What was the impact of the near failure of Bear Stearns and the failure of Lehman Brothers on Money Markets?

What actions did the Federal Reserve and the Treasury Department take? What were the impacts of the decisions if any?

.Consider the following continuous-time model of the dynamics of an epidemic system made of a growing susceptible population (x) and an infected population(y). Populations are nonnegative (i.e., x≥0, y≥0),and all the parameters are positive (i.e.,a> 0, b> 0, c> 0). dx/dt = ax ( 1 - ( x + y ) ) - b x y + c y dy/dt = bxy - cy

It is assumed that(i)the susceptible population grows until the total population (x+ y) reaches1(= the carrying capacity of the environment), (ii)the infection of the disease changes susceptible individuals into infected ones, and (iii)the infected individuals recover and become susceptible again at a certain rate.

Answer the following.

1.Explain how each of the above three assumptions were represented in the equations. (5x3 = 15points)

2.Find the equilibrium points. There are three such points. (5x3 = 15points)

3.Calculate the Jacobian matrix of the model. Keep a, b and c as symbols. (10 points)

4.Conduct linear stability analysis for each equilibrium point and discuss the conditions under which each equilibrium point is stable/unstable. (5x3 = 15points)

5.Identify the critical condition of parameter values at which a bifurcation occurs.Note that all the parameters are positive.(5points)

6.Draw the phase spaces of this model using Python for several different parameter values to confirm the prediction of bifurcation derived in the previous question.(10points)

1) Find the general solution of ??/?? + 3? = ?^3 sin (?) Using laplace transform y(0) = 2

Suppose we have two different water-benzene-acetic acid solutions, one with 40% water, 50% benzene and 10% acetic acid, the other with 52% water, 42% benzene and 6% acid.

(a) An experiment we want to conduct requires a solution with 43% water, 48% benzene and 9% acid. Representing each acid solution as a vector, determine if we can we make this new acid solution by mixing the first two solutions, or do we have to run to the chemical solutions market to get the solution we want?

(b) Using the water-benzene-acetic acid solutions in the previous problem, can we obtain an acid solution which contains 50% water, 43% benzene and 7% acid? (c)

Determine the relationship between the percentages of water, benzene, and acid in solutions which can be obtained by

mixing the two given water-benzene-acetic acid solutions above.

Hi, Could you please help me to solve the question. Also, could you please answer questions in clear hand-writing and show me the full process, thank you (Sometimes I get the answer which was difficult to read).Thanks a lot.

Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is 40 cases. Millennium purchases each case for $110, there is a $350 fixed cost for each order (independent of the quantity ordered), and its annual holding cost is 25 percent.

Show that SE(3) forms a group under the operation of matrix multiplication.

Prove the following theorem:

Theorem

∀n ∈ Z, n is either even or odd (but not both).

Your proof must address the following points:

1. n is even or odd (and nothing else).

2. n is odd =⇒ n is not even (hint: contradiction).

3. n is even=⇒ n is not odd (hint: contrapositive).

The first point is a bit more difficult. Start by making a statement about 0. Then assuming that n is even, what can you say about n−1 and n+ 1? Likewise, assuming that n is odd, what can you say about n−1 and n+ 1. Can you organize these facts into an argument that shows that you have accounted for all possible n ∈ Z?

use the method of undetermined cofficients to find the the general solution of the following differential equations. verify your solution by using dsolve in matlab.

1) y'' + 4y' + 3y =x + 1

2) y" + 2y' +2y = 2x^2 + 2x + 4

Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows:

The shaper is available for 110 hours, and the grinder is available for 100 hours. No more than 190 units of component 3 can be sold, but up to 1075 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $7, $6, and $9, respectively.

1. Formulate and solve for the recommended production quantities.
   

   	Let	C1	=	units of component 1 manufactured
   		C2	=	units of component 2 manufactured
   		C3	=	units of component 3 manufactured

   Max	__C1	+	___C2	+	___C3
   s.t	6C1	+	___C2	+	___C3	≤	____	Constraint 1
   	___C1	+	___C2	+	2C3	≤	____	Constraint 2
   					C3	≤	____	Constraint 3
   	___C1					≤	____	Constraint 4
   			___C2			≤	____	Constraint 5
   	___C1					≥	____	Constraint 6
   C1,C2,C3 ≥ 0

   
   The optimal solution is
   

   C1	=
   C2	=
   C3	=

2. What are the objective coefficient ranges for the three components? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to two decimal places.
   

   	Objective Coefficient Range
   Variable	lower limit	upper limit
   C1
   C2
   C3

   
   Interpret the above ranges for company management.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
3. What are the right-hand-side ranges? If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to two decimal places.
   

   	Right-Hand-Side-Range
   Constraints	lower limit	upper limit
   1
   2
   3
   4
   5
   6

   
   Interpret the above ranges for company management.
   
   
   
4. If more time could be made available on the grinder, how much would it be worth?
   
   
   
5. If more units of component 3 can be sold by reducing the sales price by $4, should the company reduce the price? Yes or no.
   
   

Using the appropriate general solution you found in the problem above, solve the following initial value problems. Sketch a graph of the solution that captures the initial condition, the limiting behaviour of the solution as t → ∞ and t → −∞ and the sign of the solution (positive or negative) in these limits (look at the dominant terms).

(c) 2y'' - 3y' + y = 0 , y(2) = 1 , y'(2) = 1

(e) 6y'' − 5y' + y = 0 , y(0) = 4 , y' (0) = 4

(f) y'' + 3y ' = 0, y(0) = −2 , y'(0) = 3

(g) 4y'' − y = 0 , y(−2) = 1 , y'(−2) = −1

This builds on example given in class;

Let C_R be the set of all real valued continuous functions, and S_R be the subset of all symmetric real valued continuous functions.

We have verified that S_R has the zero Vector, and is closed under pointwise addition.

Show that the subset S_R is actually a Subspace by verifying the closure under scalar multiplication, namely,

• if r is any real number,
• and f is any Symmetric real valued function,
• Show that the function (rf) is also a symmetric real valued continuous function.
• Draw a graph to show f, rf and what makes the function (rf) symmetric.

a = [4, −9, 4] b = [7, 2, 3] c = [5, −8, 9] d = [1, −3, 2] e = [6, −2, −5, 9] f = [4, −3, 7, 5] g = [1, 3, −1, 5]
h = [7, −5, 5] i = [5, 13, −7, 11]
Express the hyperplane implicitly or explicitly given the following
a) a and h
b) f and i
c) e, f, and g
d) The hyperplane containing b, c and d can be expresses both implicitly and explicitly. Express in both forms and show they are equivalent

Metro Department Store found that t weeks after the end of a sales promotion the volume of sales was given by S(t) = B + Ae−kt (0 ≤ t ≤ 4) where B = 44,000 and is equal to the average weekly volume of sales before the promotion. The sales volumes at the end of the first and third weeks were $80,930 and $60,990, respectively. Assume that the sales volume is decreasing exponentially. (a) Find the decay constant k. (Round your answer to five decimal places.) k = (b) Find the sales volume at the end of the fourth week. (Round your answer to the nearest whole number.) $

Let v and w be two nonzero vectors in R4 . Then v and w are linearly independent if only if v is not a scalar multiple of w. True or false?