Find the dimensions of a rectangle (in m) with perimeter 68 m whose area is as large as possible. (enter the dimensions as a comma-separated list.)

The expression [tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex]  is an illustration of definite integrals

The approximated value of the definite integral is 0.0059

The definite integral is given as:

[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex]

For arctan(x), we have the following series equation:

[tex]\arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}}[/tex]

Multiply both sides of the equation by x^3.

So, we have:

[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1}}{2n + 1}} * x^3[/tex]

Apply the law of indices

[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 1 + 3}}{2n + 1}}[/tex]

[tex]x^3 * \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]

Evaluate the product

[tex]x^3 \arctan(x) = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]

Introduce the integral sign to the equation

[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =\int\limits^{1/2}_{0} \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}}[/tex]

Integrate the right hand side

[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{x^{2n + 4}}{2n + 1}} ]\limits^{1/2}_{0}[/tex]

Expand the equation by substituting 1/2 and 0 for x

[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - [ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{0^{2n + 4}}{2n + 1}} ][/tex]

Evaluate the power

[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx =[ \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}} ] - 0[/tex]

[tex]\int\limits^{1/2}_{0} x^3 \arctan(x)\ dx = \sum\limits^{\infty}_{n = 0} {(-1)^n \cdot \frac{(1/2)^{2n + 4}}{2n + 1}}[/tex]

The nth term of the series is then represented as:

[tex]T_n = \frac{(-1)^n}{2^{2n + 5} * (2n + 4)(2n + 1)}[/tex]

Solve the series by setting n = 0, 1, 2, 3 ..........

[tex]T_0 = \frac{(-1)^0}{2^{2(0) + 5} * (2(0) + 4)(2(0) + 1)} = \frac{1}{2^5 * 4 * 1} = 0.00625[/tex]

[tex]T_1 = \frac{(-1)^1}{2^{2(1) + 5} * (2(1) + 4)(2(1) + 1)} = \frac{-1}{2^7 * 6 * 3} = -0.0003720238[/tex]

[tex]T_2 = \frac{(-1)^2}{2^{2(2) + 5} * (2(2) + 4)(2(2) + 1)} = \frac{1}{2^9 * 8 * 5} = 0.00004340277[/tex]

[tex]T_3 = \frac{(-1)^3}{2^{2(3) + 5} * (2(3) + 4)(2(3) + 1)} = \frac{-1}{2^{11} * 10 * 7} = -0.00000634131[/tex]

..............

At n = 2, we can see that the value of the series has 4 zeros before the first non-zero digit

This means that we add the terms before n = 2

This means that the value of [tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx[/tex] to 4 decimal points is

[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.00625 - 0.0003720238[/tex]

Evaluate the difference

[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0058779762[/tex]

Approximate to four decimal places

[tex]\int\limits^{1/2}_0 {x^3 \arctan(x)} \, dx = 0.0059[/tex]

Hence, the approximated value of the definite integral is 0.0059

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here is the answer below

The current through the 15 ohms resistor of the given circuit with a calculated voltage of 5 V is; 0.33 A

We are given;

Current through the 5 ohm resistor; i = 1 A

Formula for Voltage is;

V = iR

V = 1 * 5

V = 5V

Now, since the 5 ohms resistor and the 15 ohms resistor are in the same circuit, it means that they will have the same voltage. Thus;

Current through the 15 ohms resistor is;

I = V/R

I = 5/15

I = 0.33 A

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Answer:

ladysmith

Explanation:

because is a area i live in

Answer:

"I hit again and again, dropping the money and the grocery list. The boys scattered, yelling, nursing their heads, staring at me in utter disbelief. They had never seen such frenzy."

Explanation:

just took test

Answer: "I hit again and again, dropping the money and the grocery list. The boys scattered, yelling, nursing their heads, staring at me in utter disbelief. They had never seen such frenzy."

Explanation:

just took test

The explicit description of null A by listing vectors that span the null space.

