# Does Romeo truly love Juliet and why?

**MATH**

**∫10(2π(3−y)(1−y2))dy∫01(2π(3-y)(1-y2))dy Each integral represents the volume of a solid. Describe…**

Take out the constant 2Π2Π , and rewrite the integral. ∫10(2π(3−y)(1−y2)dy∫01(2π(3-y)(1-y2)dy = 2ππ ∫10(3−y)(1−y2)dy∫01(3-y)(1-y2)dy =2π∫10(3(1−y2)−y(1−y2)dy=2π∫10(3−3y2−y+y3)dy=2π∫01(3(1-y2)-y(1-y2)dy=2π∫01(3-3y2-y+y3)dy…

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**MATH**

**2π∫20(y1+y2)dy2π∫02(y1+y2)dy Each integral represents the volume of a solid. Describe the solid.**

The formula 2π∫bayf(y)dy2π∫abyf(y)dy gives the volume of solid obtained by rotating area under the graph of ff between y=ay=a and y=by=b around x-axis. Therefore, the solid in question is obtained by…

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**MATH**

**∫30(2πx5)dx∫03(2πx5)dx Each integral represents the volume of a solid. Describe the solid.**

∫30(2πx5dx)=∫03(2πx5dx)= 2π⋅∫30x5dx=2π⋅x66∣(0,3)2π⋅∫03x5dx=2π⋅x66∣(0,3) =π3(36−06)=π3⋅729=243π.=π3(36-06)=π3⋅729=243π.

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**MATH**

**x2−y2=7,x=4×2-y2=7,x=4Set up an integral for the volume of the solid obtained by rotating the…**

The shell has the radius 5−y5-y , the cricumference is 2π⋅(5−y)2π⋅(5-y) and the height is 4−x4-x , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**x=sin(y)−−−−−√,0≤y≤π,x=0x=sin(y),0≤y≤π,x=0 (a) Set up an integral for the volume of the solid…**

Let’s use the method of cylindrical shells. The parameter for a cylinder will be yy from y=0y=0 to y=π.y=π. The radius of a cylinder (the distance to the axis of rotation) is 4−y,4-y, the height of a…

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**MATH**

**y=x,y=2×1+x3y=x,y=2×1+x3 (a) Set up an integral for the volume of the solid obtained by…**

The shell has the radius x−(−1)x-(-1) , the cricumference is 2π⋅(x+1)2π⋅(x+1) and the height is 2×1+x3−x,2×1+x3-x, hence, the volume can be evaluated, using the method of cylindrical shells, such that:…

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**MATH**

**y=cos4(x),y=−cos4(x),−π2≤x≤π2y=cos4(x),y=-cos4(x),-π2≤x≤π2 (a) Set up an integral for the volume of…**

Let’s use the method of cylindrical shells. The parameter for a cylinder will be xx from x=−π2x=-π2 to x=π2.x=π2. The radius of a cylinder (the distance to the axis) is π−x,π-x, the height is…

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**MATH**

**y=tan(x),y=0,x=π4y=tan(x),y=0,x=π4 (a) Set up an integral for the volume of the solid obtained by…**

Let’s use the method of cylindrical shells. The parameter for a cylinder will be xx from x=0x=0 to x=π4.x=π4. The radius of a cylinder (the distance to the axis) is π2−x,π2-x, the height is…

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**MATH**

**y=xe−x,y=0,x=2y=xe-x,y=0,x=2 (a) Set up an integral for the volume of the solid obtained by…**

The shell has the radius x, the cricumference is 2π⋅x2π⋅x and the height is x⋅e−xx⋅e-x , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**x=y2+1,x=2x=y2+1,x=2 Use the method of cylindrical shells to find the volume generated by…**

The shell has the radius −2−y-2-y , the cricumference is 2π⋅(−2−y)2π⋅(-2-y)and the height is 2−x2-x , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=x3,y=0,x=1y=x3,y=0,x=1 Use the method of cylindrical shells to find the volume generated by…**

