quiz3solutions - MAC1147: Quiz #3 09/15/2009 In the...

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Unformatted text preview: MAC1147: Quiz #3 09/15/2009 In the top-right corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. √ 1. Find the domain of x in the expression 7 + 3x. The expression under the square root must be non-negative. So we set 7 7 7 + 3x ≥ 0 and solve: 7 + 3x ≥ 0 ⇒ 3x ≥ −7 ⇒ x ≥ − , or − , ∞). 3 3 2. Find the center and radius of the circle described by the equation 2x2 + 2y 2 + 8y − 10 = 0. (Hint: Complete the square) First, divide through by 2 to simplify the equation, then complete the square on the remaining y terms: x2 + y 2 + 4 y + 4 = 5 + 4 x2 + (y + 2)2 = 9 Hence, the center is (0, −2) and the radius is 3. 3. Find the equation of the line passing through the point (−1, 0) perpendicular to the line y − x = 3. Put your answer in slope-intercept form. Since y − x = 3 can be written as y = x +3, we see that the line has slope 1 1. Therefore the new line will have slope m = − = −1. So we can set 1 y = −x + b and use the point to solve for b: 0 = −(−1) + b ⇒ b = −1, so the desired equation is y = −x − 1. 1 ...
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This note was uploaded on 12/27/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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