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Solve Question - 2 Non zero values

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112716] Solve Question - 2 Non zero values
  • From: "Lea Rebanks" <lrebanks at netvigator.com>
  • Date: Tue, 28 Sep 2010 06:03:58 -0400 (EDT)

Dear All,

 

Enclosed are the workings to Solve for BOTH values of V1 and V2.

I have already shown below the Solve for just one value either V1 or V2 and
there is no problem.

The correct values required for V1 and V2 are shown below when I worked them
out individually.

However, when I setup a Solve function to evaluate BOTH V1 and V2 in the
same Solve function then I run into problems.

 

Question 1:-In the instance shown below the result shows V1 and V2 to equal'
zero'.

Therefore to avoid this could someone show me how to set Solve, (or Reduce,
or whatever) up to provide a result greater than zero.(I am sure this is
easy, but I don' t know how to do it.)

 

Secondly, I suspect there is a deeper or more involved mathematical method
to extract these 2 required values. Any ideas anyone?

Many thanks for everyones' help & attention.

Best regards,

Lea...

 

Clear[M]

M = N[45 - ArcTan[Sqrt[(4 - Pi)/Pi]]/

         Degree]

 

17.402887364309393

 

Clear[radiusD]

radiusD[x_] := Tan[M*Degree]*x; 

Null

Clear[V1]

Solve[

   (((15*360)*Sqrt[

                   radiusD[-(((15*Sqrt[2])*V1)/

                              (Tan[135*Degree] - Tan[

                                 M*Degree]))]^2 + 

                     (((15*Sqrt[2])*V1)/

                          (Tan[135*Degree] - 

                             Tan[M*Degree]))^2])/(360*15))^

           2*Pi - 

       (((45*360)*Sqrt[

                   radiusD[-(((22.5*Sqrt[2])*

                                2.8284271247461903)/

                              (Tan[135*Degree] - Tan[

                                 M*Degree]))]^2 + 

                     (((22.5*Sqrt[2])*

                             2.8284271247461903)/

                          (Tan[135*Degree] - 

                             Tan[M*Degree]))^2])/(360*45))^

           2*Pi == 0, V1]

{{V1 -> -4.242640687119285}, 

   {V1 -> 4.242640687119285}}

Null

 

Clear[V2]

Solve[

   (((13*360)*Sqrt[

                   radiusD[-(((13*Sqrt[2])*

                                4.242640687119286)/

                              (Tan[135*Degree] - Tan[

                                 M*Degree]))]^2 + 

                     (((13*Sqrt[2])*

                             4.242640687119286)/

                          (Tan[135*Degree] - 

                             Tan[M*Degree]))^2])/(360*13))^

           2*Pi - 

       (((39*360)*Sqrt[

                   radiusD[-(((19.5*Sqrt[2])*V2)/

                              (Tan[135*Degree] - Tan[

                                 M*Degree]))]^2 + 

                     (((19.5*Sqrt[2])*V2)/

                          (Tan[135*Degree] - 

                             Tan[M*Degree]))^2])/(360*39))^

           2*Pi == 0, V2]

{{V2 -> -2.8284271247461903}, 

   {V2 -> 2.8284271247461903}}

 

Null

Null

 

Clear[V1]

Clear[V2]

 

Solve[

   {

     (((15*360)*Sqrt[radiusD[-(((15*Sqrt[2])*

                                 V1)/(Tan[135*Degree] - 

                                 Tan[M*Degree]))]^2 + 

                       (((15*Sqrt[2])*V1)/

                            (Tan[135*Degree] - Tan[M*

                                 Degree]))^2])/(360*15))^2*

           Pi - 

         (((45*360)*Sqrt[

                     radiusD[-(((22.5*Sqrt[2])*V2)/(

                                Tan[135*Degree] - Tan[

                                  M*Degree]))]^2 + 

                       (((22.5*Sqrt[2])*V2)/

                            (Tan[135*Degree] - Tan[M*

                                 Degree]))^2])/(360*45))^2*

           Pi == 0, 

     (((13*360)*Sqrt[radiusD[-(((13*Sqrt[2])*

                                 V1)/(Tan[135*Degree] - 

                                 Tan[M*Degree]))]^2 + 

                       (((13*Sqrt[2])*V1)/

                            (Tan[135*Degree] - Tan[M*

                                 Degree]))^2])/(360*13))^2*

           Pi - 

         (((39*360)*Sqrt[

                     radiusD[-(((19.5*Sqrt[2])*V2)/(

                                Tan[135*Degree] - Tan[

                                  M*Degree]))]^2 + 

                       (((19.5*Sqrt[2])*V2)/

                            (Tan[135*Degree] - Tan[M*

                                 Degree]))^2])/(360*39))^2*

           Pi == 0}, {V1, V2}]

{{V1 -> 0., V2 -> 0.}, {V1 -> 0., V2 -> 0.}, 

   {V1 -> 0., V2 -> 0.}, {V1 -> 0., V2 -> 0.}}


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