Question 5.

Use MATLAB to solve for and plot the response of the following models for 0≤t ≤1.5, where the input is f (t) =5t and the initial conditions are zero

a. 3¨ x +21˙ x +30x = f (t) b. 5¨

A (Turn in the MATLAB script and answers from MATLAB, .m file, screen shots if needed)

B (Turn in the MATLAB plot with t being time in SI units)

C Comment on the response the analytical solution compared with the MATLAB and the plots. (Do the calculations and MATLAB agree ? Why and Why not.? Do the plots make sense?)

Question 1. Find the general solution of the following ODEs

a) y′′ − 2y′ − 3y = e−x + 2e3x
b) y′′ + y′ + y = x2 + 4 cos x.

class : Analysis Real

Ques : give 2 example periodic function and show the periodic function is uniform contiunity

Calculate the relative (sub-space) topology with respect to the usual (metric) topology in R (the set of real numbers), for the following sub-sets of R:

X = Z, where Z represents the set of integers

Y = {0} U {1 / n | n is an integer such that n> 0}

Calculate (establish who are) the closed (relative) sets for the X and Y sub-spaces defined above.

Is {0} open relative to X?

Is {0} open relative to Y?

A child swinging on a swingset with chains of length l wants to swing and jump off the swing to get as far as possible. At what angle θ_jump should the child let go of the swing to maximize the landing distance? What is the distance jumped as a function of θ_jump?

Results should be functions of θ_jump and variables/parameters which should be introduced as required.

Model swinging using simple pendulum and jumping using projectile motion. Note, the child is not being pushed.

At 1:43pm, a can of soda is placed in a fridge where the temperature is 34◦F.
At 1:46pm, the temperature of the can had dropped 15◦F. At 1:49pm, the temperature
of the can had dropped another 6◦F. What was the temperature of the can when it was
put in the fridge?

For a tetrahedron

-describe the type of groups of a rectangle

-describe the orders of the groups

-describe the structure of the groups

-describe the elements of the groups (make sure to name all the elements and describe them as a group of permutations on the vertices)

- describe each group as subgroups of permutation groups

-describe all possible orders, types and generators for each subgroup of the group

-are any of these groups cyclic and or abelian?

-are any of these subgroups cyclic and or abelian?

-are there subgroups of every possible order?

-which subgroups are isomorphic and how do you know?

Suppose we have a rod of material of conductivity K = 1
and situated on the x-axis, for 0 ≤ x ≤ 1. Suppose further that the rod is
laterally insulated, but has a known internal heat source f(x). The left and
right ends of the rod are held at 0 ◦C (degrees Celsius). With n = 5
Solve the linear system in Jupyter using Gauss-Jordan Elimination. See the notes on
the first problem of this set for hints on how to use and report the results from Gauss-Jordan Elimination.
This equation can be
understood as balancing the flow of heat from a node to its neighbors:
−yi−1 + 2yi − yi+1 = h2/k f(xi)

(a) Let U={(z1, z2, z3, z4, z5)∈C: 6z1=z2, z3+ 2z4+ 3z5= 0}. Check if U is a subspace. If U is a subspace, then find a basis which span U.

Lesson 8

• Explain why the word "average" should not be used to describe measures of center.
• Explain the advantages and disadvantages of the mean.
• Explain the procedure for finding the standard deviation.
• Explain why the range is not usually the best measure of variation.

Solve the following linear programming problem. You must use the dual. First write down the dual maximization LP problem, solve that, then state the solution to the original minimization problem.

(a) Minimize w = 4y₁ + 5y₂ + 7y₃

Subject to: y₁ + y₂ + y₃ ≥ 18

2y₁ + y₂ + 2y₃ ≥ 20

y₁ + 2y₂ + 3y₃ ≥ 25

y₁, y₂, y₃ ≥ 0

(b) Making use of shadow costs, if the 2^nd original constraint changed to

2y₁ + y₂ + 2y₃ ≥ 24, now what will the minimum of w be? Explain clearly.

(c) Making use of shadow costs, if the 1^st original constraint changed to

y₁ + y₂ + y₃ ≥ 21, now what will the minimum of w be? Explain clearly.

How do I graph this step function?

f(t) = -3(2t-3)H(t-2) + (2t-1)H(t-1)

Please show step by step.

How is it the same graph as

f(t) = H(t-1)-3H(t-2)+H(t-1)*2(t-1)-H(t-2)*6(t-2)?

Please show why as well.

Explain effectiveness of Cost Model Data Set in your examples.

Design a randomized comparative experiments to test whether fluoxetine is effective at reducing depression. the participants are 100 people suffering from depression and the response variable is the change on a standard questionnaire measuring level of depression.
Describe how randomization will be used in the design
Describe how the placebo will be used
Describe how to make the experiment double blind