Solve the following initial value problems

y'' + y = 2/cos x , y(0) = y'(0) = 2

x^3 y''' − 6xy' + 12y = 20x^4, x > 0, y(1) = 8/3 , y'(1) = 50/3 , y''(1) = 14

x^2 y'' − 2xy' + 2y = x^2, x > 0, y(1) = 3, y'(1) = 5

brief one paragraph summary report about a Road Plan and Profile (PnP) Drawing.

For any n ≥ 1 let Kn,n be the complete bipartite graph (V, E) where V = {xi : 1 ≤ i ≤ n} ∪ {yi : 1 ≤ i ≤ n} E = {{xi , yj} : 1 ≤ i ≤ n, 1 ≤ j ≤ n} (a) Prove that Kn,n is connected for all n ≤ 1. (b) For any n ≥ 3 find two subsets of edges E 0 ⊆ E and E 00 ⊆ E such that (V, E0 ) and (V, E00) are spanning trees which are not isomorphic.

Consider the region bounded between y = 3 + 2x - x^2 and y = e^x + 2 . Include a sketch of the region (labeling key points) and use it to set up an integral that will give you the volume of the solid of revolution that is obtained by revolving the shaded region around the x-axis, using the... (a) Washer Method (b) Shell Method (c) Choose the integral that would be simplest to integrate by hand and integrate and evaluate that integral, showing all steps.

How many bit strings of length fifteen

a) Contain at least four 0s?

b) Contain at most four 0s?

c)Contain exactly four 0s?

d) Begin with four 0s?

Fill in the blanks

USING THE TERMS LISTED BELOW, (10 TERMS LISTED) CHOOSE THE BEST ANSWERS TO FILL IN THE BLANKS.

Paragraph #1: Mark, an investor, examines the financial statements of Disney. He calculates gross profit of services and does a year-to-year variance comparison of service revenues and costs of services.

Paragraph #2: Mark then compares the net income taking into account the non-cash activity of Disney (adding it back) as well as the other expenses that he feels do not represent management discretion.

Paragraph #3: Through this calculation, Mark is able to compare the income figure that includes expenses that can be managed versus those that are somewhat "fixed" or contractual (not adding back any non-cash activity).

Paragraph #1 is an example of using _ __ information to analyze the financial results of Disney.  

Paragraph #2 is an example of using _ __ to analyze the financial results of Disney.

Paragraph #3 is an example of using _ _ to analyze the financial results of Disney.

matching at the line historical cost   
accruals below the line GAAP
EBIT above the line consistency
EBITDA gross margin conservatism

4. Consider the linear program in problem 3. The value of the optimal solution is 48. Suppose the right-hand side for constraint 1 is increased from 9 to 10.

(problem 3 linear program)

Min 8X+12Y s.t.

1X+3Y≥9

2X+2Y≥10

6X+2Y≥18

A,B≥0

A) Use the graphical solution procedure to find the new optimal solution.

b) Use the solution to part (a) to determine the shadow price for constraint 1.

c) The sensitivity report for the linear program in Problem 3 provides the following right-hand-side range information:

What does the right-hand-side range information for constraint 1 tell you about the shadow price for constraint 1?

d) The shadow price for constraint 2 is 3. Using this shadow price and the right-hand-side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?

Please show the steps to solving the problem. Thank you.

assume that U(x, y) = xy, Px = 1, Py = 4 and B = 120.

Using the Bordered Hessian matrix, verify that the second-order conditions for a maximum are satisfied. Show steps.

1. Does the Diophantine equation 3x−4y = 0 have an integer solution? If so, can you list all integer solutions?

2. Does the equation 3x − 4y = 5 have an integer solution? If so, can you list all the integer solutions?

Solve the following equation using Green’s functions. Set up the integral for the particular solution and evaluate

y''+9y=x+sinx y(0)=1,y'(0)=2

A={1,3,4},B={2,3}

Check ALL of the Cartesian products to which the following elements belong:

(1,1)
A. A×A
B. A×B
C. B×B
D. B×A

(3,3)
A. B×B
B. A×A
C. B×A
D. A×B

(3,1)
A. B×B
B. B×A
C. A×B
D. A×A

(1,2)
A. A×A
B. B×A
C. A×B
D. B×B

Use variation of parameters to solve the following differential equations

y''-5y'-6y=tln(t)

prove the following statement: If the augmented matrices of two linear systems are row equivalent, then those systems are equivalent.

(To do this, start with a solution to one of the systems and show that it is still a solution of the other system under each of the three elementary row operations.)

Suppose all even-indexed linear transformations in the chain complexC•are 0 transformations and all odd-indexed transformations are bijections.Compute the homology of this complex

From the time of early studies by Sir Francis Galton in the late nineteenth century linking it with mental ability, the cranial capacity of the human skull has played an important role in arguments about IQ, racial differences, and evolution, sometimes with serious consequences. (See, for example, S.J. Gould, "The Mismeasure of Man," .) Suppose that the mean cranial capacity measurement for modern, adult males is cc (cubic centimeters) and that the standard deviation is cc. Complete the following statements about the distribution of cranial capacity measurements for modern, adult males. (a) According to Chebyshev's theorem, at least ? of the measurements lie between 565 cc and 1481 cc. (b) According to Chebyshev's theorem, at least 36% of the measurements lie between and . (Round your answer to the nearest integer.) (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the measurements lie between and . (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ? of the measurements lie between 565 cc and 1481 cc.