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# 2 1 below 8 pts y x c very carefully sketch the graph

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2 = 1 below. (8 pts.) y x (c) Very carefully sketch the graph of the equation ( x-1 ) 2 -y 2 = 1 below. (9 pts.)

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Final Exam/MAC1114 Page 6 of 8 9. (15 pts.) Sketch the given curve in polar coordinates. Do this as follows: (a) Carefully sketch the auxiliary curve, a rectangular graph on the θ ,r coordinate system provided. (b) Then translate this graph to the polar one, the x,y one. Equation: r=1+ 2cos( θ ) (a) r θ (b) Polar y x 10. (5 pts.) Write cos(cos -1 (u ) + sin -1 (v)) as an algebraic expression containing u and v. cos(cos -1 (u ) + sin -1 (v)) = 11. (5 pts.) Find the exact value of cos -1 (cos(-7 π /5)). cos -1 (cos(-7 π /5)) =
Final Exam/MAC1114 Page 7 of 8 12. (10 pts.) To measure the height of the top of a distant object , a surveyor takes two sightings of the top of the object 100 feet apart. The first sighting, which is nearest the object, results in an angle of elevation of 45°. The second sighting, which is most distant from the object, results in an angle of elevation of 30°. If the transit used to make the sightings is 5 feet tall, what is the height of the object. You may assume the

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2 1 below 8 pts y x c Very carefully sketch the graph of...

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