Revolution Definition and 393 Threads

Hello I have a question here which I've been thinking for quite sometime. And I am still very puzzled. It goes: Find the volume generate by the curve y=lnx rotating about the line y=x. Within the interval of x [4,10]. I would like to know the approach to this problem as I have been asking...

Find the volume of the solid generated by revolving the region bounded by y = 2x - x^2 and y = x about the line x = 1 Ok, so I can solve this if it were revolved around the y-axis, it would be: \pi \int_0^1 (x)^2 - (2x - x^2)^2 dy If I have to revolve it around x = 1, what do I need to change...

Hello can someone please give me some advice on applying the area of a surface revolution. I never seem to plugin the right formula. In the formula S(from a to b) 2pi f(x)**sqrt(1 + f'(x)^2) I never know what to put for f(x)** some times the answers have just x and sometime it has the...

I'm having more Calculus troubles here. Here's the problem: Write the definite integral that represents the area of the surface formed by revolving the graph of f(x) = 81 - x^2 on the interval [0, 9] about the y axis; evaluate the integral to determine the surface area. By knowing that f(x) =...

9x=y^2+18 between 2&6..so y=(9x-18)^1/2 and dy/dx= \frac{9}{2 \sqrt{9x-18}} so S = 2 \pi \int_2^6 \sqrt{9x-18} \sqrt{1+ \frac{81}{36x+72}}dx If this is all right..then I am stuck Any help?

http://www.quietrevolution.co.uk/ I understand these things can spin, but what I'm questioning is whether they can really produce enough power to even power themselves? I mean, there have got to be a few hundred if not thousand LEDs on each one, as well as a control circuit to control the...

http://revolution.nintendo.com Nintendo recently announced the official name of their next console, previously knows as Revolution... and it's going to be called... Wii. So, what do you think? I'm curious... :smile: If you're not familiar with revolution, er, Wii, it's...

I have a question about finding the volume of a hemisphere, I've got that bit sorted but the next bit asks, if the bowl is partially filled what percentage of the bowl is filled. I think i understand the method but i need to find the x value when the bowl is filled 4.5cm of a hemisphere...

Find the volume formed by rotating the area contained by y=sqrt(6x+4), the y-axis and the line y=2x about the y-axis. Set up, but do not evaluate the integral. First I graphed it, then did the "washer" method of finding the area of the circle formed, and found that the radius is...

If the finite region bounded by the curve y = \text{e}^{x} +1 , the y-axis and the line x = \ln2 is rotatated around the x-axis by 360^{\circ} show that the volume of the solid formed is: \frac{\pi}{2} (7 + \ln4 ) I did the intergral and got: V = \pi \left[ (\text{e}^{4} + 2\text{e}^{2}...

Find the volume created by revolving: y=x^2 +x - 2 and y=0 about the x axis. y=x^2 +x - 2 intersects the x-axis at -1 and 1 so those are the bounds of integration. the radius of the figure = -( y=x^2 +x - 2 ) so: V = - \pi \int_{-1}^1 (x^2 + x - 2)^2 dx After integrating that I get...

Hello, I am trying to find the surface area of a torus. I know there are equations for finding this but in this problem I must use a surface of revolution. Given in the problem is the distance to the center of the torus is 12 and the radius of the torus is 2. By using the equation...

I know zip about biology, but I know a little physics. Before Einstein's general theory of relativity challenged it, the prevailing scientific theory of gravitation was Newton's theory. In the minds of most physicists, the issue was resolved in favor of Einstein's theory as a result of an...

Why i think this IS possible: Classes The polarization of classes in this country has become an increasingly large issue; http://www.census.gov/hhes/www/pove...04/pov04hi.html poverty was 12.7% in 2004, i don't have 2005 figures. So it is evident that the middle class is disappearing, which...

Could someone explain undulation per revolution? I would prefer to have a mathematical function defining it also if possible. Can any explain ONE also? .

http://www.1up.com/do/newsStory?cId=3143782 This is quite a departure from the standard controller. Instead of pressing a button to swing a sword, you actually swing the controller.

Could someone please explain how to do this question. Find the volume of the solid formed when the area between y=√x and y=x^4 is rotated about the line x=2. I know how to do this when it's rotated about the x and y axes, but I'm not sure how to do it with a different line. Thank you.

Ok, I was looking through technocrat and I saw a link to this article which claims, that physicists have not only succeeding in slowing down, but also in speeding up the speed of light. I assume it is actually talking about the speed of light in the medium or something, but the article doesn't...

Nanotube revolution? http://www.nature.com/news/2005/050815/pf/050815-8_pf.html 10 metres * 5 centimeters, 50 nanometers thick ribbon per minute can be produced.

