FREE Bachelor of Mathematics: Applied Mathematics Problem Solving Questions and Answers
What is the significance of the critical points of a function?
Critical points of a function are points in its domain where the derivative of the function is either zero or undefined. These points play a significant role in understanding the behavior of a function and finding its local extrema (maximum and minimum values). Critical points can indicate where the function changes from increasing to decreasing or vice versa, which are essential in identifying potential peaks and valleys in the function's graph.
What is the mathematical concept used to plot fractals over real and complex domains?
The correct answer is "Dynamical systems." This mathematical concept is employed for the plotting of fractals across both real and complex domains. It involves iterative processes that generate intricate and self-similar patterns, allowing for the visualization of fractal structures in various mathematical contexts. Therefore, the provided answer accurately identifies the mathematical principle responsible for creating fractal representations in such domains.
What is the function used to find global and local extrema and stationary points while imposing a constraint?
The correct answer is A. The function f(x) = x e^x (-x + 1) is utilized to determine both global and local extrema, as well as stationary points, within the context of applying a constraint. This function's characteristics make it suitable for analyzing optimization problems involving constraints, such as finding maximum or minimum values of a function while adhering to certain limitations or conditions.
Which object's volume and packing density are considered when estimating the number of objects required to fill a container?
The correct answer is "Baseball." When estimating the number of objects needed to fill a container, the volume and packing density of a baseball are taken into consideration. These factors play a crucial role in determining how many baseballs are required to effectively occupy the container's space. Thus, the answer accurately identifies the object that contributes to the estimation process in this context.
What is the iteration rule used for plotting the Mandelbrot set?
The correct answer is "z_(n + 1) = z_n^2 + c | z_0 = 0." This iteration rule is employed for plotting the Mandelbrot set. It defines how each term of the sequence evolves by squaring the previous term and adding a constant value 'c,' with the initial condition that the first term 'z_0' is set to 0. This process is iteratively repeated to generate the complex patterns and structures that form the Mandelbrot set. Therefore, the provided answer accurately identifies the mathematical rule used for plotting this set.
What is the primary focus of applied mathematics?
Applied mathematics involves using mathematical techniques to address real-world problems in various fields.
What is the estimated number of baseballs required to fill the interior volume of a Boeing 747?
The correct answer is 4.8 million baseballs. This estimate is based on utilizing the volume of a baseball and its associated packing density to approximate the number of baseballs needed to completely fill the interior volume of a Boeing 747. Therefore, the correct answer corresponds to the accurate estimation of the quantity of baseballs required for this purpose.