preTEST10A

3112 days ago by MATH4R2012

#1) var('y') equ=(x-0)^2==4*(25/16)*(y-0);show(equ) equ=solve(equ,y);show(equ) p1=equ[0].rhs();show(p1) plot(p1,-5,5) 
       



#2) (p+ap)/2==m==a var('p') s1=solve((p+94.5)/2==93,p);show(s1) show(s1[0].rhs().n()) 
       

#2) a=p+c var('c') solve(93==91.5+c,c)[0].rhs().n() 
       
#2) b^2+c^2==a^2 var('b') solve(b^2+1.5^2==93^2,b)[1].rhs().n() 
       
#2) equ=solve((x-0)^2/93^2+(y-0)^2/92.988^2==1,y);show(equ) equ1=equ[0].rhs();show(equ1) equ2=equ[1].rhs();show(equ2) p1=plot(equ1,-93,93,color='red') p2=plot(equ2,-93,93,color='green') p1+p2 
       



#3) b^2+c^2=a^2 solve(20^2+c^2==25^2,c) 
       
equ=solve((x-0)^2/25^2+(y-0)^2/20^2==1,y);show(equ) equ1=equ[0].rhs();show(equ1) equ2=equ[1].rhs();show(equ2) p1=plot(equ1,-25,25,color='red') p2=plot(equ2,-25,25,color='green') p1+p2 
       



#4) var('t') x(t)=145*cos(30*pi/180)*t y(t)=-16*t^2+145*sin(30*pi/180)*t+5 parametric_plot((x(t),y(t)),(t,0,4.599),aspect_ratio=1) 
       
show(solve(y(t)==0,t)[0].rhs().n()) show(solve(y(t)==0,t)[1].rhs().n()) 
       

show(y(0)) show(x(4.599).n()) show(-145*sin(30*pi/180)/-32.n()) show(x(-145*sin(30*pi/180)/-32).n()) show(y(-145*sin(30*pi/180)/-32).n()) 
       




#what about polar? if r=3, then x(t)=3*cos(t) and y(t)=3*sin(t) parametric_plot((3*cos(t),3*sin(t)),(t,0,2*pi),aspect_ratio=1) 
       
#what about polar? if r=3*cos(t) parametric_plot((3*cos(t)*cos(t),3*cos(t)*sin(t)),(t,0,2*pi),aspect_ratio=1) 
       
#what about polar? if r=3*cos(3*t) parametric_plot((3*cos(3*t)*cos(t),3*cos(3*t)*sin(t)),(t,0,2*pi),aspect_ratio=1) 
       
#what about polar? if r=3*sin(6*t) parametric_plot((3*sin(6*t)*cos(t),3*sin(6*t)*sin(t)),(t,0,2*pi),aspect_ratio=1) 
       
#what about polar? if r=3+3*sin(t) parametric_plot(((3+3*sin(t))*cos(t),(3+3*sin(t))*sin(t)),(t,0,2*pi),aspect_ratio=1) 
       
#what about polar? if r=3+2*sin(t) parametric_plot(((3+2*sin(t))*cos(t),(3+2*sin(t))*sin(t)),(t,0,2*pi),aspect_ratio=1) 
       
#what about polar? if r=4+3*sin(t) parametric_plot(((3+4*sin(t))*cos(t),(3+4*sin(t))*sin(t)),(t,0,2*pi),aspect_ratio=1)