Population density measures the number of people per square mile inhabiting a given living area. The population a local town as you move away from the city center can be approximated by the function 10,000(3-r at a distance r miles from the city center. a) the population density approaches zero at the edge of the city, what is the city's radius?

the correct answer is (E) 2 integral_pi/3^pi/2 (1/2)((8^2) - (16 cos(theta))^2) d(theta) + 2 integral_pi/2^pi 1/2 (8)^2 d theta|.

The area inside r = 8 and outside r = 16 cos(theta) can be expressed as the difference between the area enclosed by r = 8 and that enclosed by r = 16 cos(theta). Thus, we can use the formula for the area enclosed by a polar curve:

A = (1/2) integral_a^b (r^2) d(theta)

where a and b are the angles of the region of interest.

For the region inside r = 8, we have:

A1 = (1/2) integral_0^2pi (8^2) d(theta) = 32pi

For the region inside r = 16 cos(theta), we have:

A2 = (1/2) integral_0^pi/3 [(16 cos(theta))^2] d(theta) + (1/2) integral_2pi/3^pi [(16 cos(theta))^2] d(theta)
   = (1/2) integral_0^pi/3 (256 cos^2(theta)) d(theta) + (1/2) integral_2pi/3^pi (256 cos^2(theta)) d(theta)
   = 64 integral_0^pi/3 cos^2(theta) d(theta) + 64 integral_2pi/3^pi cos^2(theta) d(theta)
   = 64 integral_0^pi/3 (1 + cos(2theta))/2 d(theta) + 64 integral_2pi/3^pi (1 + cos(2theta))/2 d(theta)
   = 64 (theta/2 + sin(2theta)/4)|_0^pi/3 + 64 (theta/2 + sin(2theta)/4)|_2pi/3^pi
   = 32pi/3

Therefore, the area inside r = 8 and outside r = 16 cos(theta) is:

A = A1 - A2 = 32pi - 32pi/3 = 64pi/3

To express this area as an integral, we need to find the limits of integration. The curve r = 16 cos(theta) intersects r = 8 at theta = pi/3 and theta = 2pi/3. Therefore, the area can be expressed as:

A = (1/2) integral_pi/3^2pi/3 [(8^2) - (16 cos(theta))^2] d(theta)

Simplifying this expression, we get:

A = (1/2) integral_pi/3^2pi/3 [(64 - 256 cos^2(theta))] d(theta)
 = 32 integral_pi/3^2pi/3 (1 - 4 cos^2(theta)) d(theta)
 = 32 [theta - sin(2theta)/2]|_pi/3^2pi/3

Now, evaluating this expression, we get:

A = 32 [(2pi/3 - sqrt(3)/2) - (pi/3 - sqrt(3)/2)]
 = 32 [pi/3 - sqrt(3)]
 = 32pi/3 - 32 sqrt(3)

Therefore, the correct answer is (E) 2 integral_pi/3^pi/2 (1/2)((8^2) - (16 cos(theta))^2) d(theta) +

Visit to know more about Integral:-

brainly.com/question/30094386

#SPJ11

Answer: x<-2, x>-2, all real numbers

Step-by-step explanation:

The function is positive when it is above the x-axis.

The function is negative when it is below the x-axis.

The function is increasing when it is going "up".

The function is decreasing when it is going "down".

The function is positive when x< -2, negative when x> -2, increasing when x< = -2, or decreasing when x > -2

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x, we will get only a single image in y. It is denoted by f(x).

Given that,

we have a graph for a function, y = -x-2

it is intersecting a x-axis at (-2,0)

We can see in the graph following observations

1.   function is positive for x < -2

2.  function is negative for x > -2

3.  function is increasing for x < -2

4.  function is decreasing for x > -2

To know more about Functions check:

https://brainly.com/question/5975436

#SPJ2

Answer:

\(4x^2\left(3x-1\right)\)

Key:

• \(a^{b+c}=a^ba^c\)

• Factor out the last leading term standing to solve in the end.

