The forcing function is a linearly combination of ?(?)=3? and ?(?)=25sin(3?).

Solve the Ordinary Differential Equation, ?’’−2?’+?=3?+10sin(3?).

Task: Network planning

A university has a main campus and a remote campus at another location. The default router to the Internet on the main campus has an IP address of 10.0.0.1/24. The main campus network is connected to the Internet through a router called RouterA. The main campus has no more than 15000 staff and students. The remote campus network is connected to the main campus network through a router called RouterB. The remote campus has no more than 200 staff and students. All staff and students should be able to access to the Internet and to the resources on both campuses. Router A should have two interfaces, one goes to the Internet (thus having an address in 10.0.0.0/24 block) and the other goes to the main campus network. Router B should have two interfaces, one goes to the main campus and the other goes to the remote campus.

Your task is to plan the campus networks.

1. a) Propose appropriate subnet ranges for both campuses from the 16‐bit prefix block of IPv4 private addresses. Answer the question with your calculation.

2. b) Draw a diagram to depict the networks with IP addresses notated with CIDR notation assigned to the all interfaces of bother routers for two campuses. Label the interfaces of routers on the diagram using eth0 or eth1.

Show the routing table of the RouterA that meets the requirements of both campuses. Show the columns of Destination, Gateway, Genmask, Flags and Iface in the routing table as shown by the Linux command route.

Angela Fox and Zooey Caulfield were food and nutrition majors at State University, as well as close friends and roommates. Upon graduation Angela and Zooey decided to open a French restaurant in Draperton, the small town where the university was located. There were no other French restaurants in Draperton, and the possibility of doing something new and somewhat risky intrigued the two friends. They purchased an old Victorian home just off Main Street for their new restaurant, which they named “The Possibility.” Angela and Zooey knew in advance that at least initially they could not offer a full, varied menu of dishes. They had no idea what their local customers’ tastes in French cuisine would be, so they decided to serve only two full-course meals each night, one with beef and the other with fish. Their chef, Pierre, was confident he could make each dish so exciting and unique that two meals would be sufficient, at least until they could assess which menu items were most popular. Pierre indicated that with each meal he could experiment with different appetizers, soups, salads, vegetable dishes, and desserts until they were able to identify a full selection of menu items. The next problem for Angela and Zooey was to determine how many meals to prepare for each night so they could shop for ingredients and set up the work schedule. They could not afford too much waste. They estimated that they would sell a maximum of 60 meals each night. Each fish dinner, including all accompaniments, requires 15 minutes to prepare, and each beef dinner takes twice as long. There is a total of 20 hours of kitchen staff labor available each day. Angela and Zooey believe that because of the health consciousness of their potential clientele, they will sell at least three fish dinners for every two beef dinners. The profit from each fish dinner will be approximately $12, and the profit from a beef dinner will be about $16. - Formulate a linear programming model for Angela and Zooey that will help them estimate the number of meals they should prepare each night and solve this model graphically. * Please show graph and how to optimize step by step*

Find the change of variable that reduce the following quadratic from to a sum of squares and express the quadratic from in terms of the new variables. 8x^2+7y^2+3z^2-12xy-8yz+4zx

Using Newton-Raphson method, find the complex root of the function f(z) = z 2 + z + 1 with with an accuracy of 10–6. Let z0 = 1 − i. write program c++ or matlab

Problem 4S-1

Consider the following system:

→ 0.74 → 0.74 →

Determine the probability that the system will operate under each of these conditions:

a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)

Probability              

b. Each system component has a backup with a probability of .74 and a switch that is 100% percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)

Probability            

c. Backups with .74 probability and a switch that is 99 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)

Probability            

Let f: Q8 to D8 be a homomorphism from the quaternion Q8 to the dihedral group D8 of order 8. Suppose that f (i) = rs and f( j) = r^2.

(a) Find f (k) and f(-k) (expressed in standard form r^i*s^i for suitable i and j) ·

(b) List the elements in the kernel of f in standard form.

(c) The quotient group Q8/ker(f) is isomorphic to which one of the groups C2, C4 or C2xC2    why?

1. We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this algorithm to compute the following values. Show all of the steps involved.
   1. 9570^-1(mod 12935)
   2. 550^-1 (mod 1769)

1. Let (A, B, C, D) and (A1, B1, C1, D1) be two non-degenerate quadrilateral. Explain why there is exactly one projective transformation that maps one to the other.

5. Classify the conic x 2−4xy+4y 2−6x−8y+5 = 0. Determine its center/vertex, its axis and its eccentricity.

Given the following functions, can you have the corresponding a) Fourier series, b) Fourier transform and c) Laplace transform? If yes, find them, if not, explain why you can not.

A, x(t) = -1+cos(2t) + sin（pai*t+1)                                               (4-1)

B, x(t) = 2d(t) cos(2t) +d(t-1.5p) sin(2t)                                          (4-2)

C, x(t) = 1+cos(1.5t) + cos(4t)                                           (4-3)

Prove that if two non-equal letters are interchanged in a ISBN code word the error will be detected (the word is no longer an ISBN code word)

Let a circle inside triangle DEF have a radius = 3, and let it be tangent to EF at point Z. Suppose |EZ| = 6 and |FZ| = 7. What are the lengths of d, e, and f?