[tex]\left[\begin{array}{ccc}{7} &&&{-4} \\{1} \\{0} \end{array}\right] \left[\begin{array}{ccc}{-6} &&&{2} \\{0} \\{1} \end{array}\right][/tex]

We are given the matrix vector;

[1  3 5 0]

[0 1 4 -2]

Now, let's find the general Ax = 0 solution for the free variables. Thus;

[A, 0] =  

[1 3 5  0]

[0 1 4 -2]

Thus;

R₁ → R₁ - 3R₂

⇒ [1 0 -7  6 0]

   [0 1 4  -2 0]

The general solution is:

x₁ = 7x₃ - 6x₄

x₂ = -4x₃ + 2x₄

x₃ and x₄ are free variables

x = [tex]\left[\begin{array}{ccc}x_{1} &&&x_{2} \\x_{3} \\x_{4} \end{array}\right][/tex] = [tex]x_{3} \left[\begin{array}{ccc}{7} &&&{-4} \\{1} \\{0} \end{array}\right] + x_{4} \left[\begin{array}{ccc}{-6} &&&{2} \\{0} \\{1} \end{array}\right][/tex]

Thus, Null A is;

[tex]\left[\begin{array}{ccc}{7} &&&{-4} \\{1} \\{0} \end{array}\right] \left[\begin{array}{ccc}{-6} &&&{2} \\{0} \\{1} \end{array}\right][/tex]

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The word "base" as used in the passage refers to; loyalty to the family, to the family bond that Ismenia has.

Antigone speaks the words in the given passage to her sister Ismenia. Now, in these words, Antigone questions Ismenia's loyalty and commitment to the family by the use of the word "base" to mean family loyalty.

The reason for use of that word is because their brother was banned from receiving a decent funeral, which prevented his soul from being able to rest in peace. The king then ordered that whoever made a feneral for the brother of Ismenia and Antigona would be condemned to death. However Antígona, in loyalty to her brother, was willing to take that risk and wanted to know if Ismenia had the same loyalty.

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The sets A and sets B contains items called elements

It is true that the set A is equal to set B

The sets are given as:

Set A and set B

Since the sets have the same power set, then we have:

P(A) = P(B)

The above means that:

For every element X in A, then the element is also in B

And

For every element Y not in A, then the element is also not in B

So, we can conclude that:

All subsets of the set A are subsets of the set B and vice versa

Hence, the set A is equal to set B

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Answer:

Forgiveness can and should exist within the criminal justice system.

Explanation: I hope this helps

It is a true statement that prior to the 1860s, an adolescence was not seen as a separate life stage.

Prior to 1860s, people were usually only separated into either kids or adults.

Thus, it meant that the Kids in adolescence age already carried the burden equivalent to those of adults in this modern day.

Therefore, we can conclude that is a true statement that prior to the 1860s, an adolescence was not seen as a separate life stage.

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The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward. The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.

hope it helps...!!!

If data are categorized as, for example, places of residence, the measure of central tendency to use is the median

This is known to be the middle number in a group of sorted numbers, that are said to be ascending or descending.

From the above statement, the data of distributions that extreme values, the median is a best measure of central tendency as it will give the right accuracy we need.

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Answer:

Strong Gravitational Field

Explanation:

When block A passes point P, the negligible friction will lead to the tension, T, between the two blooks A and B increasing.

The tension in the rope can be found by the formula:

= Coefficient of friction x Mass x Acceleration

Thanks to the transition to the surface after point P, the friction is now negligible which means that there will be an increase in acceleration.

This will increase the tension as shown by the formula for tension.

Find out more on tension at https://brainly.com/question/24994188.

Answer:

In glycolysis a separate enzyme (Hexokinase) adds a phosphate onto Glucose and is ATP dependent. The reaction catalyzed by Glucose-6-Phosphatase is a hydrolysis which in water is extremely difficult to reverse- because water is in very high concentration.

Explanation:

Answer:

human papillomavirus (HPV)

Explanation:

Answer:

tu mamá

Explanation:

la mama de la mama de la mama de la mama de la mama de la mama de la mama de la mama de la mama

Answer:What does this part of the soliloquy reveal about Hamlet? He still loves Ophelia. He believes the ghost was real. He is planning his revenge.

Explanation:

First dude is correct is the correct option regarding the immigration act.

The Immigration and Nationality Act of 1965 underwent a broad national overhaul. It boosted overall immigration so that for the fiscal years 1992–1994 and going beyond, 675,000 immigrants could enter the country annually.

It offered family-based immigration visas, established five unique employment-based visas that were divided up according to occupations, and instituted a diversity.

It is a visa program that established a lottery to admit immigrants from "low admittance" countries  or nations whose citizens were underrepresented in the United States.

Therefore, First dude is correct is the correct option regarding the immigration act.

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#SPJ5

Answer: C. The law supported victims of political persecution.

Explanation:

The exercise is related to the Ratio Test for Convergence. The rules for this kind of test are given below.

The rules are:

Using this knowledge, we are able to state that

The nth-term test determines whether a series is divergent if the limit is bigger than 0, thus, both B and F are divergent series.

