LED

2546 days ago by jun

var('a b R n') n=10 eq = [1.3 + R*a == 1.7+R*b, a + (n-1)*b == n*0.05] sol=solve(eq, [a,b]) view(sol[0]) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[a = \frac{5 \, R + 36}{100 \, R}, b = \frac{5 \, R - 4}{100 \, R}\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[a = \frac{5 \, R + 36}{100 \, R}, b = \frac{5 \, R - 4}{100 \, R}\right]
fa=a.subs_expr(sol[0][0]);view(fa) fb=b.subs_expr(sol[0][1]);view(fb) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{5 \, R + 36}{100 \, R}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{5 \, R - 4}{100 \, R}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{5 \, R + 36}{100 \, R}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{5 \, R - 4}{100 \, R}
reg=[R,0,22] p1=plot(fa,reg,rgbcolor='red') p2=plot(fb,reg) (p1+p2).show(ymin=0, ymax=0.2) 
       
wa=fa^2*R wb=fb^2*R p1=plot(wa,reg , rgbcolor='red') p2=plot(wb,reg) (p1+p2).show(ymin=0, ymax=0.2) 
       
view(fa(R=10)*1000.0) view(wa(R=10)*1000.0) view(wb(R=10)*1000.0) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}86.0000000000000
\newcommand{\Bold}[1]{\mathbf{#1}}73.9600000000000
\newcommand{\Bold}[1]{\mathbf{#1}}21.1600000000000
\newcommand{\Bold}[1]{\mathbf{#1}}86.0000000000000
\newcommand{\Bold}[1]{\mathbf{#1}}73.9600000000000
\newcommand{\Bold}[1]{\mathbf{#1}}21.1600000000000
nreg=[n,2,10] p1=plot3d(fa,reg,nreg,rgbcolor='red') p2=plot3d(fb,reg,nreg) (p1+p2).show(ymin=0, ymax=0.2) 
       
var('v') i1=300*(v-0.75)^3 i2=300*(v-1.15)^3 p1=plot(i1,[v,1,1.9],rgbcolor='red') p2=plot(i2,[v,1,2.3]) (p1+p2).show() 
       
p1=list_plot([(1.55,0),(1.6,0.05),(1.7,0.6),(1.8,5),(1.9,15),(2,30),(2.1,50),(2.2,80),(2.3,120)], plotjoined=True,rgbcolor='red') lx=300*(x-1.55)^3 p2=plot(lx,[x,1.55,2.3]) (p1+p2).show(xmin=1.4,xmax=2.3) 
       
i=var('i') v1=(i/300)^(1/3)+0.75 v2=(i/300)^(1/3)+1.15 p1=plot(v1,[i,1,500],rgbcolor='red') p2=plot(v2,[i,1,500]) (p1+p2).show() 
       
float(1.7-(50/300)^(1/3)) 
       
1.1496787918508955
1.1496787918508955
eq2=[v1(i=a)+a*R/1000==v2(i=b)+b*R/1000, a+(n-1)*b==n*50] sol=solve(eq2, [a,b]) sol 
       
[a + 9*b == 500, 1/1000*R*a + 1/300*300^(2/3)*a^(1/3) + 0.75 ==
1/1000*R*b + 1/300*300^(2/3)*b^(1/3) + 1.15]
[a + 9*b == 500, 1/1000*R*a + 1/300*300^(2/3)*a^(1/3) + 0.75 == 1/1000*R*b + 1/300*300^(2/3)*b^(1/3) + 1.15]
ga=solve(sol[0],b)[0];ga 
       
b == -1/9*a + 500/9
b == -1/9*a + 500/9
val=sol[1].lhs()(a=64,R=22) float(val) 
       
2.7555206328742883
2.7555206328742883
float(sol[1].rhs()(b=48.4444,R=22)) 
       
2.7603305781566094
2.7603305781566094
p1=implicit_plot(sol[1](R=4.7),(a,40,100),(b,40,100),color='red') p2=implicit_plot(sol[1](R=6.8),(a,40,100),(b,40,100),color='orange') p3=implicit_plot(sol[1](R=10),(a,40,100),(b,40,100),color='green') p4=implicit_plot(sol[1](R=22),(a,40,100),(b,40,100),color='magenta') p5=implicit_plot(sol[0],(a,40,100),(b,40,100)) (p1+p2+p3+p4+p5).show() 
       
fb=v2(i=ga.rhs()(a))+ga.rhs()(a)*R/1000;fb 
       
-1/9000*(a - 500)*R + (-1/9*a + 500/9)^(1/3)*(1/300)^(1/3) +
1.15000000000000
-1/9000*(a - 500)*R + (-1/9*a + 500/9)^(1/3)*(1/300)^(1/3) + 1.15000000000000
fa=v1(i=a)+a*R/1000 fc=fa-fb p1=plot3d(0,[a,40,200],[R,1,22],rgbcolor='red') p2=plot3d(fc(),[a,40,200],[R,1,22]) (p1+p2).show() 
       
L=[1,1.2,1.5,1.8,2,2.2,2.4,2.7,3.3,3.9,4.3,4.7,5.1,5.6,6.8,7.5,8.2,9.1,10,11,12,13,15,18,20,22,24] ls = [(r,find_root(fc(R=r),40,200)) for r in L] ls 
       
