Cannot solve Lagrange multiplier for 2 dimensional problem in cartesian coordinates











up vote
0
down vote

favorite












My Q is this :
A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
Constraints I thought of are a2 + b2 = 400 and
y = ax/b + b (a=Y intercept, b=X intercept)
are there other constraints to use also ?
Thanks






lagrange-multiplier







share|cite|improve this question







New contributor




dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
























    up vote
    0
    down vote

    favorite












    My Q is this :
    A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
    Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
    Constraints I thought of are a2 + b2 = 400 and
    y = ax/b + b (a=Y intercept, b=X intercept)
    are there other constraints to use also ?
    Thanks






    lagrange-multiplier







    share|cite|improve this question







    New contributor




    dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      My Q is this :
      A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
      Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
      Constraints I thought of are a2 + b2 = 400 and
      y = ax/b + b (a=Y intercept, b=X intercept)
      are there other constraints to use also ?
      Thanks






      lagrange-multiplier







      share|cite|improve this question







      New contributor




      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      My Q is this :
      A rod of fixed length (20m) has its base sliding along the X axis and its top slides up the y axis simultaneously. The rod will hit a 5m by 5m box positioned at the origin of the X-Y axes (i.e. Boxes coords are (5,5), (0,0), (5,0), (0,5) ) What is the max height it can reach up the Y axis ?
      Note: I have solved this using trigonometry (18.8133m) with a quadratic in Tan A and Cot A (A is angle between rod and Y axis) - BUT I cannot seem to hit on the right constraint equations to solve it using Lagrange multipliers. Is this possible ?
      Constraints I thought of are a2 + b2 = 400 and
      y = ax/b + b (a=Y intercept, b=X intercept)
      are there other constraints to use also ?
      Thanks






      lagrange-multiplier




      lagrange-multiplier






      share|cite|improve this question







      New contributor




      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|cite|improve this question







      New contributor




      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|cite|improve this question




      share|cite|improve this question






      New contributor




      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked yesterday









      dra42841

      1




      1




      New contributor




      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      dra42841 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.



























          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });






          dra42841 is a new contributor. Be nice, and check out our Code of Conduct.










           

          draft saved


          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3005026%2fcannot-solve-lagrange-multiplier-for-2-dimensional-problem-in-cartesian-coordina%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown






























          active

          oldest

          votes













          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          dra42841 is a new contributor. Be nice, and check out our Code of Conduct.










           

          draft saved


          draft discarded


















          dra42841 is a new contributor. Be nice, and check out our Code of Conduct.













          dra42841 is a new contributor. Be nice, and check out our Code of Conduct.












          dra42841 is a new contributor. Be nice, and check out our Code of Conduct.















           


          draft saved


          draft discarded














          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3005026%2fcannot-solve-lagrange-multiplier-for-2-dimensional-problem-in-cartesian-coordina%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          android studio warns about leanback feature tag usage required on manifest while using Unity exported app?

          Image
          .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 This is a simple project showing cubes on Unity, exported to android project and imported on Android studio. On maifest file it showed following warning: Expecting <uses-feature android:name="android.software.leanback" android:required="false" /> tag I have no information about it. And also on default emptyview android project does not use/mention this feature. I know it is required by TV's and such but why its not added by default? Why is this? And Should I concern about it? android unity3d
          Read more

          SQL update select statement

          Image
          0 I'm trying to update an entry in my database (postgresql). I'm having a problem with updating the query: INSERT INTO prices (price, product_id) SELECT product_price, commn_id FROM products_temp as prod WHERE NOT EXISTS (SELECT * FROM prices od WHERE prod.commn_id = od.product_id) OR prod.product_price != ( SELECT price FROM prices as p WHERE p.product_id = prod.commn_id order by p.end desc LIMIT 1 ) Query works fine when i delete: OR prod.product_price != ( SELECT price FROM prices as p WHERE p.product_id = prod.commn_id order by p.end desc LIMIT 1 ) So it seems to me that it's looping through this operation. My question is, how can I fix it? sql postgresql
          Read more

          'app-layout' is not a known element: how to share Component with different Modules

          Image
          0 My application was working fine until I decided to go with lazy loading: So, my shared component looks like this: import { Component, Renderer2 } from '@angular/core'; export interface FormModel { captcha?: string; } @Component({ selector: 'app-layout', templateUrl: './app-layout.component.html', styleUrls: ['./app-layout.css'] }) export class FullLayoutComponent { } app-layout.component.ts I am using this component in my Another component say school-home.component.html like this: <app-layout> </app-layout> and it was working fine until I created a Module school-home.module.ts like this: import { NgModule } from '@angular/core'; import { CommonModule } from '@angular/common'; import { SchoolhomeRoutingModule
          Read more