Revolution Definition and 393 Threads

In 1983, a Yugoslavian engineer created a small computer that gave fellow Yugoslavians a taste of computing that they couldn't get otherwise because of strict import rules. https://www.theguardian.com/games/2024/oct/24/how-one-engineer-beat-the-ban-on-home-computers-in-socialist-yugoslavia

As far as I know, Bayes' theorem is ##P(A|B) = \frac{P(A) \times P(B|A)}{P(A) \times P(B|A) + P(\neg A) \times P(B|\neg A)}##. I recall someone saying Bayes' theorem revolutionized probability. Bayes himself and Laplace are supposedly key figures in this revolution. I know how to apply the...

Amazing info from a slow cooker recipes facebook group. If only Fleischmann & Pons had put a clay pot over their experiment... OTOH, they aren't exactly wrong.

Honestly i have very little idea. F * delta t = p F * delta t /m = v So i know the speed of the rod And i know that however high the rod is supposed to go, when its back down it should have done excactly one revolution. I have the feeling that I should So probably i have to use something like...

I found this problem, which I thought was interesting and somewhat original: Calculate the volume of the solid of revolution of the area between the line ##y = x## and the parabola ##y = x^2## from ##x = 0## to ##x = 1## when rotated about the axis ##y = x##.

First, I calculated the inverse of ##y=e^x## since we're talking about y-axis rotations, which is of course ##x=lny##. Then, helping myself out with a drawing, I concluded that the total volume of the solid must've been: $$V=\pi\int_{0}^{1}1^2 \ dy \ +(\pi\int_{1}^{e}1^2 \ dy \ - \pi...

So I was reading my topic named "atoms" and got confused at a paragraph. It goes like this.. I encircled the paragraph when they told " "frequency of electromagnetic waves emitted by the revolving electrons is equal to the frequency of revolution" I got confused at 'frequency of revolution'...

In the mid-1990's, an electrical engineer/computer scientist by the name of Judea Pearl started to change the world by greatly improving our understanding of causality. He brought together many strands of thought that had gone before him, then synthesized them into an integrated whole, with many...

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Please Help Me

The Singapore Flyer is a very tall Ferris wheel.It is 315 meters tall and has a diameter of 150 meters. Each revolution takes about 30 minutes. If you were allowed to ride for 3 hours, how far would you travel? How much of a mile or how many miles would you travel?

for once not a Hollywood ending. Looks like Blade Runner at first, the plot is not unfamiliar but the ending is.

My question is, why is the circled integral the chosen integral for this case? My thoughts are that we don't just use ##\int_0^1e^{-x}## because we need to make this two dimensional area into a three dimensional volume by doing 360 degrees of rotation. This would correspond to ##2πr##. ##2π## is...

Homework Statement Peter has a spherical shaped water tank with radius R. At the top of the tank there's a small hole. Peter wants to know how much water there is left in the tank by measuring the distance L from the hole to the water surface. Find an explicit form for the water volume V(L), 0...

Homework Statement Hello, a bowl is created when rotating the function f(x) = \begin{cases} 0, & 0 \leq x \lt 6 \\ (12/\pi)arcsin(x-6), & 6\leq x \leq 7 \end{cases} around the y-axis. Find the height (h) and the volume (V) of the bowl.Homework EquationsThe Attempt at a Solution So, I graphed...

Hello friends and fellow Physics enthusiasts At the beginning let me confess that I am more of a sleeping member though I do follow this forum quite closely. Today, I am posting to seek some help from fellow Physics educators. I hope this is the right section of the forum to post, if not, I...

There are two ways to revolve, around Y or X and the formulas are different. If I have something bounded by $$f(x) = x^2 + 1$$. I can write $$x = \sqrt{y - 1}$$. But, is it wrong to swap axis to show that I'm integrating dy, not dx?

Homework Statement Let R be the area in the xy-plane in the 1st quadrant which is bounded by the curves y^2+x^2 = 5, y = 2x and x = 0. (y-axis). Let T be the volume of revolution that appears when R is rotated around the Y axis. Find the volume of T. Homework EquationsThe Attempt at a Solution...

