find the matrix a of t for the following transformation. is a reflection in the line y=x

The double integral of the given equation is 101.3π/4.

What is meant by integral?

In mathematics, an integral lends numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinitesimally small amounts of data. Integration is the action of locating integrals.

The integrals of a function in two variables over a region in R², or the real number plane, are referred to as double integrals in mathematics.

The surface area of a 2D figure can be determined primarily using the double integral, which is indicated by the symbol "∫∫". By using double integration, we may quickly determine the area of a rectangular region. Double integration challenges will be easier to address if we are familiar with simple integration.

We are asked to find the double integral of

[tex]\int\int\limits_r \frac{4(1+x^2)}{1+y^2} dA,[/tex],  where region r = {(x, y) | 0 ≤ x ≤ 4, 0 ≤ y ≤ 1}

dA = dx.dy

We can then rewrite the equation as

[tex]\int\limits^4_0\int\limits^1_0 \frac{4(1+x^2)}{1+y^2} dydx[/tex] = [tex]\int\limits^4_04(1+x^2)dx \ .\int\limits^1_0 \frac{1}{1+y^2} dy[/tex]

For the first part,

[tex]\int\limits^4_04(1+x^2)dx = 4\int\limits^4_0(1+x^2)dx = 4[ x + x^3/3]\limits^4_0[/tex]

                                                = 4 [ 4 + 4³/3] - 4[ 0] = 101.3

For the second part,

[tex]\int\limits^1_0 \frac{1}{1+y^2} dy[/tex]

Take y = tan u

then dy = sec²(u) du

 Then the above equation becomes,

[tex]\int\limits^1_0 \frac{1}{1+tan^2(u)}. sec^2(u) du = \int\limits^1_0 \frac{1}{sec^2(u)}. sec^2(u) du[/tex]  

                               = [tex]\int\limits^1_0 (1.du) = [u]^1_0[/tex]

We know x = tan u

so u = tan⁻¹ x

Then the equation becomes

[tan⁻¹ x]¹₀ = [ tan⁻¹ 1 - tan⁻¹ 0] = π/4 - 0 = π/4

Therefore the double integral of the given equation is 101.3π/4.

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The number formed by 1 and 4 is 14 from the given informations.

A word problem is a type of mathematics exercise where the majority of the issue's context is supplied in spoken language as opposed to mathematical notation.

A math word problem is a question that is phrased as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The digits be x and y

x + y = 6 ...........(i)

The number is 10x + y

The number formed by interchanging is 10y + x

10y + x - 10x - y = 36

⇒9y - 9x = 36

⇒y - x = 4 ..........(ii)

Sum of the two equations are

x+ y +y -x = 6 + 4

⇒2y = 10

⇒ y = 5

Now the value of x is 1.

The number is 10x + y = 10 + 4 = 14

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In a hypothesis test, YOU presumptively believe the alternative hypothesis, a statistical hypothesis is a claim regarding a sample, If you choose to reject the null hypothesis, you can then decide whether or not the alternative hypothesis is correct.

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The probability of Vanessa selecting at random a hot Cheeto and another hot Cheeto is the fraction 1/4, 0.25 as a decimal, 25% as a percent.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

total possible outcome is the number of Cheetos in her bag = 50

probability of selecting a hot Cheetos = 25/50

probability of selecting a cheese Cheetos = 25/50

the required outcome is the two hot Cheetos selected at random

the probability of getting a hot Cheeto and another hot Cheeto is calculated as follows:

25/50 × 25/50 = 1/2 × 1/2

25/50 × 25/50 = 1/4

Therefore, the probability of Vanessa selecting at random a hot Cheeto and another hot Cheeto is 1/4

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The amount that he will have after 4 years is given as follows:

$14,983.85.

The amount of money earned, in compound interest, after t years, is given by the equation presented as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are listed as follows:

The parameters for this problem are given as follows:

P = 8000, r = 0.16, n = 4, t = 4.

