Country Boy
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It doesn't have to be prime- as long as a number is not a perfect square or divisible by a perfect square, you cannot continue. For example to simplify the square root of 216, I can observe 216= 2*2*2*3*3*3= 2^3 3^3 (that's its "prime factorization"). Since I want the square root, I look for squares- powers of 2: (2*2)(2)(3*3)(3)= 4(2)(9)(3). "4" and "9" are "perfect squares", 2 squared and 3 squared. [math]\sqrt{216}= \sqrt{4(9)(2)(3)= \sqrt{4}\sqt{9}\sqrt{2(3)}= 2(3)\sqrt{6}= 6\sqrt{6}[/math]. "6" is not prime but it is not a perfect square either.
Notice that 2*2*2= 8 and 3*3*3= 27 are "perfect cubes", $2^3$ and $3^3$ so its cube root: [math]\sqrt[3]{216}= \sqrt[3]{2^3(3^3}= 2(3)= 6[/math].
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Originally Newton tried to define the derivative as "dy divided by dx" where dy and dx are "infinitesmals" but was not able to give a rigorous definition of "infinitesimal". The Bishop Berkeley famously satirized them as "ghosts of vanished quantities". Later people like Cauchy redefined the derivative in terms of limits. But recently Abraham Robinson and others resurrected "infinitesmals" by extending the real numbers to include both "infinite" and "infinitesmals" in "non-standard analysis": https://en.wikipedia.org/wiki/Non-standard_analysis.
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When an object is sitting on the ground there are two forces- the force of gravity pointing downward and the force due to the pressure the ground is exerting on the object. Those are "equal and opposite", they cancel and one could, as well, say there is no (net) force. If an object is sitting on a frictionless tilted surface such as a wedge there is the force of gravity but now the force due to the surface is not directly opposite to gravitational force and we may have motion along the surface. In "real life", with friction, the friction force is parallel to the surface so we can think of this as three forces- the vertical force of gravity, the pressure force due to the surface which is perpendicular to the surface, and friction which is parallel to the surface.
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Do you not know how 'google' works? I entered "parts working together for one purpose" in Google and immediately got "system".
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If the weight of herbs alone is "m" and the weight of herbs and vodka is "M" then the weight of vodka alone is M-m so that the ratio of "herbs to vodka" is m/(M- m).
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No, I don't know what you by "peak state". If you know what you mean please tell us!
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Yes, but a cramp can cause a muscle strain. I thought that was what the question was asking.
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Are you asking if the universe was created by a sentient, reasoning, being?
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That is a "cramp". A "spasm" is only momentary.
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On 8/15/2018 at 12:58 AM, John Cuthber said:
if you do it by hand.
But it's quick if you use a computer.
If someone else has done the tedious work of programming the computer!
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My cleverness, on the other hand, became obsolete long ago!
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Didn't your teacher, or text book, explain what a "mole" is? One mole of any substance contains "Avogadro's number" of molecules of that substance and that number is chosen so that the mass of one mole of a substance, in grams, is equal to that substance's molecular weight. For example, carbon-12 has a molecular weight of 12 atomic units (au) (Any form of carbon has 6 protons. The isotope, carbon 12, also has 6 neutrons which have the same weight as the protons. Since an electron's weight is negligible, the "atomic weight" of carbon 12 is 12 au [and that's where the "12" in the name comes from]) so one mole of carbon 12 weighs 12 grams. A methane molecule is made from one carbon atom and four hydrogen atoms. Since we don't want to worry about isotopes here we take the average atomic weight of all isotopes of carbon, 12..011 au, and the average weight of all isotopes of hydrogen, 1.008 au, which makes the atomic weight of methane 12.011+ 4(1.008)= 16.043 au. One mole of methane has mass 16.043 grams.
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"Conservation of energy": you can't get energy out of something that does not already have energy already in it. Oil, and gasoline, have energy "trapped" in its molecules. So does wood or anything that burns. Water, even seawater, does not. As for a "chemical soup", isn't that what oil is?
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On 8/17/2018 at 10:41 PM, prashantakerkar said:
https://en.m.wikipedia.org/wiki/Draughts
Can Draughts or Checkers game played between two opponents be designed and developed using a 5*5,7*7,9*9,11*11 board ?
I.e Odd number of sides.
