Prove the following Theorems:

1. A finite union of compact sets is compact.

2. Any intersection of compact set is compact.

3. A closed subset of a compact set is compact.

4. Every finite set in IRⁿ is compact.

Given 2y' + 1.5y = 5x, y(0) = 3.3,

What is the value of y(3) using Ralston's method and a step size of h=1.5

Keep 4 decimal places

Solve the LP problem using graphical method. Determine the optimal values of the decision variables and compute the objective function.

Maximize Z = 2A + 10B

Subject to

10A + 4B ≥ 40

   A + 6B ≥ 24

               A + 2B ≤ 14

   A, B  ≥ 0

with soln pls thank you!

what are 5 college mathematics jeopardy questions
what are 5 college anatomy jeopardy questions

D22: When given any data set:

A.) How do we determine the type of model to use? (Linear, quadratic, exponential, logarithmic)?

B.) When fitting an exponential model to data, what is important to know about the input values?

C.) Provide an example to illustrate this idea.

A 128-lb weight is attached to a spring having a spring constant of 64 lb/ft. The weight is started in motion with no initial velocity by displacing it 6 in below the equilibrium position and by simultaneously applying an external force F(t) = 8sin(4t). a. Assuming no air resistance, find the equation of motion. b. What is the long term behavior of the motion? Please use differential equations to solve this

A 10- kg mass is attached to a spring, stretching it 0.7 m from its natural length. The mass is started in motion from the equilibrium position with an initial velocity of 1 m/s in the downward direction. a. Find the equation of motion assuming no air resistance. b. When is the first time the mass goes through the equilibrium position after it was set in motion. c. Find the equation of motion assuming air resistance equal to -90x’(t) Newtons. d. What is the long term behavior of the motion described in part (c)? Use differential equations to solve this.

1252) y=(C1)exp(Ax)+(C2)exp(Bx)+F+Gx is the general solution of
the second order linear differential equation:
   (y'') + ( 6y') + (-27y) = ( 2) + ( -3)x. Find A,B,F,G, where
A>B. This exercise may show "+ (-#)" which should be enterered into
the calculator as "-#", and not "+-#". ans:4

3. Let S3 act on the set A={(i,j) : 1≤i,j≤3} by σ((i, j)) = (σ(i), σ(j)).

(a) Describe the orbits of this action.

(b) Show this is a faithful action, i.e. that the permutation represen- tation φ:S3 →SA =S9

(c) For each σ ∈ S3, find the cycle decomposition of φ(σ) in S9.

(a) Prove that Sn is generated by the elements in the set {(i i+1) : 1≤i≤n}.

[Hint: Consider conjugates, for example (2 3) (1 2) (2 3)−1.]

(b) ProvethatSn isgeneratedbythetwoelements(12)and(123...n) for n ≥ 3.

(c) Prove that H = 〈(1 3), (1 2 3 4)〉 is a proper subgroup of S4.

f(x) and g(x) are both functions with Domains and Codomains all positive Reals.

f(x) = 2x² and g(x) = 4x - 1.   If f(g(x) = 8, what is x?

____________________________

If f(x) = 7x + 3 and g(x) = 4 - x³, then what is g(f(-2))?

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Let R be the relation from A to B, where A = {1,2,3} and B = { 5,6,7,8}

R = {(1,6), (2, 8), (3, 7), (2,6)}

Remove one ordered pair so that R will be a function from A to B.

2. Use the Laplace transform to solve the initial value problem.
?"+4?=?(?), ?(0)=1, ?′(0)=−1

  = { 1, ? < 1
where ?(?) =   {0, ? > 1.

1. Use the Laplace transform to solve the initial value problem.
?"+4?′+3?=1−?(?−2)−?(?−4)+?(?−6), ?(0)=0, ?′(0)=0

2. Use the Laplace transform to solve the initial value problem.
?"+4?=?(?), ?(0)=1, ?′(0)=−1

    = { 1, ? < 1
where ?(?) =   {0, ? > 1.