In: Advanced Math
How would I do this problem?
A mass of 1 kg is attached to a spring whose constant is 5 N/m. Initially the mass is released 1 m below the equilibrium position with a downward velocity of 5 m/s, and the subsequent motion takes place in a medium that offers a damping force numerically equal to two times the instantaneous velocity. Find the equation of motion if the mass is driven by an external force equal to f(t) = 12 cos (2t) + 3 sin (2t)
In: Advanced Math
Let T be a connected graph and z ∈ℤ between the closed interval of 1 and the least degree of a vertex in T. Let a z - matching be a A ⊆ E s.t. there aren’t vertices with more than z edges in A. Let a z - cover be a X ⊆ E s.t. all vertices belong to at least z edges in X.
Let:
δ (T) = Max {|A| : A is a z - matching}
μ (T) = Min {|X| : X is a z - cover}
Show that δ (T) + μ (T) = zn
In: Advanced Math
For the following questions, say you were given a line and a plane as below
Line: r(t)= < x(t), y(t), z(t) > = < t-2, t+1, 3t > , Plane: : a(x+2) + b(y-3) - 4z = 2
a) What relationship would have to exist between scalars a and b for the line not to intersect with the plane?
Hint 1) Plug in x, y, z given in the line into the plane equation.
Hint 2) Say you were solving this equation and got the following. What would that indicate?
i) t = 2: ________________________________________________________
ii) 6 = –5: ________________________________________________________
iii) 4 = 4: ________________________________________________________
So what must be true about the coefficient of t? What also can’t be true about the constant term?
b) What relationship would have to exist between scalars a and b for the plane to contain the line?
c)
Assuming the line is not contained in the plane but does
intersect it, give an expression for the time t that the line
intersects the plane. Also give the point of intersection.
(Both answers will have scalars a and b in them)
In: Advanced Math
Prove by induction that:
1) x^n - 1 is divisible by x-1
2)2n < 3^n for all natural numbers n
In: Advanced Math
SOLVE IN MATLAB. SHOW CODE.
You have decided to enter the candy business. You are considering producing two types of candies: Slugger Candy and Easy Out Candy, both of which consist solely of sugar, nuts, and chocolate. At present, you have in stock 100 oz of sugar, 20 oz of nuts, and 30 oz of chocolate. The mixture used to make Easy Out Candy must contain at least 20% nuts. The mixture used to make Slugger Candy must contain at least 10% nuts and 10% chocolate. Each ounce of Easy Out Candy can be sold for 25¢ , and each ounce of Slugger Candy for 20¢. Formulate an LP that will enable you to maximize your revenue from candy sales.
In: Advanced Math
Find the pure and mixed strategy Nash equilibriums for the following game.
Show computation how you got it
Player 2 |
|||
Player 1 |
LEFT |
RIGHT |
|
UP |
11, 12 |
15,10 |
|
DOWN |
12,1 |
6, 0 |
In: Advanced Math
Let X, Y be Banach spaces. Show that T ∈ L(X, Y) is continuous if and only if T is bounded.
In: Advanced Math
1- Let W1, W2 be two subspaces of a vector space V . Show
that
both W1 ∩ W2 and W1 +W2 are subspaces.?and Show that W1 ∪ W2 is a
subspace
only when W1 ⊂ W2 or W2 ⊂ W1.
(recall that W1 + W2 = {x + y | x ∈ W1, y ∈ W2}.)
In: Advanced Math
Problem 5. Recall that Mn,n(R) is the vector space of all n by n real matrices.
(a) Show that W = {A | tr(A) = 0} is a subspace of Mn,n(R).?
(b) Determine the dimension of W and find a basis for it.?
(c) Show that the trace map tr : Mn,n(R) → R is a linear transformation.?
In: Advanced Math
1. What are the requirements for a valid will. Explain each requirement.
2. Conduct some Internet research and find a case that involves a will contest. Briefly state the facts of the case and explain the court's decision. Provide at least a paragraph of your analysis--do you agree with the court's decision--why or why not?
PROVIDE A REFERENCE TO THE CASE THAT IS USED.
In: Advanced Math
4)
You are measuring the length of catheters from your production line. The catheters have a
mean length of 30 cm and a standard deviation of 2 cm.
a. What is the probability that a catheter will be longer than 31.7 cm?
b.What is the probability that a catheter will be between 29.3 and 33.5 cm long?
c.What is the probability that a catheter will be less than 25.5 cm long?
5) In a survey of senior citizens, you find that there is an 60% chance that any given senior citizen will disapprove of legalized marijuana.
a.What is the chance you will find between 7 – 9 senior citizens out of 12 surveyed will
disapprove of legalized marijuana?
b. What is the chance you will find between 7 – 9 senior citizens out of 12 surveyed will
approve of legalized marijuana?
c. What is the chance that no more than 5 senior citizens out of 12 surveyed will approve of
legalized marijuana?
d.What is the chance that at least 8 senior citizens out of 12 surveyed will disapprove of legalized marijuana?
In: Advanced Math
Sara Sanders purchased 50 shares of Apple stock at $ 190.35 per share using the prevailing minimum initial margin requirement of 56 %. She held the stock for exactly 6 months and sold it without any brokerage costs at the end of that period. During the 6-month holding period, the stock paid $ 1.54 per share in cash dividends. Sara was charged 4.5 % annual interest on the margin loan. The minimum maintenance margin was 25 %.
a. Calculate the initial value of the transaction, the debit balance, and the equity position on Sara's transaction.
b. For each of the following share prices, calculate the actual margin percentage, and indicate whether Sara's margin account would have excess equity, would be restricted, or would be subject to a margin call: (1) $ 174.66, (2) $ 207.62, and (3) $ 122.17.
c. Calculate the dollar amount of (1) dividends received and(2) interest paid on the margin loan during the 6-month holding period.
d. Use each of the following sale prices at the end of the 6-month holding period to calculate Sara's annualized rate of return on the Apple stock transaction: (1) $ 184.47, (2) $ 194.61, and (3) $ 206.26.
In: Advanced Math
Solve the linear system Az = b using the following methods:
I. The GE+PP algorithm for sparse (banded) linear systems, which is the default algorithm used by Matlab’s “\” operator when the matrix (call it Asparse) is of sparse type. You may find it easiest to set up the matrix using the spdiags command.
In: Advanced Math
Let B ={A1, A2, ..., An}⊆Mmn, and write B′ ={A^T 1, A^T 2, ..., A^T n}⊆Mnm. Show that:
a. B is independent if and only if B′ is independent.
b. B spans Mmn if and only if B′ spans Mnm.
In: Advanced Math