Final answer:
None of the provided equations represents the correct magnitude of the cyclist's displacement x from the starting point. Each equation only represents individual components of the total displacement vector, which are the sum of the eastward and northward components separately.
Step-by-step explanation:
The cyclist's total displacement from the starting point can be found by analyzing each leg of the journey as a vector and summing them. For the first leg of 5 miles in the direction N 30° E, we find the components of this displacement vector: (in the eastward direction) is 5 cos(30°) and (in the northward direction) is 5 sin(30°). For the second leg of 3 miles in the direction N 70° E, the components are (in the eastward direction) is 3 cos(70°) and (in the northward direction) is 3 sin(70°). Adding the eastward components and northward components separately, we get overall = 5 cos(30°) + 3 cos(70°) and = 5 sin(30°) + 3 sin(70°). To find the cyclist's total distance x from the starting point, we need to calculate the magnitude of the resultant vector, which is not directly provided in any of the given equations. Therefore, none of the options A, B, C, or D is correct for finding the total distance x from the starting point. They represent only the individual components of the displacement vector, not the magnitude of the overall displacement.