The shell has the radius 1−y1-y , the cricumference is 2π⋅(1−y)2π⋅(1-y) and the height is 1−x1-x , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=x2,y=2−x2y=x2,y=2-x2 Use the method of cylindrical shells to find the volume generated by…**

With the method of cylindrical shells we sum up the volumes of thin cylinders. The volume of a cylinder is 2π⋅r⋅h⋅dr,2π⋅r⋅h⋅dr, where hh is the height, rr is the radius of a cylinder (the distance from…

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**MATH**

**y=4x−x2,y=3y=4x-x2,y=3 Use the method of cylindrical shells to find the volume generated by…**

y=4x−x2,y=3y=4x-x2,y=3 The point of intersection of the curves will be , 4x−x2=34x-x2=3 4x−x2−3=04x-x2-3=0 −x2+4x−3=0-x2+4x-3=0 −(x2−4x+3)=0-(x2-4x+3)=0 x2−4x+3=0x2-4x+3=0 factorizing the above equation, (x−3)(x−1)=0(x-3)(x-1)=0 x=3 , x=1 The…

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**MATH**

**y=x−−√,y=0,x=1y=x,y=0,x=1 Use the method of cylindrical shells to find the volume…**

With the method of cylindrical shells we sum up the volumes of thin cylinders. The volume of a cylinder is 2π⋅r⋅h⋅dr,2π⋅r⋅h⋅dr, where hh is the height (the value of a function), rr is the radius of a…

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**MATH**

**y=x4,y=0,x=1y=x4,y=0,x=1 Use the method of cylindrical shells to find the volume generated by…**

With the method of cylindrical shells we sum up the volumes of thin cylinders. The volume of a cylinder is 2π⋅r⋅h⋅dr,2π⋅r⋅h⋅dr, where hh is the height (the value of a function), rr is the radius of a…

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**MATH**

**x+y=3,x=4−(y−1)2x+y=3,x=4-(y-1)2 Use the method of cylindrical shells to find the volume of…**

x+y=3,x=4−(y−1)2x+y=3,x=4-(y-1)2 The point of intersection of the curves, 4−(y−1)2=3−y4-(y-1)2=3-y 4−(y2+1−2y)=3−y4-(y2+1-2y)=3-y 4−y2−1+2y−3+y=04-y2-1+2y-3+y=0 3y−y2=03y-y2=0 y(3−y)=0y(3-y)=0 y=0, y=3 Height of the shell=(4−(y−1)2)−(3−y)(4-(y-1)2)-(3-y)…

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**MATH**

**x=1+(y−2)2,x=2x=1+(y-2)2,x=2 Use the method of cylindrical shells to find the volume of the…**

x=1+(y−2)2,x=2x=1+(y-2)2,x=2 Height of the shell is 2−(1+(y−2)2)2-(1+(y-2)2)The point of intersection of the curves, 1+(y−2)2=21+(y-2)2=2 (y−2)2=1(y-2)2=1 y−2=1–√y-2=1 y−2=±1y-2=±1 y=1,3 Volume of the solid obtained by rotating…

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**MATH**

**x=4y2−y3,x=0x=4y2-y3,x=0 Use the method of cylindrical shells to find the volume of the solid…**

x=4y2−y3,x=0x=4y2-y3,x=0 Refer the attached image. The curve intersects at x=0 , x=4. V=∫40(2πy(4y2−y3)dyV=∫04(2πy(4y2-y3)dy V=2π∫40(4y3−y4)dyV=2π∫04(4y3-y4)dyV=2π[4y44−y55]40V=2π[4y44-y55]04 V=2π[y4−y55]40V=2π[y4-y55]04…

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**MATH**

**y=x3,y=8,x=0y=x3,y=8,x=0 Use the method of cylindrical shells to find the volume of the solid…**

The volume of the solid obtained by rotating about x-axis by using cylindrical shell method is V=∫ba2πyf(y)dyV=∫ab2πyf(y)dy The given information is The curves y=x3=>x=y13y=x3=>x=y13 y=8y=8 ,…