Step-by-step explanation:

\(12x^3-4x^2\\x^3=xx^2\\=12xx^2-4x^2\\=4\cdot \:3xx^2-4\cdot \:1\cdot \:x^2\\=4x^2\left(3x-1\right)\)

Based on the line of best fit, the approximate maximum depth of a lake that has 31 miles of shoreline is; 142.968 ft

The line of best fit is defined as a straight line which is drawn to pass through a set of plotted data points to give the best and most approximate relationship that exists between such data points.

Now, we are given a table of values that shows the total shoreline in miles which will be represented on the x-axis and then the maximum depth of several area lakes which will be represented on the y-axis.

However, when the geologist found the graph, she arrived at an equation of best fit as;

y = 4.26x + 10.908.

Thus, for 31 miles of shoreline, the approximate maximum depth is;

Approximate maximum depth = 4.26(31) + 10.908.

Approximate maximum depth = 142.968 ft

Read more about Line of best fit at; https://brainly.com/question/1441182

#SPJ1

Answer:

143 feet

Step-by-step explanation:

its technically 142 and change but edmentum rounds up

The real solutions to the given equation are x = 1, x = 0, and x = -1.

x² + x - 1 - 1 = 0 -> x² + x - 2 = 0

(x - 1)(x + 2) = 0

x = 1 and x = -2

-(x² + x - 1) - 1 = 0

-> -x² - x + 1 - 1 = 0

-> -x² - x = 0

Plugging in the solutions, we get:

For x = 1, the left-hand side of the equation is |1 + 1 - 1| = |1| = 1, which equals the right-hand side of the equation, so x = 1 is a valid solution.

For x = -2, the left-hand side of the equation is

|-2² - (-2) - 1|

= |4 + 2 - 1|

= |5|

= 5, which doesn't equal 1, so x = -2 is not a valid solution.

For x = 0, the left-hand side of the equation is

|0² + 0 - 1|

= |-1|

= 1, which equals the right-hand side of the equation, so x = 0 is a valid solution.

For x = -1, the left-hand side of the equation is

|-1² - (-1) - 1|

= |1 + 1 - 1|

= |1|

= 1, which equals the right-hand side of the equation, so x = -1 is a valid solution.

Therefore, the real solutions to the given equation are x = 1, x = 0, and x = -1.

Read more on equations here:https://brainly.com/question/2972832

#SPJ4

1967.64 is the value of the given expression.

We must carry out the division operation in the following manner in order to assess the expression:

26,091 ÷ 13.26

= 1967.64

As a result, the expression has a value of 1967.64.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

The z-score for a subject with a score of 34 on this standardized test is approximately -2.37. This indicates that the subject's score is about 2.37 standard deviations below the population mean. The negative sign indicates that the score is below the mean.

The z-score for a subject who earns a score of 34 on a standardized test with a population mean of 115 and a standard deviation of 30 is approximately -2.37.

The z-score measures the number of standard deviations a raw score is from the mean of a distribution. It is calculated using the formula:

z = (x - μ) / σ

Where:

z is the z-score,

x is the raw score,

μ is the population mean, and

σ is the population standard deviation.

In this case, the subject's raw score is 34, the population mean is 115, and the standard deviation is 30. Plugging in these values into the formula, we have:

z = (34 - 115) / 30 ≈ -2.37

Therefore, the z-score for a subject with a score of 34 on this standardized test is approximately -2.37. This indicates that the subject's score is about 2.37 standard deviations below the population mean. The negative sign indicates that the score is below the mean.

Learn more about plugging here

brainly.com/question/31801008

#SPJ11

The equation given by Jill and Joel both are correct. Option C .

The line passing through the points (2, -1) and (-1, 14).

The equation of a line passing through a point \((x_1, y_1)\) is \(y-y_1=m (x-x_1)\) where m is the slope.

To find the slope m, using slope formula.

\(m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{14-(-1)}{-1-3} \\m=-5\)

Further simplify,

Substitute the values in the given formula.

\(y-y_1=m(x-x_1)\\y-(-1)=-5(x-2)\\y+1=-5(x-2)\)

Further simplify,

5x+y=9

Both the equations are correct.

