preTEST6+7A

3112 days ago by MATH4R2012

#1a) var('v0,t') r(v0,t)=v0^2*sin(2*t*pi/180)/32.2 r(v0,t) r(100,45) 
       
#1b) h(v0,t)=v0^2*sin(t*pi/180)^2/64.4 h(v0,t) h(100,45) 
       
#2linear) var('a,b') l = [[1,51],[2,55],[3,63],[4,67],[5,77],[6,86],[7,90],[8,90],[9,84],[10,71],[11,59],[12,52]] f(x) = a*x + b q = find_fit(l,f,solution_dict=True) points(l,color='purple') + plot(f(a=q[a],b=q[b]),(x,0,12,),color='red') 
       
#2quadratic) var('a,b,c') l = [[1,51],[2,55],[3,63],[4,67],[5,77],[6,86],[7,90],[8,90],[9,84],[10,71],[11,59],[12,52]] g(x) = a*x^2 + b*x+c q2 = find_fit(l,g,solution_dict=True) points(l,color='purple') + plot(g(a=q2[a],b=q2[b],c=q2[c]),(x,0,12,),color='red') 
       
#2power) var('a,b') l = [[1,51],[2,55],[3,63],[4,67],[5,77],[6,86],[7,90],[8,90],[9,84],[10,71],[11,59],[12,52]] h(x) = a*x^b q3 = find_fit(l,h,solution_dict=True) points(l,color='purple') + plot(h(a=q3[a],b=q3[b]),(x,0,12,),color='red') 
       
#2sinusoid) var('a,b,c') l = [[1,51],[2,55],[3,63],[4,67],[5,77],[6,86],[7,90],[8,90],[9,84],[10,71],[11,59],[12,52]] j(x) = a*sin(b*x*pi/180)+c q4 = find_fit(l,j,solution_dict=True) points(l,color='purple') + plot(j(a=q4[a],b=q4[b],c=q4[c]),(x,0,12,),color='red') 
       
#3 var('t') equ=1-cos(t)^2/(1+sin(t));equ equ=equ.simplify_trig();equ 
       
plot(sin(t),0,2*pi) 
       
plot(1-cos(t)^2/(1+sin(t)),0,2*pi) 
       
#4) plot(2*cos(t)^2+cos(t),0,2*pi) 
       
solve(2*cos(t)^2+cos(t)==0,t)