Using the trial function uh (x) = a sin(x) and weighting function wh (x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. - 2 = 0 (U₁xx) u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) -2=0 'U₁xx' u(0) = 1 u(1) = 0

27.1please complete the code

Only part d. please show all work.

HW 2_2 The volume of a partially-filled spherical tank can be computed as: V = πα 3 (3R – d); where d is the depth of the water in the tank (m) and R is the radius of the tank (m). Given that R=3m, to what depth must the tank be filled so that it holds 30 m³? Write a PYTHON code & implement the bisection algorithm to answer the question correct to 3 sig figs. Plot to select your own initial guesses. Display the answer in an informative sentence, using formatted printing.

I need help with this please.

25.18 The following is an initial-value, second-order differential equation: d²x + (5x) dx + (x + 7) sin (wt) = 0 dt² dt where dx (0) (0) = 1.5 and x(0) = 6 dt Note that w= 1. Decompose the equation into two first-order differential equations. After the decomposition, solve the system from t = 0 to 15 and plot the results of x versus time and dx/dt versus time.

Can you answer this?

I wanted to know how to create plots like these in MATLAB. I belive they were called herpolhode plots.

Q6

In your biomechanical testing lab, you perform a series of compression tests to determine the relationship between apparent bone density (p, units of g/cm³) and ultimate stress (ơult, units of MPa). Using the set of experimental measurements below, write an m-file to fit a power relationship of the form O uli = Ap to the data. Use the log transform method to linearize the system and data, followed by linear regression. Plot the data points and the power relationship on a single plot. Be sure to label your axes and provide a legend. Provide a printout of your m-file and a printout of the command window showing your results. Write down the best fit equation and box it. 8.76 5.25 4.26 5.51 3.88 18.45 2.09 13.72 5.42 2.17 Oult (MPa) p (g/cm³) 0.598 | 0.459 0.319 | 0.235 0.141 0.754 0.177 0.553 0.394 0.246