Hence the balance will be given as follows:

P = 8000 x (1 + 0.16/4)^(4 x 4)

P = $14,983.85.

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The slope criteria for parallel and perpendicular lines is a useful tool for solving geometric problems because it helps you determine whether two lines are parallel, perpendicular or neither based on their slopes.

For parallel lines, the slope must be equal. If the slopes of two lines are equal, then the lines are parallel.

For perpendicular lines, the product of their slopes must be equal to -1.

If the product of the slopes of two lines is -1, then the lines are perpendicular.

To apply the slope criteria in a problem, you need to find the equation of the two lines, either in slope-intercept form (y = mx + b) or point-slope form (y - y1 = m(x - x1)). Once you have the equation, you can find the slope of each line by either finding the coefficient of x in the slope-intercept form or finding the value of m in the point-slope form. Then you can compare the slopes to determine whether the lines are parallel, perpendicular, or neither.

For example, consider two lines with equations y = 2x + 1 and y = -(1/2)x + 3. To determine whether they are parallel or perpendicular, you first find the slope of each line: 2 for the first line and -1/2 for the second line. Since their slopes are not equal, the lines are not parallel. But since the product of their slopes is equal to -1, the lines are perpendicular.

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All of the above (a, b, c) are measures of dispersion.

If a data set has an even number of observations, the median:

b. is the average value of the two middle items when all items are arranged in ascending order.

The median is a measure of central tendency that indicates the middle value of a set of data. In a data set with an even number of observations, the median is found by taking the average of the two middle items. For example, if a data set has 8 observations, the median is the average of the 4th and 5th observations when the data is sorted in ascending order.

c. must be equal to the mean.

This statement is not always true. The median and the mean are two different measures of central tendency, and they can be equal or not equal depending on the distribution of the data. In a symmetrical data distribution, the median and the mean are equal, while in a skewed data distribution, they are not equal.

Which of the following is a measure of dispersion?

d. all of the above are measures of dispersion.

Dispersion is a statistical term that refers to the extent to which the values in a data set are spread out or dispersed. It measures how far the values are from the central tendency of the data.

a. Percentiles are a measure of dispersion that indicates the value below which a certain percentage of the data falls. For example, the 50th percentile (or median) is the value below which 50% of the data falls.

b. Quartiles are a measure of dispersion that divides a data set into four equal parts. The first quartile (Q1) is the 25th percentile, the second quartile (Q2) is the 50th percentile (or median), and the third quartile (Q3) is the 75th percentile.

c. The interquartile range (IQR) is the range between the first and third quartiles and is a measure of dispersion that indicates the spread of the middle 50% of the data.

Therefore, all of the above (a, b, c) are measures of dispersion.

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For recipe 1, 2, 3, 4 there are 1/3, 2/3, 3/5, 2/3 tablespoons of lemonade mix per cup of sparkling water respectively.

Complete Question :

Here are several recipes for sparkling lemonade. For each recipe describe how many tablespoons of lemonade mix it takes per cup of sparkling water.

Recipe 1: 4 tablespoons lemonade mix and 12 cups of sparkling water

Recipe 2: 4 tablespoons of lemonade mix and 6 cups of sparkling water

Recipe 3: 3 tablespoons of lemonade mix and 5 cups of sparkling water

Recipe 4: 1/2 tablespoon of lemonade mix and 3/4 cups of sparkling     water

The concept used in this problem is simple division and fraction reduction. For each recipe, the amount of lemonade mix is divided by the amount of sparkling water to determine the ratio of lemonade mix to sparkling water. The result is expressed as a fraction, which is then reduced to its simplest form. This allows us to easily determine the amount of lemonade mix needed for each cup of sparkling water for each recipe.

So,

Recipe 1: 4 tablespoons lemonade mix per 12 cups of sparkling water

= 4/12

= 1/3 tablespoon of lemonade mix per cup of sparkling water.