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**MATH**

**y=x−−√,x=0,y=2y=x,x=0,y=2 Use the method of cylindrical shells to find the volume of the…**

The shell has the radius y, the cricumference is 2π⋅y2π⋅y and the height is y2−0y2-0 , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**xy=1,x=0,y=1,y=3xy=1,x=0,y=1,y=3 Use the method of cylindrical shells to find the volume of the…**

The shell has the radius y, the cricumference is 2π⋅y2π⋅y and the height is 1y1y , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=x2,y=6x−2x2y=x2,y=6x-2×2 Use the method of cylindrical shells to find the volume generated…**

The shell has the radius xx , the cricumference is 2π⋅x2π⋅x and the height is 6x−2×2−x26x-2×2-x2 , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=4x−x2,y=xy=4x-x2,y=x Use the method of cylindrical shells to find the volume generated by…**

The shell has the radius xx , the cricumference is 2π⋅x2π⋅x and the height is 4x−x2−x4x-x2-x , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=e−x2,y=0,x=0,x=1y=e-x2,y=0,x=0,x=1 Use the method of cylindrical shells to find the volume…**

The shell has the radius x, the cricumference is 2π⋅x2π⋅x and the height is e−x2e-x2 , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=x3,y=0,x=1,x=2y=x3,y=0,x=1,x=2 Use the method of cylindrical shells to find the volume…**

The shell has the radius x, the cricumference is 2π⋅x2π⋅x and the height is x3x3 , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**MATH**

**y=x−−√3,y=0,x=1y=x3,y=0,x=1 Use the method of cylindrical shells to find the volume…**

The shell has the radius xx , the cricumference is 2π⋅x2π⋅x and the height is x−−√3×3 , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

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**THE GREAT GATSBY**

**What literary element is used in: “face to face for the last time in history with something…**

In this final passages of the last chapter, Nick creates a parallel between Gatsby’s dream and the dream of America. Gatsby failed to relive the past. In the end, even his idealism could not save…

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**THE PIGMAN**

**In Paul Zindel’s The Pigman, what was the only thing John did that made his dad proud?**

The kids portrayed in Zindel’s The Pigman have unique family issues. Lorraine lives with her single mother, who projects her own fears about men and life onto her daughter. As a result, Lorraine…

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**THE ROAD NOT TAKEN**

**What do you think the poet is trying to say about choices in Robert Frost’s “The Road Not Taken”?**

I don’t believe the poet intended to write an essay about choices but was only thinking about one specific choice of his own which he made a long time ago. I believe he must have been thinking…

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**HISTORY**

**What was the purpose of the gladiators in Ancient Rome?**

It seems like every culture needs a hero to worship. In Ancient Rome, gladiators filled the role of hero in much the same way that professional athletes are revered in American society. The…

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**HISTORY**

**What were three difficulties caused by the Articles of Confederation?**

One difficulty was a major fiscal crisis confronting the new nation. Both the states and the national government had enormous debts from the Revolutionary War. The problem was that under the…

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**POLITICS**

**What is Aristotle’s definition of politics? And do you agree with his definition?**

As with all Greek thinkers of the period, Aristotle categorized human activity within three domains. A human, on the most basic level, functions as an individual. The study of ethics (set out in…

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**THE GREAT GATSBY**

**What prompts Tom to break Myrtle’s nose?**

There are several contributing factors to the incident of Myrtle’s broken nose. Myrtle and Tom are both married to other people and are having an affair. They have to have somewhere else to meet,…

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**SCIENCE**

**Why can’t a single celled organism have complex systems?**

Single celled organisms or prokaryotes lack complex systems, which are a necessity to multicellular organisms or eukaryotes. Prokaryotes carry out all the life processes at very simple and…

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**CAT IN THE RAIN**

**What are characters in the short story Cat in the Rain ?**

Cat in the Rain is a very short story and does not have many characters. The American wife is the protagonist. She seems discontented by her new marriage and the transient lifestyle she shares with…

