8.6 Please solve this page! Thanks!

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May 8th, 2015

1. y=x-1

y=x^2-6x+9

x-1=x^2-6x+9

x^2-7x+10=0

D=49-4*10=9

x1=(7+3)/2=5    y1= 5-1=4

x2=(7-3)/2=2     y2=2-1=1

(5,4) and (2,1)


2. x^2+y^2=16

x^2-2y=8

x^2=16-y^2

16-y^2-2y=8

y^2+2y-8=0

D=4+32=36

y1=(-2+6)/2=2    x1,1=sqrt(16-2^2)=sqrt12=2sqrt3    x1,2=-sqrt(16-2^2)=-sqrt12=-2sqrt3

y2=(-2-6)/2=-4   x2=0

(2sqrt3,2), (-2sqrt3,2) and (0,-4)


3. y=2x-1

2x^2+y^2=1

2x^2+(2x-1)^2=1

2x^2+4x^2-4x+1=1

6x^2-4x=0

x(6x-4)=0

x1=0   x2=2/3

y1=2*0-1=-1   y2=2*2/3-1=1/3

(0,-1) and (2/3, 1/3)


4. P=16  S=15

P=2(a+b)       S=a*b

2(a+b)=16    a+b=8

a*b=15     a=15/b

15/b + b=8

15+b^2=8b

b^2-8b+15=0

D=64-60=4

b1=(8+4)/2=6    a1=15/6=2,5

b2=(8-4)/2=2      a2=15/2=7,5

The rectangle may have sides 2.5 and 6, or 7.5 and 2




May 8th, 2015

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