Final answer:
True, a vector can indeed form the shape of a right angle triangle with its x and y components.
Step-by-step explanation:
The question asks whether it is true or false that a vector can form the shape of a right angle triangle with its x and y components. The answer to this question is true. Any vector in two-dimensional space can be decomposed into x and y components that form the legs of a right-angle triangle with the vector itself as the hypotenuse, following the Pythagorean theorem: c^2 = a^2 + b^2, where c is the length of the vector (hypotenuse), and a and b are the lengths of the x and y components, respectively. This property is a fundamental concept in physics and engineering, relating to the decomposition of vectors in two-dimensional space.
The question asks whether the statement “D is bounded by the curves y - e^(2x), y - 0, x - 0, x - 1; \(\sqrt{x}, y\) - xy” is true or false. To determine if it is true or false, we need to understand what it means for a region to be bounded by certain curves. In this case, the given curves are y - e^(2x), y - 0, x - 0, x - 1; \(\sqrt{x}, y\) - xy.
To check if the region is bounded, we can graph the curves and see if they enclose a finite area. If the curves form a closed shape and do not extend infinitely, then the region is bounded. So, the student can graph the curves and see if they form a closed shape or extend infinitely. Based on this information, they can determine whether the statement is true or false.