55. Two cars approach an intersection. Car A is 25 mi west of the intersection traveling 40 mph. Car B is 30 mi north of the intersection traveling 50 mph. Place the origin of a rectangular coordinate system at the intersection. a. Write parametric equations that model the path of each car as a function of the time t > 0 (in hr). b. Determine the times required for each car to reach the intersection. Based on these results, will the cars crash? c. Write the distance between the cars as a function of the time t.
55. Two cars approach an intersection. Car A is 25 mi west of the intersection traveling 40 mph. Car B is 30 mi north of the intersection traveling 50 mph. Place the origin of a rectangular coordinate system at the intersection. a. Write parametric equations that model the path of each car as a function of the time t > 0 (in hr). b. Determine the times required for each car to reach the intersection. Based on these results, will the cars crash? c. Write the distance between the cars as a function of the time t.
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![Mixed Exercises
55. Two cars approach an intersection. Car A is 25 mi
55. Two cars approach an intersection. Car A is 25 mi
west of the intersection traveling 40 mph. Car B is
30 mi north of the intersection traveling 50 mph. Place
the origin of a rectangular coordinate system at the
intersection.
a. Write parametric equations that model the path of
each car as a function of the time t > 0 (in hr).
b. Determine the times required for each car to reach the
intersection. Based on these results, will the cars crash?
c. Write the distance between the cars as a function of
the time t.
sbilloo 1ovo
d. Determine the time at which the two cars are at their
closest point. [Hint: The function from part (c) is
minimized when the radicand is minimized.]
e. How close are the cars at their closest point? Round to
the nearest hundredth of a mile.
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Transcribed Image Text:Mixed Exercises
55. Two cars approach an intersection. Car A is 25 mi
55. Two cars approach an intersection. Car A is 25 mi
west of the intersection traveling 40 mph. Car B is
30 mi north of the intersection traveling 50 mph. Place
the origin of a rectangular coordinate system at the
intersection.
a. Write parametric equations that model the path of
each car as a function of the time t > 0 (in hr).
b. Determine the times required for each car to reach the
intersection. Based on these results, will the cars crash?
c. Write the distance between the cars as a function of
the time t.
sbilloo 1ovo
d. Determine the time at which the two cars are at their
closest point. [Hint: The function from part (c) is
minimized when the radicand is minimized.]
e. How close are the cars at their closest point? Round to
the nearest hundredth of a mile.
firod from ground level at an
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