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Is this proof valid? If so, can you help me find a reference for it on the Internet? -- Bowlhover ( talk) 02:00, 14 September 2008 (UTC)
If I may interject two points. First of all, I find the section too detailed for inclusion in the main article. Perhaps there is enough material scattered about to start an article on the square root of rational numbers. There are a number of proofs indicated in the square root of 2 article, and I would rather see the section in irrational number kept brief and in summary style. Second, the lengthy proof is not necessary. One can prove consider]ably more in much less space by appealing to Gauss's lemma (for which there already is an article): Any rational number which is an algebraic integer is a (rational) integer. siℓℓy rabbit ( talk) 14:51, 14 September 2008 (UTC)
Help me from here, please. I want to continue the line of thinking that is a derivative of internal kinetic energy.
A month ago, I realized that is a percent relative the kinetic frictional force to the Normal Force, and this insight really helped me understand everything in physics much better. i.e. =.40 means that of the Normal force, the kinetic frictional force is about 40% the Normal force.
I also really liked the algebraic proof that is the solution to the equation where alpha is the angle of incline which a block begins to slide, from rest position.
So today, I'm trying to round out my collection and would like an insightful way to represent an intuitive relationship between to work or internal-kinetic-energy.
So, ignoring angles of incline, and ignoring mass and gravity (let them be 0, m1, and g all respectively) is there any way for me to algebraically rearrange variables or shuffle equations to get a neat relation between \mu_k and work or internal kinetic energy? I haven't found one, so if one doesn't exist, are there any other outside the box ways to look at these relationships between variables?
When I usually try to creatively play with formulas, if the term is or something like a difference of terms, such as-- initial minus final, terms like these have more flexibility and you can apply more algebra to get more new equations from old ones.
Thanks in advance for any input. My goal is to learn physics slowly and very analytically, always looking for ways to inject redundant mathematical thinking into my notes that I keep. Sentriclecub ( talk) 12:23, 14 September 2008 (UTC)
where
plz help me solve this example with detailed solution. Find a root of the equation x sin x + cos x = 0, using Newton-Raphson method. Miral b ( talk) 12:42, 14 September 2008 (UTC) Retrieved from " http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Mathematics" Hidden category: Non-talk pages that are automatically signed
The function is an even function: . The Taylor series
contains only even powers of x. So it is simpler to set and solve the nth degree equation
for some sufficiently big value of n.
The two smallest solutions to x sin x + cos x = 0 are
The smallest real solutions are
In order to reach this accuracy you need n ≥ 9. The J-code used is %:_1 _2{1{>p.((*1&o.)+2&o.)t.2*i.9 , and the result produced is 0j1.19968 2.79839. Bo Jacoby ( talk) 22:14, 14 September 2008 (UTC)
OK, you need to find when x*sin(x) + cos(x) = 0. Find when cos is negative and when sine is positive. For instance in the second quadrant. Take a value in the second quadrant reasonably close to pi but also reasonably close to 3pi/2 as the first approximation (since the 'x' in x*sin(x) increases sin(x) considerably). Then apply the formulae.
Topology Expert ( talk) 13:23, 17 September 2008 (UTC)
When an object is pushed along a surface, is the ratio of the energy converted into heat vs this denominator:
How do i verbally say the denominator? Is it the indefinite integral of the Normal Force (as a function of x) with respect to x?
I am picturing an example. A constant force is applied to block A which slides 2 meters on flat surface, then up a 60 degree incline for the final 8 meters.
I see a lot of new ways to further explore uses of now, but needed to know what the denominator is in spoken words.
If this block is pulled by a string in such a way that the block has constant velocity of 1 meters per second (and the string always pulls parallel to the block's momentum), then I could integrate the normal force as a function of time, then convert it into Joules. This would involve solving for the impulse, then converting an impulse into work. I never covered subjects from Calc_II. Is it straightforward to convert an impulse to an amount of work, given this example? I have read the articles on these subjects, but they get too complicated too fast, and I get overwhelmed. I should be able to better attempt my first question if I am not afraid of making a calculus goof. Sentriclecub ( talk) 13:28, 14 September 2008 (UTC)
I began using computers to verify results of logical equations I solved previously by hand in about 1963. Then in about 1978 I found a computer method for reducing logical equations to minimum form in “Digital/Logic Electronics Handbook” by William L Hunter (pages 112-113, Tab Books, Blue Ridge summit, PA) ISBN 0830657740 ISBN 0830657746 ISBN 9780830657742 called the Harvard chart Method of logical equation reduction. In 1981, I published a modification of the method to reduce multi-valued equations to minimum form as a computer program here. In doing the modification I may have become unconsciously aware of the ability to count and to sort sets and multisets using an indexed array as demonstrated here.