Recipe 2: 4 tablespoons of lemonade mix per 6 cups of sparkling water

= 4/6

= 2/3 tablespoons of lemonade mix per cup of sparkling water.

Recipe 3: 3 tablespoons of lemonade mix per 5 cups of sparkling water

= 3/5

= 3/5 tablespoons of lemonade mix per cup of sparkling water.

Recipe 4: 1/2 tablespoon of lemonade mix per 3/4 cup of sparkling water = (1/2) / (3/4)

= 2/3 tablespoons of lemonade mix per cup of sparkling water.

Therefore, For recipe 1, 2, 3, 4 there are 1/3, 2/3, 3/5, 2/3 tablespoons of lemonade mix per cup of sparkling water respectively.

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For recipes 1, 2, 3, 4 there are 1/3, 2/3, 3/5, 2/3 tablespoons of lemonade mix per cup of sparkling water respectively.

Complete Question :

Here are several recipes for sparkling lemonade. For each recipe describe how many tablespoons of lemonade mix it takes per cup of sparkling water.

Recipe 1: 4 tablespoons lemonade mix and 12 cups of sparkling water

Recipe 2: 4 tablespoons of lemonade mix and 6 cups of sparkling water

Recipe 3: 3 tablespoons of lemonade mix and 5 cups of sparkling water

Recipe 4: 1/2 tablespoon of lemonade mix and 3/4 cups of sparkling     water

The concept used in this problem is simple division and fraction reduction. For each recipe, the amount of lemonade mix is divided by the amount of sparkling water to determine the ratio of lemonade mix to sparkling water. The result is expressed as a fraction, which is then reduced to its simplest form. This allows us to easily determine the amount of lemonade mix needed for each cup of sparkling water for each recipe.

So,

Recipe 1: 4 tablespoons lemonade mix per 12 cups of sparkling water

= 4/12

= 1/3 tablespoon of lemonade mix per cup of sparkling water.

Recipe 2: 4 tablespoons of lemonade mix per 6 cups of sparkling water

= 4/6

= 2/3 tablespoons of lemonade mix per cup of sparkling water.

Recipe 3: 3 tablespoons of lemonade mix per 5 cups of sparkling water

= 3/5

= 3/5 tablespoons of lemonade mix per cup of sparkling water.

Recipe 4: 1/2 tablespoon of lemonade mix per 3/4 cup of sparkling water = (1/2) / (3/4)

= 2/3 tablespoons of lemonade mix per cup of sparkling water.

Therefore, For recipe 1, 2, 3, 4 there are 1/3, 2/3, 3/5, 2/3 tablespoons of lemonade mix per cup of sparkling water respectively.

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The output volume is 40 x 40 x 32

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

Input volume = 121 x 121 x 16

Filters = 32 with 4 x 4

Stride = 3

Padding = False

The output element (n) is calculated as

n = (nH + 2 x p - f)/s + 1

Using the given parameters, we have

nH = 121, p = 0, f = 4 and s = 3

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

n = (121 + 2 x 0 - 4)/3 + 1

Evaluate

n = 40

This means that

Output volume = 40 x 40 x 32

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The average speed for the whole journey is 25 mph.

Completed question :

Tim goes on a car journey. For the first 15 minutes his average speed is 40 mph. He then stops for 25 minutes. He then completes the journey at an average speed of 45 mph. The total journey time is 1 hour.

a) Draw a distance-time

graph for his journey.

b) What is the average

speed for the whole

journey?

mph

Given data :

1. Tim travels first 15 minutes = [tex]\frac{1}{4}[/tex] hour at average speed of 40 mph and passed :

40 x [tex]\frac{1}{4}[/tex]  = 10 miles.

2. Time stops for 25 minutes (distance traveled = 0 miles).

3. He then completes the journey at an average speed of 45 mph. The total journey time is 1 hour, then he was travelling at 45 mph for

60 - 15 - 25 = 20 minutes = [tex]\frac{1}{3}[/tex] hour

and covered

45 x  [tex]\frac{1}{3}[/tex]  = 15 miles.

