MaplePrimes - Questions and Posts tagged with equation
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 01 Oct 2016 18:54:36 GMTSat, 01 Oct 2016 18:54:36 GMTThe most recent questions and posts on MaplePrimes tagged with equationhttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Questions and Posts tagged with equation
http://www.mapleprimes.com/tags/equation
how to get the coordinate of a swirl
http://www.mapleprimes.com/questions/217377-How-To-Get-The-Coordinate-Of-A-Swirl-?ref=Feed:MaplePrimes:Tagged With equation
<p>http://mathforum.org/kb/message.jspa?messageID=685890</p>
<p>i find equation above</p>
<p>for ii from 0 by 5 to 365 do<br> eq1 := x^2 + y^2 = arccos(x/r);<br> eq2 := y = evalf((atan(-1) - ii*Pi/180)/Pi)*(-1.0)*x;<br> xy := fsolve({eq1, eq2});<br> print("M",rhs(xy[1]),rhs(xy[2]),","):<br>od:</p>
<p>but i do not understand how to set r</p>
<p>i use a line scanning 365 degrees to get the path of swirl </p>
<p>would like to get path data for c# WPF animation</p>
<p>but this method may have multiple solution because an intersection of swirl </p>
<p>and a line can have multiple points</p><p>http://mathforum.org/kb/message.jspa?messageID=685890</p>
<p>i find equation above</p>
<p>for ii from 0 by 5 to 365 do<br> eq1 := x^2 + y^2 = arccos(x/r);<br> eq2 := y = evalf((atan(-1) - ii*Pi/180)/Pi)*(-1.0)*x;<br> xy := fsolve({eq1, eq2});<br> print("M",rhs(xy[1]),rhs(xy[2]),","):<br>od:</p>
<p>but i do not understand how to set r</p>
<p>i use a line scanning 365 degrees to get the path of swirl </p>
<p>would like to get path data for c# WPF animation</p>
<p>but this method may have multiple solution because an intersection of swirl </p>
<p>and a line can have multiple points</p>217377Sat, 10 Sep 2016 09:24:58 Zasa12asa12surd produces absurd result
http://www.mapleprimes.com/questions/216348-Surd-Produces-Absurd-Result?ref=Feed:MaplePrimes:Tagged With equation
<p>I am trying to solve an equation using surd and I get a strange result.</p>
<p><img src="https://i.imgur.com/jX4592R.png" alt="" width="553" height="207"></p>
<p>solve(surd(x^4,8)=-2)<br> 4, -4, 4 I, -4 I</p>
<p>These solutions are clearly wrong.</p>
<p>The equation (x^4)^(1/8) = -2 has no solution.</p>
<p>This problem is equivalent to asking the computer to solve sqrt(x) = -2</p>
<p>which has no solution in R or C.</p>
<p> </p>
<p>However if I type</p>
<p>solve((x^4)^(1/8) = -2) , then I get no answer, which is what I expected.</p>
<p>Why does surd behave in this unexpected way.</p>
<p> </p>
<p>Also another thing I am wondering, why doesn't Maple simplify (x^4)^(1/8) to x^(1/2).</p>
<p>I tried the simplify command it didn't work.</p>
<p> </p><p>I am trying to solve an equation using surd and I get a strange result.</p>
<p><img src="https://i.imgur.com/jX4592R.png" alt="" width="553" height="207"></p>
<p>solve(surd(x^4,8)=-2)<br> 4, -4, 4 I, -4 I</p>
<p>These solutions are clearly wrong.</p>
<p>The equation (x^4)^(1/8) = -2 has no solution.</p>
<p>This problem is equivalent to asking the computer to solve sqrt(x) = -2</p>
<p>which has no solution in R or C.</p>
<p> </p>
<p>However if I type</p>
<p>solve((x^4)^(1/8) = -2) , then I get no answer, which is what I expected.</p>
<p>Why does surd behave in this unexpected way.</p>
<p> </p>
<p>Also another thing I am wondering, why doesn't Maple simplify (x^4)^(1/8) to x^(1/2).</p>
<p>I tried the simplify command it didn't work.</p>