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**SONG OF SOLOMON**

**In Song of Solomon, what lessons does Milkman learn on his journey south? How do these lessons…**

Really, Milkman learns that the world does not revolve around him. I know that may seem like a broad answer, but think about how he lives his life in the first part of the story – his parents, his…

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**MARRIAGE IS A PRIVATE AFFAIR**

**Why does Nene think Nnaemeka should write to his father?**

Nene thinks Nnaemeka should write a letter to his father, Okeke, to give him the good news about Nene and Nnaemeka’s engagement. They love each other very much and are happy and excited to be…

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**ULYSSES**

**What are Ulysses’ feelings about aging?**

This question, the question of confronting the process of aging, is at the heart of Tennyson’s “Ulysses.” The poem is essentially the soliloquy of an aging Ulysses (the Latin form of Odysseus)…

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**SOCIAL SCIENCES**

**How is the interactionist perspective useful in explaining racial tensions in contemporary…**

The interactionist perspective of sociology views a society as the sum of all social interactions between individuals, and explains how individuals develop worldviews based on the meanings they…

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**OTHELLO**

**In Othello, what makes Othello a loyal character?**

In Othello, Othello proves his loyalty in his actions as the general of the Navy. First, Othello is a Moor in a land of Italians, and although people harbor prejudicial ideas about him because of…

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**HISTORY**

Squanto was a Native American man, part of the Wampanoag Confederation, who helped the Pilgrims when they arrived in Plymouth. The Pilgrims faced many obstacles when they arrived in North America….

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**ALL QUIET ON THE WESTERN FRONT**

**How are the men alerted that a gas attack is coming in Chapter 4 of All Quiet on the Western…**

In Chapter 4 of All Quiet on the Western Front, the men fall into several attacks, and by the time gas is used, the men are in a graveyard. All along, Kat has been having premonitions about…

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**FAHRENHEIT 451**

**From Bradbury’s Fahrenheit 451, what textual evidence would support Montag if he were to protest…**

If Montag from Bradbury’s Fahrenheit 451 were to protest against censorship and the laws against having books, he would need to show that the information in books doesn’t hurt people. The society…

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**LAW AND POLITICS**

**Which powers are granted to Congress by the Constitution?**

In Article I of the Constitution are listed the powers granted to Congress. Generally, Congress is empowered to create all legislation for the United States. This is stated in the first section of…

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**LITERATURE**

**What is the summary for Frangipani House by Beryl Gilroy?**

Stated simply, this is a book about Mama King: a strong, elderly woman in Guyana who is condemned to a rest home by her daughters. Mama King has been ailing physically for a while, and is almost…

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**A CHRISTMAS CAROL**

**In A Christmas Carol by Charles Dickens, what type of literary device is “golden idol”?**

In Charles Dickens’ A Christmas Carol, the Ghost of Christmas Past takes Ebenezer Scrooge back in time to when he was dating Belle. The reader witnesses their breakup when Belle and Scrooge have…

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**THE MINISTER’S BLACK VEIL**

**In “The Minister’s Black Veil,” what does Mr.Hooper mean when he says “There is an hour to come…**

In the story, Mr. Hooper’s fiance begs him to take off his veil. She states that the veil hides the face that she is always glad to look upon. However, no matter how much she protests at his…

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**SOCIAL SCIENCES**

**Are there any social benefits of war?**

Wars have at least two social benefits for a nation—first, wars can create a sense of unity and shared identity. Second, wars can boost economic production and stimulate an economy. Wars boost…

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**NUMBER THE STARS**

**Why, when his sister and his nieces were visiting, would Uncle Henrik spend the whole night on…**

Uncle Henrik spent the night on his boat so that he could help the Rosen family and several other Jews escape from Denmark. Uncle Henrik left early to go to his boat while everyone else remained at…

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**ROMEO AND JULIET**

**Does Romeo truly love Juliet and why?**

In Shakespeare’s Romeo and Juliet, the love affair between the two teenagers is not meant to signify a story of true love, but a story of silly family rivalry that has driven a well-matched couple…

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