The distance-time graph for his journey is attached.

Find the average speed for the whole journey:

Average speed = Total distance / Total time = [tex]\frac{10 + 15}{1}[/tex] = 25 mph.

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a) The derivative of f(x) = x^4 + 4x is f'(x) = 4x^3 + 4.

b) The antiderivative of f'(x) = 4x^3 + 4 is f(x) = (1/4)x^4 + 4x + C

What is derivative of function ?

The derivative of a function of a real variable measures the function's sensitivity to change in relation to a change in its input. Calculus relies heavily on derivatives.

a) To find the derivative of f(x) = x^4 + 4x, we can use the power rule and the linear rule of differentiation. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1). The linear rule states that if f(x) = cx, then f'(x) = c. Applying these rules, we have:

f'(x) = (x^4)' + (4x)'

= 4x^3 + 4

So, the derivative of f(x) = x^4 + 4x is f'(x) = 4x^3 + 4.

b) The question is asking for f(x), not f'(x). To find f(x), we need to integrate the derivative f'(x) with respect to x. We can use the power rule and the linear rule of integration to find an antiderivative for f'(x). The power rule states that if f'(x) = x^n, then f(x) = (1/(n+1))x^(n+1) + C, where C is an arbitrary constant of integration. The linear rule states that if f'(x) = c, then f(x) = cx + C. Applying these rules, we have:

f(x) = ∫(4x^3 + 4)dx

= (1/4)x^4 + 4x + C

So, The antiderivative of f'(x) = 4x^3 + 4 is f(x) = (1/4)x^4 + 4x + C, where C is an arbitrary constant of integration.

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Answer:

maybe you do 5 times -6+2

Step-by-step explanation:

The 0.28 in the function f(x) = 5719(0. 28)^x represents the rate of decrease in the cat population over time.

This is because the function is decreasing, meaning as time progresses, the cat population decreases. The number 0.28 is equal to the mouse-catch-rate for each cat, which is 72%. This means that each cat can catch 72% of the mice, which means that the cat population decreases by 28% each year.

The number 5719 is the initial cat population in Ellison before they are sent to Clarksville. The function f(x) is used to represent the change in the cat population over time. As the value of x increases, the value of f(x) decreases, indicating a decrease in the cat population.

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So the values of c that satisfy the conclusion of the Mean Value Theorem are c = 1 and c = -1.

The answer is 1, -1.

Yes, the function f(x) = 1/x satisfies the hypothesis of the Mean Value Theorem on the interval [1, 6].

To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to find values of c in the interval (1, 6) such that f'(c) = (f(6) - f(1)) / (6 - 1).

Taking the derivative of f(x) = 1/x, we get f'(x) = -1/x^2.

Setting f'(c) = (f(6) - f(1)) / (6 - 1) and solving for c, we find that:

-f'(c) = -1/c² = (1/6 - 1) / (6 - 1) = -5/5

-c² = 5/5

-c = +/- √(5/5) = +/- √(1) = +/- 1

So the values of c that satisfy the conclusion of the Mean Value Theorem are c = 1 and c = -1.

The answer is 1, -1.

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Answer:

[tex]4a^3b^2[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{20a^5b^3}{5a^2b}=\frac{20}{5}\cdot a^{5-2}\cdot b^{3-1}=4a^3b^2[/tex]

Answer:

4a^3b^2 ----> [tex]=4a^3b^2[/tex]  So (A)

Step-by-step explanation:

[tex]\frac{20a^5b^3}{5a^2b}[/tex]

[tex]\mathrm{Factor\:the\:number:\:}\:20=5\cdot \:4[/tex]

[tex]=\frac{5\cdot \:4a^5b^3}{5a^2b}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:5[/tex]

[tex]=\frac{4a^5b^3}{a^2b}[/tex]

Simplify

[tex]=\frac{4a^3b^3}{b}[/tex]

and simplify one more time!

