1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DedPeter [7]
3 years ago
8

3x-y+2=0 in rectangle form

Mathematics
1 answer:
kotegsom [21]3 years ago
8 0

Complete Question:

Convert 3x-y+2=0 in rectangle form to polar form

Answer:

r ( 3cosθ - sinθ) = -2

Step-by-step explanation:

The equation so given is already in rectangular form, the task is to convert it to polar form.

3x - y + 2 = 0

To transform an equation from the rectangular to the polar coordinate:

x = r cosθ

y = r sinθ

Substitute the representations for x and y into the given equation:

3(r cosθ) - (r sinθ) + 2 = 0

3rcosθ - rsinθ = -2

The polar representation of the equation then becomes:

r ( 3cosθ - sinθ) = -2

You might be interested in
A recent survey describes the total sleep time per night among college students as approximately Normally distributed with mean
marin [14]

Answer:

a) \sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981

b) We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

c) z = \frac{6.9-6.72}{0.0981}= 1.835

And we can use the z normal table or excel and we got:

P(Z

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the total sleep time of a population, and for this case we know the distribution for X is given by:

X \sim N(6.72,1.26)  

Where \mu=6.72 and \sigma=1.26

(a)  What is the standard deviation for the average time in hours? (Round your answer to four decimal places.)

For this case the sample mean have the following distirbution

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the deviation is given by:

\sigma_{\bar X}= \frac{1.26}{\sqrt{165}}= 0.0981

in minutes?= (Round your answer to three decimal places.)  

(b)  Use the 95 part of the 68–95–99.7 rule to describe the variability of this sample mean. (Round your answer to four decimal places.)

The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".

• The probability of obtain values within one deviation from the mean is 0.68

• The probability of obtain values within two deviation's from the mean is 0.95

• The probability of obtain values within three deviation's from the mean is 0.997

We expect 68% of the values between : (6.6219, 6.8181)

We expect 95% of the values between : (6.5238, 6.9162)

We expect 99.7% of the values between : (6.4257, 7.0143)

(c) What is the probability that your average will be below 6.9 hours? (Round your answer to four decimal places.)

For this case we can use the z score formula given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And we can find the z score for 6.9 and we got:

z = \frac{6.9-6.72}{0.0981}= 1.835

And we can use the z normal table or excel and we got:

P(Z

4 0
3 years ago
How to Simplify the rational expression.
alexandr402 [8]
  2r - 4       2(r - 2)
--------- = -----------   = 2
 r - 2            r - 2

answer
2
3 0
3 years ago
At the beginning of a basketball season, the panthers won 20 games out of 50 games. At this rate, how many games will they win i
Anton [14]

Answer:

They will win 48 games in a 120 game season.

Step-by-step explanation:

The team won 20 games out of 50; that is a 20:50 ratio, that is equal to x:120.  x is the amount of games won in the 120 game season.

Set up the ratios like this:

\frac{20}{50} = \frac{x}{120}

cross multiply the numerators and denominators to get this:

20*120 = 50x

solve for x:

2,400 = 50x

x = 48

8 0
3 years ago
Find the missing side in the similar figures below
Lerok [7]

Answer:

a. 28.8

Step-by-step explanation:

Using the theorem of similarity, the following equation can be generated:

\frac{x}{12} = \frac{25 + 35}{25}

Solve for x

\frac{x}{12} = \frac{60}{25}

Cross multiply

x*25 = 60*12

25x = 720

Divide both sides by 25

x = 28.8

5 0
3 years ago
Ross has to fill up a 300 gallon tank. There are already 75
stepan [7]

Answer: He needs 9 hours  to finish the task.

Step-by-step explanation:

Hi, first we have to subtract the gallons of water already in the tank (75) to the total capacity of the tank (300).

300-75 = 225

He needs to fill 225 gallons.

Since the pump Ross uses can fill 25 gallons of water per hour, the proportion is :

25 g / 1h

For 225 gallons:

225 g / x hours  

Solving for x

25/1 = 225/x

x= 225/ (25/1)

x = 9 hours

5 0
3 years ago
Other questions:
  • Describe the rule for multiplying powers with the same base and give an example please
    7·1 answer
  • Please help .<br> From the equation, what is the value of the radius, r ? x2 + y2 = 144
    6·1 answer
  • An item on sale costs 40% of the original price. if the original price was $30, what is the sale price?
    8·1 answer
  • AGain, I need help, hehe. I'm awful at maths.
    15·1 answer
  • There are 18 muffins on a plate. If they are split equally among 9 people, how many muffins will each person get?
    14·2 answers
  • Jacob ran 2/3 of the length of a football field before he was tackled. if the filled is 100 yards long. how far is did Jacob run
    14·1 answer
  • 2 angles are complementary. One of the angles is 30 degrees. The other has a label of 5n + 20. What would "n" have to be?
    5·1 answer
  • 21.6% can u please change this to a decimal and include the work like I had it in the little picture . Plss and thank you .
    9·1 answer
  • Aight come on i need the answer to this question
    15·1 answer
  • Solve the equation 7z=105
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!