#1)
A=point((0,0))
B=point((4,0))
C=point((3,3))
D=point((1,3))
l1=line([(0,0),(4,0)])
l2=line([(4,0),(3,3)])
l3=line([(3,3),(1,3)])
l4=line([(1,3),(0,0)])
A+B+C+D+l1+l2+l3+l4
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#1A+1B practice)
AC=sqrt(((4-1)-0)^2+(3-0)^2)
BD=sqrt((1-4)^2+(3-0)^2)
show(AC)
show(BD)
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#1C+1D practice)
AD=sqrt((1-0)^2+(3-0)^2)
BC=sqrt(((4-1)-4)^2+(3-0)^2)
show(AD)
show(BC)
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#1A+1B)
var('a,b,h')
AC=sqrt(((b-a)-0)^2+(h-0)^2)
BD=sqrt((a-b)^2+(h-0)^2)
show(AC)
show(BD)
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#1C+1D)
AD=sqrt((a-0)^2+(h-0)^2)
BC=sqrt(((b-a)-b)^2+(h-0)^2)
show(AD)
show(BC)
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#2A)
equ=sqrt(15-2*x)==x;show(equ)
equ=equ^2;show(equ)
equ=equ+2*x-15;show(equ)
show(equ.factor())
show(solve(equ,x))
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#2B)
plot([sqrt(15-2*x),x],-8,8)
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#3A)
v(t)=-175*t+875
#3B)
v(2)
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#3C)
var('t')
show(solve(v(t)==200,t))
show(27/7.n(digits=100))
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plot([-175*x+875,200],0,4)
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#4g linear)
var('a,b')
l = [[0,58],[1,60],[2,59],[3,61],[4,63],[5,66],[6,65],[7,67],[8,70]]
f(x) = a*x + b
q = find_fit(l,f,solution_dict=True)
show(q[a])
show(q[b])
points(l,color='purple') + plot(f(a=q[a],b=q[b]),(x,0,8,),color='red')
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x=range(9);show(x)
y=[58,60,59,61,63,66,65,67,70];show(y)
xy=[x[i]*y[i] for i in range(9)];show(xy)
xSqr=[x[i]^2 for i in range(9)];show(xSqr)
#4a)
sumX=sum(x);show(sumX)
#4b)
sumY=sum(y);show(sumY)
#4c)
sumXY=sum(xy);show(sumXY)
#4d)
sumXsqr=sum(xSqr);show(sumXsqr)
#4e)
m=(9*sumXY-sumX*sumY)/(9*sumXsqr-sumX^2);show(m.n())
#4f)
b=(sumY-m*sumX)/9;show(b.n())
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#4a-4f)
print "x\ty\txy\tx^2"
for i in range(9):
print x[i],"\t",y[i],"\t",xy[i],"\t",xSqr[i]
print "sumX = ", sumX
print "sumY = ", sumY
print "sumXY = ", sumXY
print "sumXsqr = ", sumXsqr
print "m = ", m
print "b = ", b
print "m = ", m.n()
print "b = ", b.n()
x y xy x^2 0 58 0 0 1 60 60 1 2 59 118 4 3 61 183 9 4 63 252 16 5 66 330 25 6 65 390 36 7 67 469 49 8 70 560 64 sumX = 36 sumY = 569 sumXY = 2362 sumXsqr = 204 m = 43/30 b = 2587/45 m = 1.43333333333333 b = 57.4888888888889 x y xy x^2 0 58 0 0 1 60 60 1 2 59 118 4 3 61 183 9 4 63 252 16 5 66 330 25 6 65 390 36 7 67 469 49 8 70 560 64 sumX = 36 sumY = 569 sumXY = 2362 sumXsqr = 204 m = 43/30 b = 2587/45 m = 1.43333333333333 b = 57.4888888888889 |
#correlation coefficient?
#r=(n*sumXY-sumX*sumY)/sqrt(n*sumXX-sumX^2)/sqrt(n*sumYY-sumY^2)
ySqr=[y[i]^2 for i in range(9)];show(ySqr)
sumYsqr=sum(ySqr);show(sumYsqr)
show(((9*sumXY-sumX*sumY)/sqrt(9*sumXsqr-sumX^2)/sqrt(9*sumYsqr-sumY^2)).n())
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#4g quad)
var('a,b,c')
l = [[0,58],[1,60],[2,59],[3,61],[4,63],[5,66],[6,65],[7,67],[8,70]]
f(x) = a*x^2+b*x+c
q = find_fit(l,f,solution_dict=True)
show(q[a])
show(q[b])
show(q[c])
points(l,color='purple') + plot(f(a=q[a],b=q[b],c=q[c]),(x,0,8,),color='red')
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#4h)
var('t')
y(t)=1.433333*t+57.488888;show(y)
y(10)
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