Final answer:
A linear inequality constraint defines a convex feasible region (True). The position vs. time graph of an object speeding up is a curve if acceleration is constant, not a straight line (False). Displacement vs. time squared is a straight line for constant acceleration (True). Vectors can form right angle triangles and use Pythagorean theorem (True). Market revolution brought socio-economic changes (True). Wave amplitudes affect each other when aligned (True).
Step-by-step explanation:
A linear inequality constraint indeed always defines a convex feasible region, making the statement True. In the context of linear programming and mathematical optimization, this means that any region defined by linear inequalities will be convex, which implies that if you take any two points within the region and connect them with a straight line, the line segment will remain entirely within the region.
The position vs. time graph of an object that is speeding up is not necessarily a straight line. If the object is speeding up at a constant rate (constant acceleration), the graph will be curved, specifically a parabola, making the statement False.
For an object moving with constant acceleration, the displacement vs. time graph is indeed a curved line, and the displacement vs. time squared graph is a straight line. This is because the relationship between displacement and time squared is linear when acceleration is constant, thus making the statement True.
Vectors can indeed form the shape of a right angle triangle with their x and y components, making this statement True. Consequently, the Pythagorean theorem can be used to calculate the length of the resultant vector when two vectors are at right angles to each other, also making this statement True.
Regarding the market revolution in the United States, it is True that it brought many social and economic changes. The market revolution was a time of increased production, improved transportation, innovations in technology, and the growth of markets.
The interaction of waves can be complex, and it is indeed True that the amplitude of one wave is affected by the amplitude of another wave when they are precisely aligned—a concept known as constructive and destructive interference in wave physics.