quiz10solutions - MAC1147: Quiz #10 11/17/2009 In the...

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Unformatted text preview: MAC1147: Quiz #10 11/17/2009 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. √ y = 3x 1. Solve the system of equations: y =6−x √ 3x = 6 − x ⇒ 3x = x2 − 12x + 36 ⇒ x2 − 15x + 36 = 0 ⇒ (x − 12)(x − 3) = 0 ⇒ x = 12 or x = 3. x = 12 gives 6 in the rst equation, but −6 in the second equation. Only x = 3 works. 2. If θ is in the standard position such that the terminal point is on the equation x−3y = 0, with x ≤ 0, nd sin(90◦ − θ). The line has positive slope and passes through the origin, so it passes through quadrants I and III. The condition x ≤ 0 implies that we are in quadrant III. Our reference angle θ therefore has a tangent of 3, so according to the unit circle, θ = 60◦ , hence 1 θ = 180◦ + θ = 240◦ . sin(90◦ − θ) = cos(θ) = cos(240◦ ) = − 2 . 1 ...
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