[(1, 150.38340051335024), (1.20000000000000, 144.18414810147002),
(1.50000000000000, 136.30561053360734), (1.80000000000000,
129.73458182045155), (2, 125.92180300878586), (2.20000000000000,
122.48176558257494), (2.40000000000000, 119.36026179730356),
(2.70000000000000, 115.18134384724675), (3.30000000000000,
108.24367512046084), (3.90000000000000, 102.70391478805516),
(4.30000000000000, 99.58628807880761), (4.70000000000000,
96.83189332807957), (5.10000000000000, 94.37912116472768),
(5.60000000000000, 91.66488049765573), (6.80000000000000,
86.36736092726744), (7.50000000000000, 83.87237719232813),
(8.20000000000000, 81.70605754420205), (9.10000000000000,
79.30573199687353), (10, 77.25033928901229), (11, 75.28618058261806),
(12, 73.59064137557372), (13, 72.11151665785333), (15,
69.65404427898852), (18, 66.85440399758862), (20, 65.39619077153463),
(22, 64.1720081388397), (24, 63.12939842098529)]
[(1, 150.38340051335024), (1.20000000000000, 144.18414810147002), (1.50000000000000, 136.30561053360734), (1.80000000000000, 129.73458182045155), (2, 125.92180300878586), (2.20000000000000, 122.48176558257494), (2.40000000000000, 119.36026179730356), (2.70000000000000, 115.18134384724675), (3.30000000000000, 108.24367512046084), (3.90000000000000, 102.70391478805516), (4.30000000000000, 99.58628807880761), (4.70000000000000, 96.83189332807957), (5.10000000000000, 94.37912116472768), (5.60000000000000, 91.66488049765573), (6.80000000000000, 86.36736092726744), (7.50000000000000, 83.87237719232813), (8.20000000000000, 81.70605754420205), (9.10000000000000, 79.30573199687353), (10, 77.25033928901229), (11, 75.28618058261806), (12, 73.59064137557372), (13, 72.11151665785333), (15, 69.65404427898852), (18, 66.85440399758862), (20, 65.39619077153463), (22, 64.1720081388397), (24, 63.12939842098529)]
list_plot(ls, plotjoined=True) 
       
lw=[(ls[i][0],ls[i][1]^2*ls[i][0]/10^6) for i in (0..len(L)-1)];lw 
       
[(1, 0.02261516714995871), (1.20000000000000, 0.0249468822764960),
(1.50000000000000, 0.0278688291944092), (1.80000000000000,
0.0302959110962294), (2, 0.031712600945966944), (2.20000000000000,
0.0330039223804946), (2.40000000000000, 0.0341924930311700),
(2.70000000000000, 0.0358202033202358), (3.30000000000000,
0.0386650875718268), (3.90000000000000, 0.0411375670398892),
(4.30000000000000, 0.0426449437252556), (4.70000000000000,
0.0440691531578527), (5.10000000000000, 0.0454278344103144),
(5.60000000000000, 0.0470537217732372), (6.80000000000000,
0.0507233830280780), (7.50000000000000, 0.0527593174191912),
(8.20000000000000, 0.0547422146832149), (9.10000000000000,
0.0572335320607954), (10, 0.05967614920267515), (11,
0.06234809885390434), (12, 0.06498698997681965), (13,
0.06760092085104616), (15, 0.07277528826628941), (18,
0.08045120400971029), (20, 0.08553323534853903), (22,
0.09059702582856881), (24, 0.09564770267989199)]
[(1, 0.02261516714995871), (1.20000000000000, 0.0249468822764960), (1.50000000000000, 0.0278688291944092), (1.80000000000000, 0.0302959110962294), (2, 0.031712600945966944), (2.20000000000000, 0.0330039223804946), (2.40000000000000, 0.0341924930311700), (2.70000000000000, 0.0358202033202358), (3.30000000000000, 0.0386650875718268), (3.90000000000000, 0.0411375670398892), (4.30000000000000, 0.0426449437252556), (4.70000000000000, 0.0440691531578527), (5.10000000000000, 0.0454278344103144), (5.60000000000000, 0.0470537217732372), (6.80000000000000, 0.0507233830280780), (7.50000000000000, 0.0527593174191912), (8.20000000000000, 0.0547422146832149), (9.10000000000000, 0.0572335320607954), (10, 0.05967614920267515), (11, 0.06234809885390434), (12, 0.06498698997681965), (13, 0.06760092085104616), (15, 0.07277528826628941), (18, 0.08045120400971029), (20, 0.08553323534853903), (22, 0.09059702582856881), (24, 0.09564770267989199)]
list_plot(lw, plotjoined=True) 
       
vv1=v1(i=a)+R*a/1000 vv2=v2(i=b)+R*b/1000 p1=plot(vv1(R=22),[a,40,100]) p2=plot(vv2(R=22),[b,40,100],color='green') w1=(a*a*10^(-6)*R)(R=22) p3=plot(w1,[a,40,100],color='red') p4=plot(vv1(R=22,a=64),[a, 40,100],color='orange') view(float(w1(a=64))) (p1+p2+p3+p4).show() 
       
\newcommand{\Bold}[1]{\mathbf{#1}}0.090112
\newcommand{\Bold}[1]{\mathbf{#1}}0.090112
implicit_plot.options 
       
{'cmap': ['blue'], 'contours': (0, 0), 'plot_points': 150, 'fill':
False}
{'cmap': ['blue'], 'contours': (0, 0), 'plot_points': 150, 'fill': False}