Thanks & Regards,
Prashant S Akerkar
Odd number of sides or odd number of squares on each side?
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1 hour ago, Antony Howard Stark said:
Well the last thread didn't really turn up satisfactory answers
You mean people didn't rush to bow before you?
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Back in July, you started a thread saying that you had proved the Collatz conjecture. Want happened to that? Why are you starting a new thread saying the same thing?
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[tex]\frac{f(x+h)- f(x)}{h}[/tex] is the "difference quotient". Geometrically, it gives the average "slope" of a graph between the points (x, f(x)) and (x+ h, f(x+h)). That is the slope of the straight line between those points. Taking the limit as h goes to 0, if it exists, gives the slope of the tangent line to the graph at (x, f(x)). (The graph has a tangent line at that point if and only if that limit exists.) In some textbooks the "derivative" of f at that value of x is defined to be that limit and then that is shown to be the slope of the tangent line. In other textbooks the derivative is defined as "the slope of the tangent line" and that formula derived.
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4 hours ago, TheDragon said:
We did an experiment in Lab with a Pascal Timer and a Free Fall device with one small sphere and one larger. I was wondering how mass could influence the results calculated using the accepted value of Earths acceleration in our area. Would the mass of the spheres affect the acceleration? I know that all of this has to do with Newton's second law. I just need help understanding this.
What results did you get from that experiment?
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Yes, and a constant
24 minutes ago, StringJunky said:If you change any aspect of an object's motion you are accelerating it.
Yes, and a constant acceleration, with no "change in acceleration" is a change in velocity requiring that inertia be overcome.
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14 hours ago, StringJunky said:
Inertia is resistance to change of acceleration[/quote]
resistance to change of velocity.
14 hours ago, StringJunky said:Quoteand is a function of mass and velocity. Acceleration due to gravity (free fall) is not affected by mass, so it should be clear that inertia does not affect free fall.
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In order to answer this, I would have to know what you mean by "acceleration" and "free fall". The way I understand them, an object "in free fall" is accelerating!
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How you would approach this depends upon what you know. If you know a little Calculus then you can start from the fact that there is no horizontal acceleration while the vertical acceleration is that of gravity, -g or approximately -9.8 m/s.
That horizontal acceleration is the derivative of the horizontal velocity function: dvx/dt= 0 so vx is a constant. You are told that, initially, the speed is "20m/s at an angle of 50° above the horizontal" so that constant is 20 sin(50). The horizontal velocity is the derivative of the horizontal position, x, so the horizontal position, taking the point at which the ball is kicked to be x= 0, is x(t)= 20 sin(50)t.
The vertical acceleration is the derivative of the vertical velocity function: dvy/dt= -g so vy= -gt plus the initial vertical velocity which is 20 cos(50). vy= -gt+ 20 cos(50). The vertical velocity is the derivative of the vertical position, y, so taking the point at which the ball is kicked to be y= 0, y(t)= -(g/2)t^2+ 20 cos(50)t.
If you have not learned any Calculus, you probably have just learned that "x(t)= vx(0)t+ x(0)" and "y(t)= -(g/2)t^2+ vy(0)t+ y0" where vx(0), vy(0), x(0), and y(0) are the initial values put in above.
The question asks for the highest point the ball reaches. Again, there are several ways of doing that. If you know a little Calculus, you know that a maximum of a differentiable function is reached where the y derivative is 0. If not the you probably realize that, at the highest point, the vertical velocity, vy, is 0. Or, since the vertical position function is quadratic, its graph is a parabola with vertex at its highest point- you can simply "complete the square" in the quadratic formula for the height.
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Darn! If I could just remember where I put my time machine!
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I would like to know what the OP means by "perfect". "Perfect" for what? Certainly NOT "perfect" for life! Almost all of the universe is terribly hostile to life. If the earth is "perfect" for life that is because life has evolved to fit it.
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Will epigenetic changes in my body be passed down to my offspring?
in Anatomy, Physiology and Neuroscience
Posted
According to Wikipedia, "Epigenetics most often denotes changes that affect gene activity and expression, but can also be used to describe any heritable phenotypic change" so, yes epigenetic changes affect genes and can be passed on to off spring. However, "working out" and "eating lots of nutrient dense food" are NOT "epigenetic". They are phenotypic, do not affect genes, and are NOT passed on to offspring.