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Question: Take the positive solution and plotting

Question:Take the positive solution and plotting

MOD 10 Maple
solve area plotting
February 09 2015
2

Hi,

I'm pretty new into MAPLE andI'm trying to get into it.

I have these four equations:


eq1:=1.6*10^(-7)*R*sin(t)-4.4*10^(-14)*R^2*cos(t)*sin(t)-1.6*10^(-14)*R^2*cos(t)^2+4.2*10^(-14)*R^2-1.3+2.1*10^(-9)*R*cos(t)=0;

eq2 :=8.3*10^(-8)*R*sin(t)-1.2*10^(-13)*R^2*cos(t)*sin(t)-2.9*10^(-44)*R^2*cos(t)^2+7.1*10^(-14)*R^2-1.3+8.3*10^(-8)*R*cos(t)=0;

eq3 :=8.3*10^(-8)*R*sin(t)-1.2*10^(-13)*R^2*cos(t)*sin(t)-2.2*10^(-44)*R^2*cos(t)^2+7.1*10^(-14)*R^2-1.3+8.3*10^(-8)*R*cos(t)=0;

eq4 :=2.1*10^(-9)*R*sin(t)-4.4*10^(-14)*R^2*cos(t)*sin(t)+1.6*10^(-14)*R^2*cos(t)^2+2.6*10^(-14)*R^2-1.3+1.6*10^(-7)*R*cos(t)=0;
  1. I want to solve each equation for R, each obviously yielding two roots and I'm always assured that one root is above the horizontal axis while the other is below it, and pick only the four non-negative roots without doing it manually i.e. for instance, write something like res:=solve(eq1,R), plotting each one as a function of t and only then taking the positive root. I want the code to do it.

  2. After obtaining the positive roots, say {r1,r2,r3,r4}, I want to plot on the same figure, the following 4 graphs

    plot([r1*cos(t),r1*sin(t),t=0..2*Pi]);

    plot([r2*cos(t),r2*sin(t),t=0..2*Pi]);

    plot([r3*cos(t),r3*sin(t),t=0..2*Pi]);

    plot([r4*cos(t),r4*sin(t),t=0..2*Pi]);

  3. Finally, I need to outline the intersection area with some color and shade it.

I would appreciate your help.

 Thanks.

 
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