Answer:
465.988 mph
Explanation:
The two speed vectors form two sides of a triangle. Their included angle is 45°, so the law of cosines can be used to find the resultant magnitude x.
x^2 = 500^2 +50^2 -2·500·50·cos(45°) ≈ 217,144.66
x ≈ √217,144.66 ≈ 465.988 . . . . miles per hour
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You may find you need to round the answer to the nearest whole number.