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Will someone please explain step by step how to do this question? Thank you!

Will someone please explain step by step how to do this question? Thank you!-example-1
User Mrtnmgs
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1 Answer

3 votes

Answer:

(1000, 179°)

Explanation:

In rectangular coordinates, where east is the +x direction and north is the +y direction, the woman's final position is (1000 yards west, 20 yards north) or (-1000, 20).

This is translated to polar coordinates (r, θ) using ...

r = √(x² +y²)

θ = arctan(y/x) . . . . with attention to quadrant

The magnitude of the distance (r) is ...

r = √((-1000)² +20²) = √1000400 ≈ 1000.2 ≈ 1000

θ = arctan(20/-1000) in quadrant 2, so is 180° -1.15° = 178.85° ≈ 179°

In polar coordinates, the final position is (1000, 179°).

User Austin
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