NAME Thursday 10/19/17 QUIZ 2 (P7-P8. 1.1 -1.2) SHW TAKE HOME QUIZUE TUESDAY 10/

Question

NAME Thursday 10/19/17 QUIZ 2 (P7-P8. 1.1 -1.2) SHW TAKE HOME QUIZUE TUESDAY 10/24/17-BEGINNING OF CLASS SCRATCH PAPER NOT GRADED 26 1 Solve 2. Find the equation of the circle with endpoints of a diameter (7,-8) and13,10) Center Radius 3. Simplity x+y8x +16y-100-0 4. Rewrite in standard form. Find the center and radius of the circle Find the equation of the line that is perpendicular to the line 2x +7y -21 and contains the point Write your answer in general form. (8-3) 4 5. Test for symmetry. You must show all three tests to receive full credit for this problem. (5) 5ry_y2=4 Show all work on the back of this page ONLY. No scratch paper will be graded.

Explanation / Answer

4 / ( x- 5) - 7 / ( 3x + 4) = 26 / ( 3x^2 - 11x - 20 )

factoring 3x^2 - 11x - 20 = ( x- 5) ( 3x+4 )

lcd = ( x- 5) ( 3x+4 )  

multiplying entire equation by ( x- 5) ( 3x+4 )

4 ( 3x + 4) - 7 ( x- 5) = 26

12x + 16 - 7x + 35 = 26

5x = -25

x = -5

solution is x = -5

2) endpoints of diameter = ( 7,-8 ) and ( -13 , 10)

applying mid point formula to find the center

h = 7 - 13 / 2 = -3

k = -8-10 /2 = 1

hence, center = (-3,1)

radius = diameter / 2

diameter = sqrt ( -13-7)^2 + (10+8)^2

diameter = 26.90

radius = 13.46

hence, equation of circle is

( x + 3)^2 + (y - 1)^2 = 13.46^2

3) 6 / ( 3 - sqrt 7 )

multiplying both top and bottom by conjugate of denominator

6 ( 3 + sqrt 7 ) / ( 3 - sqrt 7 ) ( 3 + sqrt 7 )

( 18 + 6 sqrt 7 ) / ( 9 - 7 )

( 18 + 6 sqrt 7 ) / 2

= ( 9 + 3 sqrt 7 )

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