Nonetheless, I did not become consciously aware of this method until at least 1995, followed by its copyright and online publication in 1996 here and again in 2006 here. Consequently, I am searching for any publication prior to my own which might describe or demonstrate this method to count and to sort sets and multisets or to find the date the Counting sort was first described or published with its original definition found here and the date the Pigeonhole sort was first described or published with it's original definition found here. 71.100.10.11 ( talk) 14:04, 14 September 2008 (UTC)
Mathematics desk | ||
---|---|---|
< September 13 | << Aug | September | Oct >> | September 15 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Is this proof valid? If so, can you help me find a reference for it on the Internet? -- Bowlhover ( talk) 02:00, 14 September 2008 (UTC)
If I may interject two points. First of all, I find the section too detailed for inclusion in the main article. Perhaps there is enough material scattered about to start an article on the square root of rational numbers. There are a number of proofs indicated in the square root of 2 article, and I would rather see the section in irrational number kept brief and in summary style. Second, the lengthy proof is not necessary. One can prove consider]ably more in much less space by appealing to Gauss's lemma (for which there already is an article): Any rational number which is an algebraic integer is a (rational) integer. siℓℓy rabbit ( talk) 14:51, 14 September 2008 (UTC)
Help me from here, please. I want to continue the line of thinking that is a derivative of internal kinetic energy.
A month ago, I realized that is a percent relative the kinetic frictional force to the Normal Force, and this insight really helped me understand everything in physics much better. i.e. =.40 means that of the Normal force, the kinetic frictional force is about 40% the Normal force.
I also really liked the algebraic proof that is the solution to the equation where alpha is the angle of incline which a block begins to slide, from rest position.
So today, I'm trying to round out my collection and would like an insightful way to represent an intuitive relationship between to work or internal-kinetic-energy.
So, ignoring angles of incline, and ignoring mass and gravity (let them be 0, m1, and g all respectively) is there any way for me to algebraically rearrange variables or shuffle equations to get a neat relation between \mu_k and work or internal kinetic energy? I haven't found one, so if one doesn't exist, are there any other outside the box ways to look at these relationships between variables?
When I usually try to creatively play with formulas, if the term is or something like a difference of terms, such as-- initial minus final, terms like these have more flexibility and you can apply more algebra to get more new equations from old ones.
Thanks in advance for any input. My goal is to learn physics slowly and very analytically, always looking for ways to inject redundant mathematical thinking into my notes that I keep. Sentriclecub ( talk) 12:23, 14 September 2008 (UTC)
where
plz help me solve this example with detailed solution. Find a root of the equation x sin x + cos x = 0, using Newton-Raphson method. Miral b ( talk) 12:42, 14 September 2008 (UTC) Retrieved from " http://en.wikipedia.org/wiki/Wikipedia:Reference_desk/Mathematics" Hidden category: Non-talk pages that are automatically signed
The function is an even function: . The Taylor series
contains only even powers of x. So it is simpler to set and solve the nth degree equation
for some sufficiently big value of n.
The two smallest solutions to x sin x + cos x = 0 are
The smallest real solutions are
In order to reach this accuracy you need n ≥ 9. The J-code used is %:_1 _2{1{>p.((*1&o.)+2&o.)t.2*i.9 , and the result produced is 0j1.19968 2.79839. Bo Jacoby ( talk) 22:14, 14 September 2008 (UTC)
OK, you need to find when x*sin(x) + cos(x) = 0. Find when cos is negative and when sine is positive. For instance in the second quadrant. Take a value in the second quadrant reasonably close to pi but also reasonably close to 3pi/2 as the first approximation (since the 'x' in x*sin(x) increases sin(x) considerably). Then apply the formulae.
Topology Expert ( talk) 13:23, 17 September 2008 (UTC)
When an object is pushed along a surface, is the ratio of the energy converted into heat vs this denominator:
How do i verbally say the denominator? Is it the indefinite integral of the Normal Force (as a function of x) with respect to x?
I am picturing an example. A constant force is applied to block A which slides 2 meters on flat surface, then up a 60 degree incline for the final 8 meters.
I see a lot of new ways to further explore uses of now, but needed to know what the denominator is in spoken words.
If this block is pulled by a string in such a way that the block has constant velocity of 1 meters per second (and the string always pulls parallel to the block's momentum), then I could integrate the normal force as a function of time, then convert it into Joules. This would involve solving for the impulse, then converting an impulse into work. I never covered subjects from Calc_II. Is it straightforward to convert an impulse to an amount of work, given this example? I have read the articles on these subjects, but they get too complicated too fast, and I get overwhelmed. I should be able to better attempt my first question if I am not afraid of making a calculus goof. Sentriclecub ( talk) 13:28, 14 September 2008 (UTC)
I began using computers to verify results of logical equations I solved previously by hand in about 1963. Then in about 1978 I found a computer method for reducing logical equations to minimum form in “Digital/Logic Electronics Handbook” by William L Hunter (pages 112-113, Tab Books, Blue Ridge summit, PA) ISBN 0830657740 ISBN 0830657746 ISBN 9780830657742 called the Harvard chart Method of logical equation reduction. In 1981, I published a modification of the method to reduce multi-valued equations to minimum form as a computer program here. In doing the modification I may have become unconsciously aware of the ability to count and to sort sets and multisets using an indexed array as demonstrated here.
Nonetheless, I did not become consciously aware of this method until at least 1995, followed by its copyright and online publication in 1996 here and again in 2006 here. Consequently, I am searching for any publication prior to my own which might describe or demonstrate this method to count and to sort sets and multisets or to find the date the Counting sort was first described or published with its original definition found here and the date the Pigeonhole sort was first described or published with it's original definition found here. 71.100.10.11 ( talk) 14:04, 14 September 2008 (UTC)