Final answer:
The fox is approximately 758.3 yards from its den after traveling 725 yards northeast and 950 yards west.
Step-by-step explanation:
The fox first travels 725 yards northeast, which can be represented as a displacement vector. This vector has a magnitude of 725 yards and is at an angle of 45 degrees with respect to the positive x-axis.
Next, the fox travels 950 yards west, which can also be represented as a displacement vector. This vector has a magnitude of 950 yards and is in the opposite direction of the positive x-axis.
To find the fox's net displacement, we can add the two displacement vectors.
The x-component of the net displacement is the sum of the x-components of the individual displacement vectors, which is 725 yards - 950 yards = -225 yards.
The y-component of the net displacement is the sum of the y-components of the individual displacement vectors, which is 725 yards.
Using the Pythagorean theorem, we can find the magnitude of the net displacement:
magnitude = sqrt((-225)^2 + 725^2) ≈ sqrt(50625 + 525625) ≈ sqrt(576250) ≈ 758.3 yards
Therefore, the fox is approximately 758.3 yards from its den.