[tex]=4a^3b^2[/tex]

hope this helps ~~wdfadss~~

The premium in 6 years is $17828

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

Initial = 10630

Rate per year = 9% per year

So, the function can be represented as

f(t) = 10630 * (1 + 9%)^t

This gives

f(t) = 10630 * (1 + 9%)^6

Evaluate

f(t) = 17828

Hence, the premium is 17828

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Using decimals, 4/3 equals 1.33.

In this handbook, we'll show you how to use the division method to convert a fraction to a decimal. There are many other ways to convert numbers into decimals, percentages, and other units.

Solution: The decimal equivalent of 4/3 is 1.33.

The divide approach to explaining:

The numerator and denominator of a fraction are the numbers above and below the line, respectively. A fraction is essentially represented by two pieces separated by a line.

To obtain a decimal, use the division method to respond to the following query:

To get the decimal, just divide the numerator (4), by the denominator (3). This gives you 1.33.

The result of translating 4/3 to is 1.33.

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The system of linear equations 2 · x + 4 · y = 7 and 2 · x + 4 · y = 9 has no solutions.

In this case we find a representation of two linear equations with two variables, each represented by two orthogonal axes, whose mathematical representation is described below:

a · x + b · y = c

e · x + f · y = g

Where a, b, c, d, e, f, g are real coefficients.

A system has no solution when a = e and b = f but c ≠ g. Graphically speaking, this case is represented by two parallel lines. One example is the following system:

2 · x + 4 · y = 7

2 · x + 4 · y = 9

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Answer:

wala po may pake ang sagot

Because he multiplied the triangle's base by its height, Kelvin's solution is incorrect

Use the equation area = 1/2 * bases * altitude to determine a triangle's surface area Choose which side will be the triangle's base, and then measure the height of the triangle from that base.. After that, enter the height and base measurements you have into the formula.

Area of triangle= 1/2 base × height

The base of the triangle= 5 in

The height of the triangle = 8 in

Area of triangle= 1/2 base × height

=  1/2 × 5 in × 8 in

=  1/2 × 40 square inches

= 20  square inches

As a result, Kelvin's estimation of the triangle's area is incorrect.

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The value of a determined from the linear combination of the vector is a = -2 and option 4 is correct answer.

In mathematics, objects with both magnitude and direction are called vectors. The vector's size is determined by the magnitude. It is shown as a line with an arrow, where the length of the line indicates the vector's magnitude and the arrow points in the desired direction. In addition, it goes by the names Euclidean vector, Geometric vector, Spatial vector, or just "vector."

The vector are:

u = <-7, -5 >, v = <-1, 1> , w = <-3, -1>.

To find the value of a substitute the value of the vectors in the given equation:

u = av+bw

<-7, -5 > = a <-1, 1> + b <-3, -1>

The vector can be written as follows:

-a - 3b = -7..........(1)

a - b = - 5..........(2)

From equation 2 we can write:

b = a+ 5

Substituting the value of b in equation 1 we have:

- a - 3(a + 5) = -7

- a - 3a - 15 = -7

-4a = 8

a = -2

Hence, the value of a determined from the linear combination of the vector is a = -2 and option 4 is correct answer.

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Answer:

76

Step-by-step explanation:

m∠N : y

4x+36+y=180

6x-2+y=180

=>x=17

y=76

1.34 is the critical value Za/2 that corresponds to a 82% level of confidence.

A critical value in statistics is a cut-off number that is compared to a test statistic in hypothesis testing to determine if the null hypothesis can be rejected or not. The value of the test statistic that establishes the upper and lower boundaries of a confidence interval or that establishes the level of statistical significance in a statistical test is known as the crucial value. The term "critical value" in statistics refers to the unit statisticians use to determine the accuracy margin within a collection of data and is denoted as: Critical probability.

