Final answer:
The statements concern the principles of vector mathematics. The Pythagorean theorem can be used for vectors at right angles, vector components can form a right triangle, walking 2 blocks east and 5 north results in the same displacement regardless of order, and vector component magnitudes are related to angles between 0° and 45°. Finally, adding more vectors does not necessarily result in a larger magnitude.
Step-by-step explanation:
The question posed does not correspond to a specific mathematical compound inequality but appears related to physics and vector mathematics. Below are responses to statements made presumably about vector mathematics:
- True: The Pythagorean theorem can be used to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other.
- True: A vector can indeed form the shape of a right triangle with its x and y components, as these components can be seen as the legs of a right triangle.
- False: If a person walks 2 blocks east and 5 blocks north, and another person walks 5 blocks north and then two blocks east, both will have the same displacement since both have traversed the same distance in an east-north direction, just in a different order.
- The x-component of a vector with an angle will be greater than its y-component when the angle is between 0° and 45°.
- It is false to claim that the addition of five vectors always results in a vector with a greater magnitude than if only two of the vectors were added. The resultant vector's magnitude depends on the vectors' magnitudes and directions.