Answer:
The bee is 300 meters away from the hive.
Explanation:
To understand, we can visualize the bee's movements on a coordinate plane with the hive as the origin. The bee's first movement is 500 meters due east, which it to the point (500, 0). The bee's second movement is 400 meters due west, which takes it to the point (100, 0). Finally, the bee's third movement is 700 meters due east, which takes it to the point (800, 0).
Now, we can use the Pythagorean theorem to find the distance between the hive and the bee's final position. The distance is the square root of the sum of the squares of the coordinates, or sqrt(800^2 + 0^2) = sqrt(640000) = 800 meters. However, we need to subtract the distance the bee traveled west, which means we need to subtract 400 meters from this total, giving us 800 - 400 = 400 meters.
Therefore, the bee is 300 meters away from the hive (400 meters - 100 meters).
