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Unformatted text preview: MAC1147: Quiz #3
09/15/2009
In the topright 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 nonnegative. 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 slopeintercept
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.
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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.
 Summer '08
 GERMAN
 Calculus

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