<p> </p>216348Mon, 22 Aug 2016 22:04:22 Zmax125max125Application of first order equations
http://www.mapleprimes.com/posts/205303-Application-Of-First-Order-Equations?ref=Feed:MaplePrimes:Tagged With equation
<p>It is very important that you learn to pose and solve equations in practical problems. Ernest Mach, a famous scientist of the nineteenth century, said that algebra is characterized by a lightening of mind, because the solution of a problem, after building the equation, you can "forget" all the practical situation to focus on the mathematical expression; everything that is not necessary to solve the problem no longer interfere with your mind. Another famous scientist, Isaac Newton, wrote that the language of algebra is the equation. To see a problem concerning abstract relations of numbers or amounts, simply translate the problem of colloquial language to the algebraic language. Here I leave the application for first order equations developed in 2016 Maple.</p>
<p> </p>
<p><a href="/view.aspx?sf=205303_post/Aplicativo_Ecuaciones.mw">Aplicativo_Ecuaciones.mw</a><a href="/view.aspx?sf=205303_post/Application_of_first_order_equations.mw"><br></a></p>
<p>(In Spanish)</p>
<p>Lenin Araujo Castillo</p>
<p>Ambassador of Maple - Perú</p>
<p> </p><p>It is very important that you learn to pose and solve equations in practical problems. Ernest Mach, a famous scientist of the nineteenth century, said that algebra is characterized by a lightening of mind, because the solution of a problem, after building the equation, you can "forget" all the practical situation to focus on the mathematical expression; everything that is not necessary to solve the problem no longer interfere with your mind. Another famous scientist, Isaac Newton, wrote that the language of algebra is the equation. To see a problem concerning abstract relations of numbers or amounts, simply translate the problem of colloquial language to the algebraic language. Here I leave the application for first order equations developed in 2016 Maple.</p>
<p> </p>
<p><a href="/view.aspx?sf=205303_post/Aplicativo_Ecuaciones.mw">Aplicativo_Ecuaciones.mw</a><a href="/view.aspx?sf=205303_post/Application_of_first_order_equations.mw"><br></a></p>
<p>(In Spanish)</p>
<p>Lenin Araujo Castillo</p>
<p>Ambassador of Maple - Perú</p>
<p> </p>205303Sun, 07 Aug 2016 07:48:38 ZLenin Araujo CastilloLenin Araujo CastilloWith(rootfinding) Isolate help!!
http://www.mapleprimes.com/questions/214363-Withrootfinding-Isolate-Help?ref=Feed:MaplePrimes:Tagged With equation
<p>I am having 26th degree polynomial univariate equation , I used Isolate to get the roots. but I am getting some extra roots which are not true they I even tried to substitute those roots in original equation then I got non zero answer instead of getting nearly zero answer.How is it possible??</p>
<p> </p>
<p>equation looks like:</p>
<p>-12116320194738194778134937600000000*t^26+167589596741213731838990745600000000*t^24+1058345691529498270472972795904000000*t^22-4276605572538658673086219419648000000*t^20-23240154739806540070988490473472000000*t^18-5442849111209103187871341215744000000*t^16+49009931453396028716875310432256000000*t^14+74247033158233643322704589225984000000*t^12-2762178990802317464801412907008000000*t^10-25947900993773120244883450232832000000*t^8-7468990043547273070742668836864000000*t^6-567730116675454293925108383744000000*t^4+3703566799705707258760396800000000*t^2-4742330812072533924249600000000</p>