Homework Statement A container with height 4.5 is created by rotating the curve y = 0.5x^2 0 \leq x \leq 3 around x = -3 and putting a plane bottom in the box. Find the volume V of the box. Homework EquationsThe Attempt at a Solution I want to solve this by using the shell method. I have...

Classical physics is difficult because it is based on differential equations, and the differential equations of interest are usually unsolvable. The student must invest a lot of time in learning difficult math, and still can only analyze very simple systems. This difficulty arises in the first...

O'Neill's Elementary Differential Geometry contains an argument for the following proposition: "Let C be a curve in a plane P and let A be a line that does not meet C. When this *profile curve* C is revolved around the axis A, it sweeps out a surface of revolution M." For simplicity, he...

Why is this way of thinking wrong?. can't I assume that when Δx tends to zero is a sufficient approximation of what I want to get? It confuses me with the basic idea of integrating a function to get the area beneath a curve of a function (which isn't also as perfect) . PD: I put Δx tends to...

The problem is, find the surface area of the volume of revolution generated by rotating the curve y=e2x between x=0 and x=2 about the x-axis. Here's what I have so far... SA=∫y√(1+y2)dx =∫e2x√(1+4e4x)dx and from here I'm not really sure what to do. Any help would be appreciated.

Hello. I am looking for guidance. I have been working in software industry for about eight years now. I see that the trend is moving towards making a machine intelligent. I want to be part of this trend and move forward. My questions is: What skills do I need to become part of this era of...

Lets suppose for a stroy, that a time traveller arrive in a civilization that hasnt reached iron age yet. He isn't a well qualified engineer or doctor, but he becomes a king. How much he could help their development by simply telling : with really hot fire, you could produce iron, not just shape...

Is drawing of graphs of solids of revolutions important topic of mathematics? This makes me remerber conic sections topic. Conic sections topic belongs to algebra and drawing their graphs is important. So where does solids of revolutions belong to? I know calculation of their volumes belongs to...

Homework Statement an object starts from rest and has a final angular velocity of 6 rad/s. the object makes 2 complete revolutions. find the object's angular acceleration. Homework Equations wf^2=wi^2+2αd The Attempt at a Solution Not sure what to do with the revolutions, would it take act as...

Homework Statement Find the area of the surface generated by revolving the curve y=√x+1, 1≤ x ≤5, about the x-axis. I'm stuck trying to figure out how I can use substitution...if I am even able. I was trying to rewrite 1 as 4(x+1)/4(x+1) but still can't seem to get the right terms to cancel...

HELP I can't find the surface of revolution! By donuts I mean a circle that doesn't touch the axes (tore in french) y^2+(x-4)^2=2^2 is my function ( y^2+x^2=r^2) and the axe of rotation is y so y= sqrt(r^2-x^2) the formula I know : 2* pi (Integral from a to b (F(x)*sqrt( 1+ (f``(x))^2))...

Hi! I guess this question must be easy, but it's driving me crazy: in what time of the year does the Earth "trails" the Sun in its current galactic movement towards Vega? And, could you please confirm that during this period Vega is not visible because it's always facing the "day side" of the...

According to quantum mechanics, an electron possesses orbital angular momentum. And we know that orbital angular momentum is possessed by revolving body. Does electron revolve around the nucleus? Please explain. I shall be very much thankful to you.

Homework Statement Suppose that a surface has an equation in cylindrical coordinates of the form ##z=f(r)##. Explain why it must be a surface of revolution. Homework EquationsThe Attempt at a Solution I consider ##z=f(r)## in terms of spherical coordinates. ## p cosφ = f \sqrt{(p sinφcosθ)^2...

Some say block-chain economies, some say driver-less cars and some say clean energy. What do you think?

Hello, I'm trying to calculate Moon revolution period but always got 27.53 instead of 27.32. G = 6.674e-11 (m^3 kg^-1 s^-2) M = 5.9724e24 (kg) from http://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html R = 384400000 (m) Earth Moon distance From 4π^2 * R^3 = GM*T^2, got moon revolution...

