Pre-Calculus Homework Solutions 73

Pre-Calculus Homework Solutions 73 - 8. x x 3y 3y y 3y 3y 3...

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8. x 1 3 y 5 ¬ 6 3 y 5 ¬ 2 x 1 6 y 5 ¬ 2 } 1 3 } x 1 2 x 1 3 y 5 ¬ 2 14 3 y 5 ¬ 2 x 2 14 y 5 ¬ 2 } 1 3 } x 2 } 1 3 4 } First, write an equation of a line p perpendicular to the given lines. The slope of p is the opposite reciprocal of 2 } 1 3 } , or 3. Use the y -intercept of y 52 } 1 3 } x 1 2, (0, 2), as one of the endpoints of the perpendicular segment. y 2 y 1 5 ¬ m ( x 2 x 1 ) y 2 2 5 ¬ 3( x 2 0) y 2 2 5 ¬ 3 x y 5 ¬ 3 x 1 2 Next, use a system of equations to determine the point of intersection of y } 1 3 } x 2 } 1 3 4 } and p . 2 } 1 3 } x 2 } 1 3 4 } 5 ¬ 3 x 1 2 2 } 1 3 } x 2 3 x 5 ¬ 2 1 } 1 3 4 } 2 } 1 3 0 } x 5 ¬ } 2 3 0 } x 5 ¬ 2 2 y 5 ¬ 3( 2 2) 1 2 y 5 ¬ 2 4 The point of intersection is ( 2 2, 2 4). Then, use the Distance Formula to determine the distance between (0, 2) and ( 2 2, 2 4). d 5 ¬ Ï ( x 2 2 w x 1 ) 2 1 w ( y 2 2 w y 1 ) 2 w 5 ¬ Ï ( 2 2 2 w 0) 2 1 w ( 2 4 2 w 2) 2 w 5 ¬ Ï 40 w 5 ¬ 2 Ï 10 w The distance between the lines is 2 Ï 10 w ,or approximately 6.32 units. 9. 1. Graph y } 3 4 } x 1 } 1 4 } and point P .Place the compass at point P .Make the setting wide enough so that when an arc is drawn, it intersects y } 3 4 } x 1 } 1 4 } in two places. Label these points of intersection A and B . 2. Put the compass at point A and draw an arc below the line. 3. Using the same compass setting, put the compass at point B and draw an arc to intersect the one drawn in step 2. Label the
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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