<p>Solutions i got:</p>
<p>[t = -4.162501845, t = -2.295186769, t = -1.300314688, t = -.8048430445, t = -0.6596008501e-1, t = -0.4212510777e-1, t = 0.4212510777e-1, t = 0.6596008501e-1, t = .8048430445, t = 1.300314688, t = 2.295186769, t = 4.162501845]</p>
<p>t=4.162501845 give me non zero answer when I substitute it in the equation given above:</p>
<p>I got this answer: 4.750212083*10^39</p>
<p> </p><p>I am having 26th degree polynomial univariate equation , I used Isolate to get the roots. but I am getting some extra roots which are not true they I even tried to substitute those roots in original equation then I got non zero answer instead of getting nearly zero answer.How is it possible??</p>
<p> </p>
<p>equation looks like:</p>
<p>-12116320194738194778134937600000000*t^26+167589596741213731838990745600000000*t^24+1058345691529498270472972795904000000*t^22-4276605572538658673086219419648000000*t^20-23240154739806540070988490473472000000*t^18-5442849111209103187871341215744000000*t^16+49009931453396028716875310432256000000*t^14+74247033158233643322704589225984000000*t^12-2762178990802317464801412907008000000*t^10-25947900993773120244883450232832000000*t^8-7468990043547273070742668836864000000*t^6-567730116675454293925108383744000000*t^4+3703566799705707258760396800000000*t^2-4742330812072533924249600000000</p>
<p>Solutions i got:</p>
<p>[t = -4.162501845, t = -2.295186769, t = -1.300314688, t = -.8048430445, t = -0.6596008501e-1, t = -0.4212510777e-1, t = 0.4212510777e-1, t = 0.6596008501e-1, t = .8048430445, t = 1.300314688, t = 2.295186769, t = 4.162501845]</p>
<p>t=4.162501845 give me non zero answer when I substitute it in the equation given above:</p>
<p>I got this answer: 4.750212083*10^39</p>
<p> </p>214363Sun, 10 Jul 2016 13:35:40 ZvirajvirajHow can I find a real positive solution of an symbolic eqution?
http://www.mapleprimes.com/questions/214359-How-Can-I-Find-A-Real-Positive-Solution?ref=Feed:MaplePrimes:Tagged With equation
<p>Hi there,</p>
<p> Recently, I encountered a problem. I have a function( omega as its variable) (18)</p>
<p> gamma*sqrt(4)*sqrt(omega^2*C2^2*R4^2/(C2^4*R4^4*beta^2*gamma^2*omega^4+C2^2*(1+gamma^2*(beta+1)^2-2*gamma)*R4^2*omega^2+1))</p>
<p>I tried to find a point where its first derivative equals 0. In this case, Maple returned four solutions. In my</p>
<p>question, <strong>both beta, gamma, R4 and C2 >0</strong>， I want it to return a real positive solution, the first term</p>
<p>in (19) (i.e. <strong>1/(sqrt(beta *gamma) *1/R4 C2</strong>).</p>
<p> </p>
<p>I know it is easy to find out the positive real roots in this case. This question seems to make no sense.</p>
<p>However, sometime I came across an expression complicated enough that I cannot tell whether it is real</p>
<p>positive.</p>
<p><strong>Is there a approach to find a real positive solution of an symbolic eqution?</strong></p>
<p>Thanks in advance!</p>
<p> </p>
<p> A University student in BeiHang University, Beijing</p><p>Hi there,</p>
<p> Recently, I encountered a problem. I have a function( omega as its variable) (18)</p>
<p> gamma*sqrt(4)*sqrt(omega^2*C2^2*R4^2/(C2^4*R4^4*beta^2*gamma^2*omega^4+C2^2*(1+gamma^2*(beta+1)^2-2*gamma)*R4^2*omega^2+1))</p>
<p>I tried to find a point where its first derivative equals 0. In this case, Maple returned four solutions. In my</p>
