Midterm 2 PExam

# Midterm 2 PExam - ° = 1 2 ± ° = √± 5 A tank contains...

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Math 1272 – 30 “P RACTICE M IDTERM E XAM 2 6 March 2011 1.) Find the length of the curve. Cartesian a.) ° = 2 3 ( ± 2 1) ² ³ , 1 ± ≤ 3 b.) ± = 1 3 ° ( ° − 3), 1 ° ≤ 9 Parametric c.) ± = ´ 1 + ´ , ° = ln(1 + µ ) , 0 µ ≤ 2 Polar d.) = · 2 , 0 ≤ · ≤ 2 ¸

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2.) Find the area of the surface obtained by rotating the curve about the x -axis Cartesian a.) ° = sin ±² , 0 ² ≤ 1 b.) ² = 1 3 ( ° 2 + 2) ³ ´ , 1 ° ≤ 2 Parametric c.) ² = µ 3 , ° = µ 2 , 0 µ ≤ 1 about the y -axis Cartesian a.) ° = sin ±² , 0 ² ≤ 1 b.) ² = 1 3 ( ° 2 + 2) ³ ´ , 1 ° ≤ 2 Parametric c.) ² = µ 3 , ° = µ 2 , 0 µ ≤ 1
3.) A dam that is shaped like an isosceles triangle is 18 m wide at the top with a total height of 15 m. If the water is present from the base of the dam (the tip of the triangle) up to a height of 12 m, find the total hydrostatic force against the side of the dam. SET UP ONLY 4.) Find the centroid (center of mass) of the region bounded by the given curves.

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Unformatted text preview: ° = 1 2 ± , ° = √± 5.) A tank contains 50 kg of salt dissolved in 4000 L of water. Brine that contains 0.05 kg salt per liter of water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after 2 hours ? 6.) Find the area Parametric enclosed by the x-axis and the curve: ° = 1 + ± ² , ³ = ´ − ´ 2 enclosed by the y-axis and the curve: ° = ´ 2 − 2 ´ , ³ = √´ Polar of the region that lies inside the first curve and outside the second curve: µ = 3 cos ¶ , µ = 1 + cos ¶ 7.) Eliminate the parameter to find a Cartesian equation of the curve. ° = 3 ´ − 5 , ³ = 2 ´ + 1 8.) Identify the curve by finding a Cartesian equation for the curve. µ = csc ¶...
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Midterm 2 PExam - ° = 1 2 ± ° = √± 5 A tank contains...

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