Convert x2 + y2 = 16 to polar form.r = 16

r = 4

θ = 16

θ = 4

Answers

Answer 1

Answer:

The polar form of the equation x² + y² = 16 is x = 4 or y = 4 or r = 4 ( x = y = r = 4) option (B) is correct.

What is the polar equation?

A polar coordinate system is a two-dimensional coordinate system in which a distance from a reference point and an angle from a reference direction identify each point on a plane.

It is given that:

The rectangular form of an equation is:

x² + y² = 16

The above equation representing a circle equation:

We can write the above equation as follows:

x² + y² = 4²

As we know, the polar form of the equation is:

x = r cos(θ)

y = r sin(θ)

r is the radius of the circle

r = 4

θ is the angle made by the component of x and y:

tanθ = y/x

tanθ = r/r; x = y = r

tanθ = 1

θ = 45 degrees

Thus, the polar form of the equation x² + y² = 16 is x = 4 or y = 4 or r = 4 ( x = y = r = 4) option (B) is correct.

Learn more about the polar form here:

brainly.com/question/13640455

#SPJ5

Answer 2

Answer: The Correct Answer is Option B

r = 4

Ex. CONVERT 2 + 2 = 4 x 4 = 16

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Eric has attended summer camp for 5 weeks every summer for 6 years. How many days has he attended camp in 6 years?

Answers

Answer:

210 days

Step-by-step explanation:

There are 7 days in a week and since he goes for 5 weeks every summer, he goes for 35 days every year. Since he has attended for 6 years, multiply 35 by 6 to get 210, the number of days he has attended camp for.

Answer:

210 days

Step-by-step explanation:

Eric has attended 5 weeks summer camp for a year.

They are asking for 6 years

∴6*5 = 30 weeks Eric had totally in 6 years.

But they want the answer in days:

1 week = 7 days

30 weeks = 30*7 = 210 days

(If this helps you I am happy, if there is a mistake let me know.)

Your welcome

In the equation y = -2x + 5, what is the average rate of change (slope)?a. 5
b. 2
c. -2x
d. -2

please explain

Answers

Answer:

-2

Step-by-step explanation:

Slope = -2

y= Mx+b M= slope
y=-2x+b. -2 is in the m spot

The inside diameter of a randomly selected piston ring is a randomvariable with mean value 12 cm and standard devtiation of .04cm. a. If Xbar is the sample mean diameter form a random sample of=16 rings, where is the sampling distrbution of Xbar centered andwhat is the standard deviation of the Xbar distribution?

b. Answer the questions above for a sample of size n=64

c.find the probability that the average diameter of pistonrings from a sample size 16 is more than 11.95cm

d. For which of the above two random saples is Xbar morelikely to be within .01cm of 12cm? Explain.

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.01 cm.

b) The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.005 cm.

c) 100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm.

d) Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

In this problem:

Mean of 12 cm, thus $\mu = 12$
Standard deviation of 0.04 cm, thus $\sigma = 0.04$ .

Item a:

Sample of 16, thus $n = 16$ and $s = (0.04)/(√(16)) = 0.01$

The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.01 cm.

Item b:

Sample of 64, thus $n = 64$ and $s = (0.04)/(√(64)) = 0.005$

The sampling distribution is approximately normal,centered at 12 cm and with a standard deviation of 0.005 cm.

Item c:

This probability is 1 subtracted by the p-value of Z when X = 11.95, thus:

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem:

$Z = (X - \mu)/(s)$

$Z = (11.95 - 12)/(0.01)$

$Z = -5$

$Z = -5$ has a p-value of 0.

1 - 0 = 1.

100% probability that the average diameter of piston rings from a sample size 16 is more than 11.95 cm.

Item d:

Due to the lower standard error, the sample of 64 is more likely to be within 0.01 cm of 12 cm.

A similar problem is given at brainly.com/question/24663213

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean value (μ) = 12 cm and standard deviation (σ) = 0.04 cm

a) Since a random sample (n) of 16 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

$\mu_x=\mu=12\ cm\n\sigma_x=(\sigma)/(√(n) )=(0.04)/(√(16) )=0.01$

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.01 cm

b) Since a random sample (n) of 64 rings is taken, therefore the mean (μx) ans standard deviation (σx) of the sample mean Xbar is given by:

$\mu_x=\mu=12\ cm\n\sigma_x=(\sigma)/(√(n) )=(0.04)/(√(64) )=0.005\ cm$

The sampling distribution of Xbar is centered about 12 cm and the standard deviation of the Xbar distribution is 0.005 cm

c) n = 16 and the raw score (x) = 11.95 cm

The z score equation is given by:

$z=(x-\mu_x)/(\sigma_x) =(x-\mu)/(\sigma/√(n) ) \nz=(11.95-12)/(0.04/√(16) )\n z=-5$

P(x > 11.95 cm) = P(z > -5) = 1 - P(z < -5) = 1 - 0.000001 ≅ 1 ≅ 100%

d) for n = 64, the standard deviation is 0.01 cm, therefore it is more likely to be within .01cm of 12cm

Which expression represents the phrase " the difference of 18 and 12"?

Answers

Given:

The statement is "the difference of 18 and 12".

To find:

The expression for the given statement.

Solution:

We have,

Given statement = The difference of 18 and 12.

We use subtraction, to find the different between two numbers and subtraction is represented by negative sign. So, we need to subtract second number form the first number.

The difference of 18 and 12 = 18 - 12

Therefore, the required expression for the given statement is 18-12.

2. Anne needs to know how much of her back yard will be used by her newcircular pool. *
1 point
11 feet
What is the area of the pool? Use 3.14 for T.

Answers

Answer:

see below

Step-by-step explanation: 6 13 8 09

area = π r² is the equation to calculate the area of the pool r = radius

I don't no if the 1.11 ft is the diameter of the radius, so I will use the 1.11 ft as the diameter

diameter = 2×radius

diameter / 2 = radius

area = π (d/2)² = T (d/2)² d = diameter π = T

= 3.14(1.11 / 2)²

= 3.14 × (0.555)²

= 0.9677 ft² which seems like a small pool!

8) Which equations below would be parallel by just looking at theequations

1. y=2x + 10 and y= 3x -12
2. y= 4x -2 and y= 4x + 3
3. y=10 and y= 15x
4. not given