Answer :
Final answer:
The statement regarding the use of the Pythagorean theorem for vectors at right angles is true as they form a right-angle triangle. The position vs time graph for an object speeding up is not a straight line but a curve, making the statement false. Vectors can form the shape of a right-angle triangle with their x and y components which is true, and the Binomial Theorem provides an expansion of expressions raised to a power.
Explanation:
Understanding the True or False Statements and Corrections:
In Math 141 Homework 10, several true or false questions are presented. Let's address each point mentioned in the question:
- Pythagorean Theorem: The statement that we can use the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors at right angles is True. This theorem is applicable here because the vectors form a right-angle triangle, where the vectors are the perpendicular sides, and the resultant is the hypotenuse.
- A position vs time graph of an object that is speeding up shows a curve, not a straight line, thus the statement is False. A correct statement would be: The position vs time graph of an object that is moving with a constant acceleration is a parabola.
- Vectors can indeed form the shape of a right-angle triangle with their x and y components, which is True.
- Regarding waves, the amplitude of the resultant wave in a medium where waves are propagating along the same line will be the sum of the individual amplitudes, if they are coherent. Therefore, in this context, the statement might be deemed True, especially in the context of constructive interference.
The Binomial Theorem is a significant concept in algebra which allows us to expand expressions raised to a power. Its formula is: (a + b)n = an + n an-1b + n(n-1)/2! an-2b2 + ...