To learn more about slope refer the link:

https://brainly.com/question/3605446

#SPJ4

The answer to the question is that there were 101.1010 2-person tents.

The formula to solve this problem is: (202 ÷ 2) + (202 ÷ 4) = number of tents.

To calculate the number of 2-person tents, we need to divide the number of people (202) by 2, and then add the result to the number of tents we get when we divide the number of people by 4.

So, (202 ÷ 2) + (202 ÷ 4) = 60.6060 tents.

To find out how many of these tents are 2-person tents, we need to divide the number of people (202) by 2. This gives us the result of 101.1010. This is the number of 2-person tents.

So, to summarise, the answer to the question is that there were 101.1010 2-person tents.

The answer to the question is that there were 101.1010 2-person tents.

Learn more about  number of people here:

https://brainly.com/question/15839036

#SPJ4

When dealing with random walk data, Holt's method is preferred due to its ability to capture short-term fluctuations and changing trends without assuming a specific pattern.

A random walk is a time series where the future values are dependent on the previous values and exhibit a random or unpredictable behavior. In such cases, using methods like Moving Average, Holt-Winters, or Logistic Regression may not yield accurate results because they assume certain patterns or trends in the data.

Holt's method, also known as exponential smoothing, is particularly suitable for handling random walk data. It is a forecasting technique that takes into account both the level and the trend of the time series. This method assigns exponentially decreasing weights to past observations, giving more weight to recent data points. By incorporating a level and trend component, Holt's method can capture the short-term fluctuations and gradual changes in the data without assuming a specific pattern.

Unlike Moving Average or Holt-Winters, Holt's method does not rely on a fixed window of past observations, which can be limiting for random walk data. Instead, it adapts dynamically to the changing characteristics of the time series.

Learn more about Logistic Regression here:

https://brainly.com/question/32687117

#SPJ11

Jacquelyn added the numbers 249 and 3922 to obtain a sum of 4171.

To determine which equation represents the sum of the two numbers that Jacquelyn added, we need to find the equation that results in a sum of 4171.

Let's evaluate each equation:

1. 248 + 3922 = 4170

2. 249 + 3922 = 4171

3. 259 + 3922 = 4181

Out of the three equations, only the second equation, 249 + 3922, results in a sum of 4171. Therefore, the correct equation is:

249 + 3922 = 4171

Thus, Jacquelyn added the numbers 249 and 3922 to obtain a sum of 4171.

Lean more about Sum here

https://brainly.com/question/123868

#SPJ4

Answer:

See below

Step-by-step explanation:

a). 3y-6x=48

soln

or, 3xy=48

or, xy=48÷3

or, xy=32,,

b). y=3x+11

soln

or, y=13x

or, xy=13,,

The height of Jane's shadow who is 5.9 feet tall is appoximately 6.3 feet

Given that, a tree 54 feet tall casts a shadow 58 feet long and Jane is 5.9 feet tall.

To find the height of Jane's shadow, we can use proportions and ratios.

Hence:

(Height of the tree) : (Length of the tree's shadow) = (Height of Jane) : (Length of Jane's shadow)

Plug in:

Height of the tree = 54

Length of the tree's shadow = 58

Height of Jane = 5.9

Let Length of Jane's shadow = x

54 feet : 58 feet = 5.9 feet : x

54/58 = 5.9/x

Cross multiply:

54 × x = 58 × 5.9

54x = 342.2

x = 342.2/54

x = 6.3 feet

Therefore, the measure of her shadow is approximately 6.3 feet.

Learn more about ratios and proportions at :

https://brainly.com/question/29774220

#SPJ1

im confused, what is it that you are asking?

The probability of the event that at most 50 out of 87 people say yes is approximately 0.0188 or 1.88%.

At first, we have to find the probability that at most 50 out of 87 people say yes, we need to use the binomial probability formula.

The binomial probability formula is given by:

P(X ≤ k) = Σ [ \(C(n, k) * p^k * (1 - p)^{(n - k)\) ]

where:

P(X ≤ k) is the probability that the random variable X is less than or equal to k.

n is the total number of trials or people surveyed (87 in this case).

k represents the number of successes (in this case, the number of people who believe the employees are at least somewhat rude).

p is the probability of success on a single trial (64% or 0.64 in decimal form).