Finding critical value of Z at 82% confidence level:

Step 1: α% = 100%-82% = 18%

Step 2: α = 18% = 0.18

Step 3: α/2 = 0.18/2 = 0.09

Step 4: 1- α/2 = 1-0.09 = 0.91

Step 5: Critical value of Z at 82%confidence level:

= Z at 0.91 (from Z tables) ≈ 1.34

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Jack is 100 ft away from the trail guide.

The angle of depression is the angle between the horizontal line and the  observation line of the object from the horizontal line.

Given is that Jack is one side of a 200 foot wide canyon and Jill is on the other side. Jack and Jill can both see the trail guide at angle of depression of 50 degrees.

From the figure, we can write -

tan (50) = OB/OC

OB = OC tan(50)                                   ......... { 1 }

and

tan (50) = OB/OA

OB = OA tan (50)                                  ......... { 2 }

Equation { 1 } and { 2 } -

OC tan(50) = OA tan(50)

OC = OA                                                   ...... { 3 }

Now -

AC = AO + OC

2OA = AC

2OA = 200

OA = 100 ft

Therefore, jack is 100 ft away from the trail guide.

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Solving provided question, we can say that Using the Pythagorean theorem,  [tex]15^2 = h^2 + 5^2 \\[/tex] => h = 14.14 feet

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

Using the Pythagorean theorem,

[tex]15^2 = h^2 + 5^2 \\[/tex]

[tex]h^2 =\sqrt{200}[/tex]

h = 14.14 feet

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Answer:

Step-by-step explanation:

I am preaty positve that it is 99

The absolute maximum value of f(x) = ln(x)/x is f(e) = ln(e)/e.

What is a function?

A function is a relationship or expression involving one or more variables.  It has a set of inputs and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

The absolute maximum value of a function is the largest value that the function takes on its entire domain.

For the function f(x) = ln(x)/x, the domain is x > 0, since the natural logarithm and division by x are undefined for x <= 0.

To find the absolute maximum value of f(x), we can use calculus. Taking the first derivative of f(x) and setting it equal to zero, we get:

f'(x) = (1 - ln(x))/x^2 = 0

Solving for x, we find x = e, where e is the mathematical constant approximately equal to 2.71828.

To determine whether f(x) has an absolute maximum at x = e, we can take the second derivative of f(x) and evaluate it at x = e:

f''(x) = -(2 + 1/x)/x^3

f''(e) = -(2 + 1/e)/e^3 < 0

Since the second derivative is negative at x = e, this means that f(x) has a relative maximum at x = e, which is also the absolute maximum, since the function is defined on a closed and bounded interval (0, ∞).

Therefore, the absolute maximum value of f(x) = ln(x)/x is f(e) = ln(e)/e.

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The length of h in the given parallelogram is 0.24

To help us solve this problem, please refer to the attached picture below for each corner annotation of the parallelogram.

First, we will try to focus on triangle AOD to find the length of OD.

We know that ABCD is a parallelogram and AD is parallel to BC; then AD = BC

AD = 5

To find the length of OD we will use the phytagoras theorem:

AD² = AO² + OD²

0.5² = 0.3² + OD²

0.25 = 0.9 + OD²

OD² = 0.16

OD = 0.4

Then, we will use the congruent triangle concept between triangle AOD and triangle CPD to find the length of h or PD.

Based on the congruent triangle concept; we know that AD and DC should be congruent; then:

AD / DC = AO / DP

0.5 / 0.4 = 0.3 / h

h = 0.24

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The x-value gives the maximum area is 450 ft.

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Given that, a rectangular corral is to be built using 900 ft of fencing.

Here, 900=2l+w

w=900-2l

b) Area = Length×width

So, area = l×(900-2l)

Let the length be x, we get

Area =900x-2x²

f(x)=900x-2x²

d) The x-value gives the maximum area is

900x-2x²=0

900x=2x²

x=450

Therefore, the x-value gives the maximum area is 450 ft.

To learn more about the area of a rectangle visit:

https://brainly.com/question/20693059.

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