Please see the attached for the full question and the link below for more about Ratio Test for Convergence:

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The answers to the labels in their appropriate location are:

The term hydrophilic is known to be a term that connote the ability of an organism or object to be attracted to water.

It is also said to be the ability of a substance to be able to easily dissolve in, or be mix up and saturated by water. They are substance or objects that do interact with or are known to be influenced by water.

See full question below

Drag the labels to their appropriate locations in the figure.

First, drag labels to targets (a) and (b) to indicate whether these environments are hydrophilic or hydrophobic.

Next, drag the phospholipid layers to targets (c) and (d) to indicate how they are oriented in the plasma membrane.

Finally, drag labels to targets (e), (f), and (g) to indicate which portions of the membrane protein are hydrophilic and which are hydrophobic.

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The parametric equation of the line illustrates the independent variables x, y and z

The parametric equation of the line and direction is x = 5 + t; y = -1; z = 3 -2t

The question is incomplete, as the points and the lines are not given.

So, I will make use of the following assumed parameters:

The parametric equation of the line is represented as:

r<x,y,z> = Line + t<direction>

This gives

r<x,y,z> = (5, -1, 3) + t<1, 0, -2>

Express the equation in terms of x, y and z

x = 5 + t * 1

y = -1 + 0 * t

z = 3 -2 * t

Solve the equations

x = 5 + t

y = -1

z = 3 -2t

Hence, the parametric equation of the assumed line and direction is x = 5 + t; y = -1; z = 3 -2t

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There are different kinds of character. The character of Su-Jen is mainly revealed through her  thoughts.

The story about Su-Jen is gotten from a novel that was written about Su-Jen, a young girl who had to go all the way to  China from US. along with her to meet her father.

It was a first time meeting for Su-Jen and it was an emotional one. All the character seen about Su-Jen is from her thoughts that were written out.

See options below

actions

dialogue

appearance

thoughts

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An example of Fundamentals of algebra practice book grade 7 question is A game-worn jersey sells for $100 more than a new jersey. Write an equation for this scenario.

The Fundamentals of Algebra is a book that is made for Grade 7. It is a practice book that is made up of exercise and answers that help the student to have a better knowledge of algebra.

The equation for the above scenario is:

g = game - worn jersey

The Equation therefore will be: g=100+n

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Taking into account the definition of molarity, 14.028 grams of sodium chloride must be added to make 400 mL of a 0.600 M sodium chloride.

Molar concentration or molarity is a measure of the concentration of a solute in a solution and indicates the number of moles of solute that are dissolved in a given volume.

The molarity of a solution is calculated by dividing the moles of solute by the volume of the solution:

[tex]Molarity=\frac{number of moles}{volume}[/tex]

Molarity is expressed in units [tex]\frac{moles}{liter}[/tex].

In this case, you know:

Replacing in the definition of molarity:

[tex]0.600 M=\frac{number of moles}{0.400 L}[/tex]

Solving:

number of moles= 0.600 M× 0.400 L

number of moles= 0.24 moles

Being the molar mass of sodium chloride 58.45 [tex]\frac{g}{mole}[/tex], that is the amount of mass that a substance contains in one mole, the mass of sodium chloride can be calculated as:

0.24 moles×58.45 [tex]\frac{g}{mole}[/tex]= 14.028 grams

Finally, 14.028 grams of sodium chloride must be added to make 400 mL of a 0.600 M sodium chloride.

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Answer:

Whats your question?

What do you need help on?

I took algebra a while ago so I may be able to help you

Explanation:

Answer:

Data are getting more concentrated around the mean

Explanation:

The solution of the equation x² = 8 - 5x is startfraction negative 5 minus startroot 57 endroot over 2 endfraction comma startfraction negative 5 + startroot 57 endroot over 2 endfraction

x² = 8 - 5x

x² + 5x - 8 = 0

Using quadratic formula

x = -b ± √b² - 4ac / 2a

= -5 ± √5² - 4(1)(-8) / 2(1)

= -5 ± √25 -(-32) / 2

= -5 ± √25 + 32 / 2

= -5 ± √57 / 2

= -5 + √57 /2 or -5 -√57/2

Therefore, the correct answer is; startfraction negative 5 minus startroot 57 endroot over 2 endfraction comma startfraction negative 5 + startroot 57 endroot over 2 endfraction

-5 - √57 / 2, -5 + √57 / 2

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Answer:

B)

Image to help is below here, sorry if its bad quality but good luck <3

Answer:

Incorrect

Explanation:

Answer:

incorrect

Explanation:

edge 2021