Now, we find the probability that at most 50 out of 87 people say yes:

P(X ≤ 50) = Σ [ \(C(87, k) * 0.64^k * (1 - 0.64)^{(87 - k)\) ]

We need to sum the individual probabilities for k = 0, 1, 2, ..., 50.

we get,

P(X ≤ 50) ≈ 0.0188

So, the probability that at most 50 out of 87 people say yes is approximately 0.0188 or 1.88%.

To learn more on probability click:

brainly.com/question/11234923

#SPJ12

As a result, the triangle's centroid at vertices A(2, 6), B(4, 9), and C(6, 15) is (4, 10).

To learn more about triangle's centroid  refer

https://brainly.com/question/7644338

#SPJ4

As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

To know more about Confidence interval here.

https://brainly.com/question/24131141

#SPJ4

Answer: 1.05

Step-by-step explanation:

Fro one to solve a decimal multiplier, we need to either add or subtract the number that we are given in percentage from 100% ane then convert the value we get to a decimal.

In this case, since we want to increase the value by 5%, we add the value to 100% and then change to decimal. This will be:

= 100% + 5%

= 105%

We then divide 105% by 100%

= 105%/100%

= 1.05

The answer is 1.05

O is not reflexive because m - m is not odd. O is symmetric because if m - n is odd, then n - m is also odd. O is not transitive because there exist m, n, and o (1, 2, and 3) such that m - n and n - o are odd, but m - o is not odd

Let's address each part and find the correct values of m, n, and o.

(a) Is O reflexive?
To determine if O is reflexive, we need to check if m O m for every m ∈ Z. We know that m O n if m - n is odd.

When m = n, we have m - m = 0, which is not odd. Therefore, O is not reflexive.

(b) Is O symmetric?
To determine if O is symmetric, we need to check if m O n implies n O m for every m, n ∈ Z. We know that m O n if m - n is odd.

If m - n is odd, then n - m = -(m - n), which is also odd since the negation of an odd number is still odd. Therefore, O is symmetric.

(c) Is O transitive?
To determine if O is transitive, we need to check if m O n and n O o imply m O o for every m, n, o ∈ Z. We know that m O n if m - n is odd.

Let's find values for m, n, and o:
- m = 1
- n = 2
- o = 3

Then, m - n = 1 - 2 = -1 (odd), n - o = 2 - 3 = -1 (odd), but m - o = 1 - 3 = -2, which is not odd. Therefore, O is not transitive.

You can learn more about reflexive at: brainly.com/question/29119461

#SPJ11

The answer is  True, the percentile rank identifies the percentile of a particular value within a set of data.

The percentile rank is a measure that identifies the percentage of scores in a distribution that are equal to or lower than a given score. It is calculated by dividing the number of scores that are equal to or lower than the given score by the total number of scores in the distribution, and multiplying the result by 100 to obtain a percentage. The percentile rank can be used to compare individual scores to the rest of the distribution, and can provide useful information about the relative standing of a score within a particular group or population. Therefore, it is true that the percentile rank identifies the percentile of a particular value within a set of data.

To know more about percentile visit :-

https://brainly.com/question/1594020

#SPJ11

Given differential equation is y" +8ty' + t²y = 0. We need to calculate H using the formula above and then check whether it is possible to transform the differential equation into one with constant coefficients using this method.

Formula given is: H = (q'(t) + 2p(t)q(t))/(2(q(t))^3/2. Let's find the value of H.Hence, p(t) = 8t, q(t) = t²Hence, q'(t) = 2t
Now, let's find the value of H:H = (q'(t) + 2p(t)q(t))/(2(q(t))^3/2= (2t + 16t * t²) / 2(t²)^(3/2)= (2t + 16t³) / 2t³= 1 + 8t²Clearly, H is not constant and hence, it is not possible to transform the differential equation into one with constant coefficients using this method.

Thus, the value of H is 1 + 8t² and it is not possible to transform the differential equation into one with constant coefficients using this method. Hence, this is the required solution.

