Homework Number 4

Math 17 - HOMEWORK # 4 Directions: Answer in a yellow pad paper and use black ballpen. Write your name and student number on the top-left part of your paper. Show all solutions as necessary and BOX your final answers. Deadline: July 24, 2009 I. Find the solution set of the following ( 5 points each ) x K1 x C2 C R0 2 2 x K18 9 x K3 x2 5 2 5 2.) x K K2 x K =8 x x 3x 3.) !8 x C1 1.)

II. Simplify the expression x2 K8 x C16 expression equivalent to 2 x ? ( 5 points )

1/2

C x2 C8 x C16

1/2

. For what values of x is this

III. Find the value of k such that the lines whose equations are 3 kx C8 y = 5 and 6 y K4 kx =K1 are perpendicular. ( 2 points ) IV. --- ( Do page 168 no.34 of Leithold ) --- ( 5 points ) V. Let r and s be the roots of a quadratic equation in x such that r ,s = 5 and r2 Cs2 = 6. Find all such quadratic equations in x which satisfies these conditions. ( 5 points ) VI. Find the equation of a circle whose center is the midpoint of the line segment joining K1, 6 and 7,K16 and which passes through the point 2, 7 . ( 5 points ) VII. --- ( Do page 95 no.20 of Leithold ) --- ( 3 points ) VIII. BONUS --- Research and write something about the golden ratio Φ (phi). What is its value in radical form? How was it derived from the quadratic equation? Also, give some manifestations of the golden ratio in nature, architecture, art, the human body, etc. ( 10 points ) TOTAL: 50 points