How can inhabitants of the far side of moon guess that the moon is revolving around the earth?

1. Find the centroids of the solids formed by rotating completely about the x-axis the plane regions defined by the following inequalities: (a) y^2 < 9x, y>0, x<1 (b) xy<4, y>0, 1<x<2 2. I used the equation for solids of revolution: Integral from a to b of (x[f(x)]^2.dx) / Integral from a to b...

Homework Statement Find the volumes of the solid formed when each of the areas in the following perform one revolution about the X axis... Question: The volume line in the first quadrant and bounded by the curve y=x^3 and the line y=3x+2. Homework Equations Volume of revolution about X-axis...

Homework Statement The total area between a straight line and the parabola is revolved around the y-axis. What is the volume of revolution? According to the book, the answer is ; My answer comes out to be Homework Equations The Attempt at a Solution 1. Rewrite the second equation in...

To start with, we should find the points of intersection of the two functions, as these will be the terminals of our regions of integration. $\displaystyle \begin{align*} 2\,x^2 &= x + 1 \\ 2\,x^2 - x - 1 &= 0 \\ 2\,x^2 - 2\,x + x - 1 &= 0 \\ 2\,x\,\left( x - 1 \right) + 1 \,\left( x - 1...

Here is a graph of the region to be rotated. Notice that it is being rotated around the same line that is the lower boundary. The volume will be exactly the same if everything is moved down by 4 units, with the advantage of being rotated around the x-axis. So using the rule for finding the...

Given $$x_1^2 -y^2=a^2, \ \ x_2=a+h$$ Or $$x_1=\sqrt{a^2+y^2}$$ Find Volume about the $y$-axis So... $$\pi\int_{a}^{h} \left(x_2^2-x_1^2\right)\,dy$$ Actually I am clueless?!

Let $$f(x) = x^3 + 4x^2 - x + 5$$ revolve about the line $$y(x) = -x + 5$$. There will form one solid with finite volume. Find the volume of that solid.

I've been trying to figure out why you can't use the average value of a function to determine the volume of a solid of revolution. As an example: Trying to find the volume of a solid of revolution on y=√x from 0 to 1 around the x-axis. The definite integral is 2/3, which divided by one is...

why was Earth considered to revolve around the sun and nt the other way round? why is it wrong to analyze planetary motion from Earth frame?

Homework Statement Find the volume of the solid obtained by rotating y=x^2 and x = y^2 about y=2 Homework Equations V= 2πrh The Attempt at a Solution When I had constructed the graph I determined the following: r= 2-(y(1/2)) h= 1-y2 after converting V into an integral I applied fundamental...

Consider the solid in three dimensions that is formed when the graph of a function $f(x)$, with $f(x) \ge  0$ for all $x \in [a, b]$, is revolved around the $x$-axis on the segment $x \in [a, b]$. Derive the following formula for the volume $V$ of this solid: $V = \pi\int_a^b f^2(x)dx$. Use...

Here is my 210 word summary of the causes of the French Revolution: The French government borrowed huge sums of money to pay for France's military support of the USA in the American Revolution. The government of France owed a huge financial debt to the French banks the French government...

So I'm getting ready for an exam on tuesday, and I'm using each method for volumes of revolutions for every problem but I'm not getting the same answers. So, let's use this as an example: y = 5x; the shaded region is from [1,2] Using the disk method (about the x-axis) I find: R(x) = 5x; r(x)...

When I learned about volumes of solids of revolution, I never really memorized any formulas for specific cases per se. I used two expressions for area, either ##A = \pi (R^2 - r^2)## and ##A = 2\pi r h##. Those expressions worked for rotations about any horizontal/vertical axis (not necessarily...

I have a few questions about finding volumes of solids of revolution (in a typical first year single variable calculus course). 1) I can rotate any region about any horizontal/vertical axis. How exactly do I rotate a region about a line that is neither horizontal nor vertical (##y = x - 1## for...