Problem 5 (10 points, CCOs 2 & 5) A spacecraft engineering team is evaluating a new thermal protection panel for atmospheric entry. The panel contains several conductive layers, and its surface temperature depends on aerodynamic heating and temperature-dependent radiation. The thermal protection panel is modeled using three temperature nodes. Applying an energy balance at each node gives

Equation Sheet – Module 4: Curve fitting and interpolation Linear least squares regression: linear function that best fits n given data points :

Problem 2 (4 points, CCOs 1, 2) A model calculates the pressure in a pipe as a function of the pipe diameter. You are tasked to find the pipe diameter for a given target pipe pressure within a given tolerance of the diameter. Part (A) From the given list of options below, which is the appropriate accuracy measure to solve this problem? true tolerance tolerance in solution absolute error true relative error tolerance in function truncation error round-off error Part (B) From the given list of options below, which method covered in this class should be used to find the diameter?  Secant method Newton’s method Bisection method Gauss-Jordan with partial pivoting cubic spline interpolation linear least squares regression

Problem 3 (10 points, CCO 2) An experiment produces 4 measurements for the pair . The experiment is repeated 4 times resulting in the below 4 different data sets A, B, C, and D. Data Set A2 measurements yielding the same values of 2 3 3 4 4 5 5 7 Data Set Bsame value of in all entries 0 1 2 3 5 5 5 5   Data Set Csame value of  in all entries 2 2 2 2 -1 0 7 5   Data Set D4 unique data pairs with unsorted -2 -1 2 1 -1 5 0 1   For the methods as covered in class, answer the following questions with either Y for Yes, or N for No. Can linear least squares regression be used for data set A? Can linear least squares regression be used for data set B? Can linear least squares regression be used for data set C? For data set A, does polynomial regression for a quadratic polynomial result in a function that passes through all data points? For data set A, can interpolation with Lagrange polynomials be done? For data set B, can interpolation with Lagrange polynomials be done? Does the method covered in class to generate a cubic spline result in a valid interpolation method for data set D?

All of the following are reasons hysterosalpingography are performed, except:Choose one or multiple correct answers.

Choose the structures that are included as components of the alimentary canal. Choose one or multiple correct answers.

A large learning rate can speed up learning but risks overshooting the optimal weights.

One complete pass through the entire training dataset is called:

In the perceptron update rule w ← w + η(t − ŷ)x, η is the [Box] rate and t is the target output.   *All small characters! 

An agent that learns by trial and error, taking actions in an environment to maximize cumulative reward (like learning to play Super Mario), is using: