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Optimization of the least used wire


Optimization of the area of a cross inscribed in a circleMax and min of a wire cut into a square and triangleHow to find minimum distance path between 2 points on a surfaceCutting the wire - optimalizationOptimization of a piece of wire used to construct a square and a rectangle, minimize area“Consistent multiplication” puzzleWhat is the best rest position for two elevators in a 10-story building?How to prove the maximum number of chords those can not across more than one other chord from points around the circle?Equivalence and convexity in optimization problems with restrictionsCalculus Optimization Problem: Wire Triangle and Circle













1












$begingroup$


question:There are two trees that are spaced 30 meters apart. The height of one of them is 12 meters and the other is 28 meters. The two trees should be kept by two wires so that both wires are connected to a point on the ground with a nail and the other head they reach the end of both trees. Where to knock down the nail to get the least wire.



my try:



assume that, $$ Z=T_1+T_2 $$ $$28^2+ x^2=T_1^2$$ $$12^2+(30-x)^2=T_2^2$$



by this way: $$Z=sqrt28^2+x^2 +sqrt12^2+(30-x)^2$$



and for the maximum $Z$ we have:$$fracddxZ$$



The final answer is $x=9$.



if my solution is true does it different if I say:



$28^2+left(30-xright)^2=T_1^2$



$12^2+x^2=T_2^2$
and ...










share|cite|improve this question











$endgroup$
















    1












    $begingroup$


    question:There are two trees that are spaced 30 meters apart. The height of one of them is 12 meters and the other is 28 meters. The two trees should be kept by two wires so that both wires are connected to a point on the ground with a nail and the other head they reach the end of both trees. Where to knock down the nail to get the least wire.



    my try:



    assume that, $$ Z=T_1+T_2 $$ $$28^2+ x^2=T_1^2$$ $$12^2+(30-x)^2=T_2^2$$



    by this way: $$Z=sqrt28^2+x^2 +sqrt12^2+(30-x)^2$$



    and for the maximum $Z$ we have:$$fracddxZ$$



    The final answer is $x=9$.



    if my solution is true does it different if I say:



    $28^2+left(30-xright)^2=T_1^2$



    $12^2+x^2=T_2^2$
    and ...










    share|cite|improve this question











    $endgroup$














      1












      1








      1





      $begingroup$


      question:There are two trees that are spaced 30 meters apart. The height of one of them is 12 meters and the other is 28 meters. The two trees should be kept by two wires so that both wires are connected to a point on the ground with a nail and the other head they reach the end of both trees. Where to knock down the nail to get the least wire.



      my try:



      assume that, $$ Z=T_1+T_2 $$ $$28^2+ x^2=T_1^2$$ $$12^2+(30-x)^2=T_2^2$$



      by this way: $$Z=sqrt28^2+x^2 +sqrt12^2+(30-x)^2$$



      and for the maximum $Z$ we have:$$fracddxZ$$



      The final answer is $x=9$.



      if my solution is true does it different if I say:



      $28^2+left(30-xright)^2=T_1^2$



      $12^2+x^2=T_2^2$
      and ...










      share|cite|improve this question











      $endgroup$




      question:There are two trees that are spaced 30 meters apart. The height of one of them is 12 meters and the other is 28 meters. The two trees should be kept by two wires so that both wires are connected to a point on the ground with a nail and the other head they reach the end of both trees. Where to knock down the nail to get the least wire.



      my try:



      assume that, $$ Z=T_1+T_2 $$ $$28^2+ x^2=T_1^2$$ $$12^2+(30-x)^2=T_2^2$$



      by this way: $$Z=sqrt28^2+x^2 +sqrt12^2+(30-x)^2$$



      and for the maximum $Z$ we have:$$fracddxZ$$



      The final answer is $x=9$.



      if my solution is true does it different if I say:



      $28^2+left(30-xright)^2=T_1^2$



      $12^2+x^2=T_2^2$
      and ...







      optimization






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Mar 21 at 18:51







      black rose

















      asked Mar 21 at 18:41









      black roseblack rose

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