mass * acceleration due to gravity * distance

Given mass = 1.4kg, distance = 0.7m and g = 9.8m/s²

Workdone in lifting the book off the floor = 1.4*0.7*9.8

Workdone = 9.604Joules

- Similarly, work done in lifting a 21-lb weight book 6 ft off the ground is expressed using the same formula as above;

Given mass = 21-lb, g = 32ft/s² and distance = 6ft

Workdone = 21 * 32 * 6

Workdone = 4,032 lb-ft²/s²

Hence, work-done in lifting a 21-lb weight book 6 ft off the ground is  4,032 lb-ft²/s²

Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.

Answers

Answer:

A. The point that splits a line segment into two equal parts.

Step-by-step explanation:

A. The point that splits a line segment into two equal parts.

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.

Learn more about Midpoint:

https://brainly.com/question/5127660

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The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?

Answers

Answer:5

Step-by-step explanation:

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