I had the opportunity the other day to watch a most enlightening program broadcast by UCTV. The one-hour program was called "How Unequal Can America Get Before We Snap?" presented by President Clinton's former labor secretary Robert Reich. "Inequality of income, wealth, and opportunity in...

Why was the number '360' chosen to be the number of degrees in a complete revolution? How far back does the number go?

If you are getting one, what would it be. Im getting the new xbox. simply because of halo 3

A planet has mass Mplanet = 4.46e24 Kg and a radius Rplanet = 5900 Km Some space explorer lands on the equator of this planet and he weighs 161lbs, whereas he weight 185lbs on Earth. He journeys over to the North pole and he finds himself weight only 95% of what he did at the equator. Now the...

R is bounded by the curves y=(x-1)^2 and y=2(x-1). Axis of revolution: y-axis. How am i supposed to do this. I know how to do the washer method, I know how to apply it when it is revolved arround the x-axis, but I don't know how to do it when it is the y axis. Can anybody explain to me the...

Is the Human Genome project complete? How is the current technology advancing in comparison to the predictions made in Visions

matlab & solids of revolution?? Does anyone know if MATLAB can graph solids of revolution by just using the information contained in the integral form of the problem? :confused:

There isn't a thread about this yet? Honestly people... http://www.eurasianet.org/departments/civilsociety/articles/pp032605.shtml http://www.antiwar.com/justin/?articleid=5301

Why does this sound like the beginning of something really scary? http://www.guardian.co.uk/life/science/story/0,12996,1403780,00.html

So this question has been bothering me for a very long time... but only recently have I mustered up courage to register to ask it. Before though, let me draw a parallel analogy, so you can see where I'm coming from. When you take the volume of a region enclosed by one or more functions...

I'm in India, I don't know about other places. I can't seem to find a channel broadcasting programmes and commercials without a woman. It's not that I don't want women on TV, but its the way they potray women that I don't like. Is this what Men and women who fought for equal rights for women...

I need software that can calculate volumes of revolutions, the only requirement is that it runs on any of the following: * Linux (i386) * Mac OS X * Windows XP (i386) Like calculate the volume when tan x is rotated around the y-axis with upper boundaries 0.2 and lower boundraries 0.1.

Ok. I just need someone to explain the methods for me, if it's not too much trouble. I know you have the shell method, disk method, and washer method. I am taking AP Caclulus BC in high school. I want to know if all of these methods are useful of if one of them is more important. Thanks...

http://g-wash.com/index.php?pageid=content_launch&id=192

Obviously, the first and second paragraph of the Declaration of Independence clearly state that when a government fails to serve the people properly and abuses their power etc. that it is the right of the people, and their duty, to overthrow such a form of government. Let's say someone feels...

The spotting of the factor {D-2 \over 24} outside of the scope of string theory should be the trigger for a new revolution in this field. It could mean that a critical dimension is not exclusive of strings, or it could show how to avoid criticality after all. The term itself is not rare, the...

Columbus report of another continent helped to create a widespread state of mind in which things are discovered. An epidemic of bold optimism and imagination ensued (at first primarily in Europe) Of course there was a downside---the Europeans got syphillis and the Aztecs and Incas got...

The genesis of this thread is Why this is still Amerikkka, where there was a lively discussion of the extent to which many sub-Saharan countries are still economically undeveloped as a result of the genes of their inhabitants, the extent to which those genes are responsible for agriculture and...

Hello. I was wondering what you guys think about time travelling. I read Paul Davies's book called How to Build a Time Machine which left me more confused about this topic. What do you think :smile:

I know that the equation for the surface area of any solid of revolution around, say, the x-axis is SA = 2\pi\int_{a}^{b} y\sqrt{1 + (\frac{\,dy}{\,dx})^2} \,dx What I need is the same formula except in parametric terms, like if the problem was given in terms of x(t) and y(t). Any takers?

Included is my attempt at the following question. I get an answer of 10pi, whereas the right answer is (10pi)/3 from my textbook. Here is the question: Rotate the triangle described by (-1,0),(0,1),(1,0) around the axis x=2 and calculate the volume of the solid. I basically changed the...

Can you please answer me a few questions: 1) Did Neo die ? 2) How was Mr Smith defeated? 3) Who actually created Matrix? The old man? 4) Who actually is Oracle? A programme or real person? 5) Eventually, was the world restored to Reality ?

President Bush is touring the midwest trying to drum up support for his decidedly not "teeny-tiny" tax cut, which includes tax cuts on stock dividend income and raises the amount of money that business can write off from equipment purchases to $100,000 from $25,000. Meanwhile, stocks have...

With the news that Prince Charles is campaining against it this week I want to hear your views (although since most of you are scientists I think you'll be for it). Just for the record I am looking forward to the nanotechnological revolution.