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Math 153 exam_1_soln

# Math 153 exam_1_soln - in interval notation(a 4 x 1< 2 x...

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Math 153 Name: SOLUTIONS Exam 1 February 12, 2008 Show your work for full credit. 1. The endpoints of a diameter of a circle are ( - 4 , - 1) and (4 , 1). Write the equation of this circle in standard form. Center of circle : - 4 + 4 2 , - 1 + 1 2 = (0 , 0) Radius of circle : (4 - 0) 2 + (1 - 0) 2 = 17 Equation of circle : x 2 + y 2 = 17 2. Solve the equation. If the equation has no solution, explain why. (a) 2 x 2 = 3 x + 20 2 x 2 - 3 x - 20 = 0 (2 x + 5)( x - 4) = 0 x = - 5 2 or x = 4 (b) 6 x - 2 x + 3 = 3( x + 5) x 2 + 3 x 6 x x ( x + 3) - 2 x + 3 x ( x + 3) = 3( x + 5) x 2 + 3 x x ( x + 3) 6( x + 3) - 2 x = 3( x + 5) 6 x + 18 - 2 x = 3 x + 15 4 x + 18 = 3 x + 15 x = - 3 Since x = - 3 does not check, the equation has no solution. (c) ( x + 13) 2 = 25 ( x + 13) = ± 5 x = - 13 ± 5 x = - 18 or - 8 (d) 16 x 2 - 4 x + 3 = 0 x = - ( - 4) ± ( - 4) 2 - 4(16)(3) 2(16) = 4 ± - 176 32 = 4 ± 4 11 i 32 = 1 8 ± 11 8 i

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(e) x 4 + 5 x 2 - 36 = 0 x 2 + 9 x 2 - 4 = 0 x = ± 3 i, ± 2 3. Write the quotient 6 - 7 i 1 - 2 i in standard form. 6 - 7 i 1 - 2 i = 6 - 7 i 1 - 2 i 1 + 2 i 1 + 2 i = 6 + 12 i - 7 i - 14 i 2 1 - 4 i 2 = 20 + 5 i 5 = 4 + i 4. Solve the inequality, graph the solution on the real number line, and write the solution set
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Unformatted text preview: in interval notation. (a) 4( x + 1) < 2 x + 3 4 x + 4 < 2 x + 3 2 x <-1 x <-1 2 (b) | 1-2 x | ≥ 5 1-2 x ≥ 5 or 1-2 x ≤ -5-2 x ≥ 4 or-2 x ≤ -6 x ≤ -2 or x ≥ 3 5. A salesperson’s weekly paycheck is 12% less than her coworkers paycheck. The two pay-checks total \$875. Find the amount of each check. You must do this by deﬁning variables, setting up an equation, and solving. Let x denote the coworker’s (larger) paycheck, then x + ( x-. 12 x ) = 875 1 . 88 x = 875 x = 465 . 43 So, the coworker’s paycheck is \$465.43 and the salesperson’s paycheck is \$409.57....
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Math 153 exam_1_soln - in interval notation(a 4 x 1< 2 x...

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