To know more about differential equation Visit

https://brainly.com/question/32645495

#SPJ11

To answer this question we will set and solve a system of equations.

Let A be the speed (in miles per hour) of the airplane in still air, and W be the wind speed (in miles per hour).

Since the airplane flying with the wind takes 4 hours to travel a distance of 1200 miles and flying against the wind takes 5 hours to travel the same distance, then we can set the following equation:

Dividing the first equation by 4 we get:

Subtracting A from the above equation we get:

Substituting the above equation in the second one we get:

Simplifying the above result we get:

Adding 1500 to the above equation we get:

Dividing the above equation by 10 we get:

Finally, substituting A=270 at W=300-A we get:

Answer:

The speed of the airplane in still air is 270 miles per hour.

The wind speed is 30 miles per hour.

The relation R represented by the given matrix is not reflexive and not symmetric, but it is transitive.

The matrix represents a relation where the rows and columns are labeled in the order of w, x, y, and z. By reading the matrix, we can identify the ordered pairs that make up the relation. In this case, the pairs are {(w, x), (x, x), (y, z)}.

To determine if the relation is reflexive, we check if every element in the set has a pair with itself. In this case, the pair (w, w) is missing, so the relation is not reflexive.

To check if the relation is symmetric, we examine if for every pair (a, b) in the set, the pair (b, a) is also present. Here, we see that the pair (x, y) is missing, while (y, x) is present, indicating that the relation is not symmetric.

Finally, to assess transitivity, we need to verify that if (a, b) and (b, c) are present in the set, then (a, c) should also be present. In this case, we don't have any such counterexamples, so the relation is transitive.

In summary, the relation R represented by the given matrix is not reflexive and not symmetric, but it is transitive.

Learn more about reflexive here:

https://brainly.com/question/29119461

#SPJ11

The measure of the segment JK is 0 unit

A line is the shortest distance between two points

Given the following parameters

GJ = 70.2

JH = 26.5

GK = 70.2

Determine the measure of JK

JK = JG + GK

Since JG = -GJ then;

JK = -GJ + GK

JK = -70.2 + 70.2

JK = 0

Hence the measure of the segment JK is 0 unit

Learn more on line segment here: https://brainly.com/question/2437195

#SPJ1

Answer:

181/8

Step-by-step explanation:

Answer:

5x/8 + 43/2

Explanation:

The answer is the exact value.

It will take Thoriso 30 minutes to walk to school.

what is speed ?

Speed is a measure of how quickly an object is moving. It is defined as the distance traveled by an object in a given amount of time. The formula for speed is:

Speed = distance / time

The unit of speed depends on the units of distance and time used. Common units of speed include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Given by the question:
We can use the formula:

time = distance / speed

to calculate the time it will take Thoriso to walk to school.

Let d be the distance from Thoriso's home to school. Since the distance is the same whether she walks or rides her bicycle, we have:

distance walked = distance biked = d

Let's first calculate how long it takes Thoriso to bike to school:

time biked = distance biked / biking speed

time biked = d / 15 km/h

We are given that it takes her 10 minutes (0.167 hours) to bike to school, so we can set up the following equation:

0.167 hours = d / 15 km/h

Solving for d, we get:

d = 2.5 km

Now, we can calculate how long it will take Thoriso to walk to school:

time walked = distance walked / walking speed

time walked = d / 5 km/h

time walked = 2.5 km / 5 km/h

time walked = 0.5 hours or 30 minutes

Therefore, it will take Thoriso 30 minutes to walk to school.

To know more about speed visit:
https://brainly.com/question/13263542
#SPJ1

If 800g:1kg is equal to 1:n then the value of n is 1/8.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

800g : 1kg = 1 : n

This can be written as,

800g/1kg = 1/n

Cross multiply.

n = 1kg/800g

[ 1 kg = 1000g ]

n = 1000g/8000g

n = 1/8

Thus,

The value of n is 1/8.

Learn more about ratios here:

https://brainly.com/question/2462048

#SPJ1

Answer:

The answer my friend is B. :)

Step-by-step explanation: