6 calculus II questions

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San Ramon (Out of 30 points.) Calculators okay. Please show all work. t 1. (6 points) The path of a math puppy after t seconds is described by the following set of parametric equations: = 4-t x=4f= tyattt y = -t? + t, where the units of the r- and y- axes are meters. Set up, but do not evaluate, an integral that represents the distance traveled by the puppy between t = 2 and t = 7 seconds. 2. (6 points) Find the point(s) (x, y) on the following parametric curve at which the tangent is horizontal or label them as such.) x=+² +44 3. (6 points) Plot the following polar coordinates (r.) on the same set of axes, and converted (a) (3, 3) (b) (-1, -5 do not evaluate, an integral that represents the area of the shaded re cos 3 (6 points) Plot the following polar coordinates (ro) on the same set of axes, and convert (a) (3. Texas INSTRU 5. ( points) (b) (-1, -*) BE DE DE ANK en ST PR E N 4. (6 points) Set up, but do not evaluate, an integral that represents the area of the shaded region: y T=1+cos og 2 1 х 3 -1 -2 8. (6 points) Find the centrond (2,3) of the triangle with vertice (0,0), (0.4), (2,6). At what time t is the puppy in number 4 traveling at a 45-degree angle Extra Credit (+3 points) 5. (6 points) Find the centroid) of the lange At what time t is the puppy in number 4 traveling at a 45-degree angle to the 2 - at? Extra Credit (+3 points)
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