<p>question, <strong>both beta, gamma, R4 and C2 >0</strong>， I want it to return a real positive solution, the first term</p>
<p>in (19) (i.e. <strong>1/(sqrt(beta *gamma) *1/R4 C2</strong>).</p>
<p> </p>
<p>I know it is easy to find out the positive real roots in this case. This question seems to make no sense.</p>
<p>However, sometime I came across an expression complicated enough that I cannot tell whether it is real</p>
<p>positive.</p>
<p><strong>Is there a approach to find a real positive solution of an symbolic eqution?</strong></p>
<p>Thanks in advance!</p>
<p> </p>
<p> A University student in BeiHang University, Beijing</p>214359Sun, 10 Jul 2016 06:19:26 ZJohn_DirichletJohn_DirichletFundamental theorem of calculus
http://www.mapleprimes.com/questions/214133-Fundamental-Theorem-Of-Calculus?ref=Feed:MaplePrimes:Tagged With equation
<p>Hello people in mapleprime,</p>
<p>Though I wrote the title as Fundamental theorem of calculus,</p>
<p>what I am considering is just how to continue the chain of codes in calculation.</p>
<p>restart;</p>
<p>#I defined F__0 as</p>
<p>F__0:=x->Int(f(t),t=a..x);</p>
<p>#Then, the difference between a p<span>rimitive function of f(x), F(x), and F__0 is no more than a constant C, so I write. </span></p>
<p>bb:=F(x)-F__0(x)=C;</p>
<p>#Then, substituting "a" into equation "bb", I obtain the value of F(a)</p>
<p>bb1:=subs(x=a,bb):cc:=simplify(%);</p>
<p>#Then, I substituted the value of C in "bb1" into "bb," obtaining the following "cc1."</p>
<p>cc1:=subs(isolate(cc,C),bb);</p>
<p>#And, then, I isolated the term of Int(f(t),t=a..x) in cc1,</p>
<p>dd:=isolate(cc1,Int(f(t), t = a .. x));</p>
<p>#And, then, I substitute x=b into the outcome of dd, and obtain the final equation.</p>
<p>subs(x=b,dd);</p>
<p> </p>
<p>Surely, with the above code, I could get the fundamental theorem. But, it looks in a little roundabout way.</p>
<p>So, I thought I would ask here about whether there aren't any better ways to do the fundamentally the same thing or</p>
<p>hints to improve the above code.</p>
<p>Please teach me about this.</p>
<p> </p>
<p>Thanks in advance.</p>
<p> </p>
<p>taro</p><p>Hello people in mapleprime,</p>
<p>Though I wrote the title as Fundamental theorem of calculus,</p>
<p>what I am considering is just how to continue the chain of codes in calculation.</p>
<p>restart;</p>
<p>#I defined F__0 as</p>
<p>F__0:=x->Int(f(t),t=a..x);</p>
<p>#Then, the difference between a p<span>rimitive function of f(x), F(x), and F__0 is no more than a constant C, so I write. </span></p>
<p>bb:=F(x)-F__0(x)=C;</p>
<p>#Then, substituting "a" into equation "bb", I obtain the value of F(a)</p>
<p>bb1:=subs(x=a,bb):cc:=simplify(%);</p>
<p>#Then, I substituted the value of C in "bb1" into "bb," obtaining the following "cc1."</p>
<p>cc1:=subs(isolate(cc,C),bb);</p>
<p>#And, then, I isolated the term of Int(f(t),t=a..x) in cc1,</p>
<p>dd:=isolate(cc1,Int(f(t), t = a .. x));</p>
<p>#And, then, I substitute x=b into the outcome of dd, and obtain the final equation.</p>
<p>subs(x=b,dd);</p>
<p> </p>
<p>Surely, with the above code, I could get the fundamental theorem. But, it looks in a little roundabout way.</p>
<p>So, I thought I would ask here about whether there aren't any better ways to do the fundamentally the same thing or</p>
<p>hints to improve the above code.</p>
<p>Please teach me about this.</p>
<p> </p>
<p>Thanks in advance.</p>
<p> </p>
<p>taro</p>214133Sun, 03 Jul 2016 12:51:30 Ztarotaro