CALCULUS QUESTIONS |
| 1. Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour? (Show work)
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| 2. The senior class is having a fundraiser to help pay for the senior trip. Selling a box of chocolates yields a profit of $2.45, while selling a box of cookies yields a profit of $2.70. The demand for cookies is at least twice that of chocolates, but the amount of cookies produced must be no more than 550 boxes plus 3 times the number of chocolates produced. Assuming that the senior class can sell every box that they order, how many boxes of each should they order to maximize profit if they cannot order more than 1950 boxes combined? (Show work)
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| 3. A projectile is fired from ground level with an initial velocity of 35 m/s at an angle of 35° with the horizontal. How long will it take for the projectile to reach the ground? (Show work)
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| 4. A discus is thrown from a height of 4 feet with an initial velocity of 65 ft/s at an angle of 44° with the horizontal. How long will it take for the discus to reach the ground? (Show work)
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| 5. A rock is tossed from a height of 2 meters at an initial velocity of 30 m/s at an angle of 20° with the ground. Write parametric equations to represent the path of the rock. (Show work)
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| 6. An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S47°E. Find a vector that represents the resultant velocity of the plane relative to the point of takeoff. Let i point east, j point north, and k point up. (Show work)
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| 7. A 2600-pound truck is stopped at a red light on a hill with an incline of 25°. Ignoring the force of friction, what force is required to keep the truck from rolling down the hill? (Show work)
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| 8. While doing bicep curls, Tamara applies 155 Newtons of force to lift the dumbbell. Her forearm is 0.366 meters long and she begins the bicep curl with her elbow bent at a 15° angle below the horizontal, in the direction of the positive x-axis. Determine the magnitude of the torque about her elbow. (Show work)
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| 9. Jenny is sitting on a sled on the side of a hill inclined at 15°. What force is required to keep the sled from sliding down the hill if the combined weight of Jenny and the sled is 90 pounds? (Show work)
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| 10. Anne is pushing a wheelbarrow filled with mulch to place in her garden. She is pushing the wheelbarrow with a force of 70 N at an angle of 50° with the horizontal. How much work in joules is Anne doing when she pushes the wheelbarrow 25 meters? (Show work)
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| 11. A baseball player running forward at 3 meters per second throws a ball with a velocity of 20 meters per second at an angle of 20o with the horizontal. What is the resultant speed and direction of the throw? (Show work)
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| 12. Write 18(cos169° + isin169°) in rectangular form. Round numerical entries in the answer to two decimal places. (Show work)
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| 13. Find the rectangular coordinates of . (Show work)
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| 14. Find the distance between (7, ) and (5, ) on the polar plane. (Show work)
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| 15. A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. (Show work)
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| 16. Makya was conducting a physics experiment. He rolled a ball down a ramp and calculated the distance covered by the ball at different times. The ball rolled a distance of 1 foot during the first second, 3 feet during the next second, and so on. If the distances the ball rolled down the ramp each second form an arithmetic sequence, determine the distance the ball rolled down during the fifteenth second. (Show work)
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| For each statement, write the null and alternative hypotheses. State which hypothesis represents the claim. |
| 17. Evaluate the limit, if it exists. Show work.
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| 18. Use limits to find the area between the graph of the function and the x axis given by the definite integral.
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| 19. A company’s marginal cost function is where x is the number of units. Find the total cost of producing units 144 to 625. (Show work)
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| 20. A technician can test video player chips at the rate of chips per hour (for ), where t is the number of hours after 9:00 am. How many chips can be tested between 11:00 a.m. to 3:00 p.m.? (Assume for 9:00 a.m.) (Show work)
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