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 #4
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Find an equation of the line that satisfies the given conditions.Through (1/2, -2/7) perpendicular to the line 5x-10y=1

5x10y=1g(x)=0.5x0.1f(x)=ax2+bx+c1. f(x)=g(x)and2. f(x)g(x)=1

f(x)=ax2+bx+c2=a12+b1+c7=a(2)2+b(2)+c(2)2=a+b+c(1)7=4a2b+c(1)(2)5=3a3bb=a53 and c=1132a

f(x)=g(x)ax2+bx+c=0.5x0.1ax2+(a53)x+1132a=0.5x0.1x1,2=136a12a±(6a13)2(12a)2(11360a)30a

f(x)g(x)=1f(x)=2ax+bg(x)=0.5(2ax+b)0.5=1b=a532ax+b=22ax+(a53)=22ax+a=13

2a[136a12a±(6a13)2(12a)211360a30a]+a=13324a2542.4a56=0a1,2=22.6±636.7627

a must be negative: a=22.6636.7627

a=(22.6636.76)27a=0.0975594039708354

b=(22.6636.76)2753b=1.7642260706375021

c=1132×((22.6636.76)27)c=3.8617854746083375

The eqaution is:

f(x)=ax2+bx+cf(x)=0.0975594039708354x21.7642260706375021x+3.8617854746083375

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11 juin 2014