Final answer:
The statement that squaring any integer results in an even value is false because squaring an odd integer produces an odd result. Vectors can indeed form right angle triangles with their components, and the Pythagorean theorem applies to calculate their magnitude. Kinetic and potential energy vary inversely during the movement of a rock thrown into the air.
Step-by-step explanation:
To address the statement "For any integer x² will always produce an even value." we must consider that integers can be either even or odd. If you square an even integer (e.g., 2, 4, 6), the result will indeed be even (e.g., 4, 16, 36). However, if you square an odd integer (e.g., 1, 3, 5), the result will also be odd (e.g., 1, 9, 25). Therefore, the statement is False.
The concept of even and odd functions relates to a different area of mathematics, namely function symmetry. An even function times an even function results in an even function, and the same applies for two odd functions. But these properties are not directly relevant to squaring integers and determining if the result is even or odd.
Related to vectors, it is True that a vector can form the shape of a right angle triangle with its x and y components, which is an application of the Pythagorean theorem to find the vector's magnitude.
It is also True that every 2-D vector can be expressed as the product of its x and y-components, and that the Pythagorean theorem applies to calculate the length of a resultant vector at right angles. As for the kinetic and potential energy question, the correct response is False; as a rock is thrown into the air, its kinetic energy decreases while its potential energy increases, and when it falls back down, its potential energy decreases while its kinetic energy increases.