Find the intervals of increase and decrease, find the local maximum and minimum values, find the intervals of concave up and concave down, find the inflection points and sketch the graph

f(deta) = 2cos(deta)+cos^2(deta), 0<=deta<=2pi

IS623 practice

Short Answer Questions

1. Suppose you have a secure system with three subjects and three objects, with levels as listed below. (10 points)

Here H dominates L. You wish to implement a Bell and LaPadula model of security for this system. Fill in the access rights (R and/or W) permitted by the model for each subject/object pair in the access matrix below:

2. Suppose a department has determined that some users have gained unauthorized access to the computing system. Managers fear the intruders might intercept or even modify sensitive data on the system. Cost to reconstruct correct data is expected to be $2,000,000 with 5% likelihood per year.

One approach to addressing this problem is to install a more secure data access control problem. The cost of access control software is is $50,000 with 80% effectiveness. Here is the summary of risk and control:

• Cost to reconstruct correct data = $2,000,000 with 5% likelihood per year
• Effectiveness of access control software: 80%
• Cost of access control software: $50,000

Determine the expected annual costs due to loss and controls. Also, determine whether the costs outweigh the benefits of preventing or mitigating the risks. (5 points)

3. Suppose your data’s binary stream is 1110101. What is the XOR result with the bit stream of 1111111? (2 points)

4. Suppose the following:
   • James’ public key = K_j, James’ private key = K_j^-1
   • Randy’s public key = K_r, Randy’s private key = K_r^-1
   • Each person’s public key is known to others; Each one’s private key is only known to the owner

1. Explain how Randy can send a plaintext P to James secretly (2 points)

2. Explain how James can verify if a plaintext P is sent from Randy (2 points)

3. Explain how Randy can verify if a plaintext P is sent from James and at the same time P is sent secretly from James to Randy. (2 points)

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = 9y cos(x), 0 ≤ x ≤ 2π

local maximum?

local minimum?

saddle point(s)?

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x, y) = y² − 2y cos(x),    −1 ≤ x ≤ 7

local maximum?

local minimum?

saddle points?

You have studied different types and application of Data Warehousing (DWH). In this assignment you have to create dimensional model for DWH of any type and discuss it in detail. Identify the business objective and design Star and Snowflake schemas. Use erwin data modeling tool.

Among the various types of the gas filled radiator detectors the Geiger Murller (GM) types of detects are commonly used in personal contamination detectors. Describe the purpose of the quench gas

We can use our knowledge of air resistance to calculate its effect on a baseball in 2-dimensional projectile motion.

The effect of air resistance can be modeled with an extra acceleration term, so that the acceleration is no longer simply ⃗a = ⃗g but rather

⃗a = ⃗g − bv⃗v
We will use b = 0.002 m^(−1), a reasonable value for a baseball flying through the air.

Let the initial velocity of the ball be 35 m/s at an angle of 42◦ above the horizontal.

(a) Write the expressions for ax and ay as functions of vx and vy.

(b) Write the expressions for x,y,vx, and vy as a function of t during the flight of the ball.

(c) How much shorter is the total range of the ball, due to losses from air resistance?

7. Finding Roots Using the Bisection Method

Write a function that implements the "bisection method" for finding the roots of function. The signature of your function should look like

def find_root(f,a,b,n):

where n is the maximum number of iterations of to search for the root.

The code should follow this algorithm:

• We are given a continuous function f and numbers a and b and with a<b with f(a)<0<f(b). From the intermediate value theorem we know that there exists a c with a<c<b with f(c)=0. We want to find c.

• Set a1=a and b1=b and m=12(a+b).

• For i=1 to n do

  • If f(m)=0, then c=m so break and return m.
  • Else If f(m)>0 then set ai+1=ai and bi+1=m.
  • Else If f(m)<0, then set ai+1=mi and bi+1=bi.

Find the intersection of the line passing through P=(-10,-6,-6) and Q(50,-18,-18) and the plane passing through points R(-10,0,0), S(0,-6,0) and T(0,0,-6).

Kane Manufacturing has a division that produces two models of hibachis, model A and model B. To produce each model A hibachi requires 6 lb of cast iron and 12 min of labor. To produce each model B hibachi requires 7 lb of cast iron and 6 min of labor. The profit for each model A hibachi is $5, and the profit for each model B hibachi is $4.50. If 2200 lb of cast iron and 40 labor-hours are available for the production of hibachis each week, how many hibachis of each model should the division produce each week to maximize Kane's profit?

What is the largest profit the company can realize?
$  

Is there any raw material left over? (If so, give the amount remaining. If not, enter 0.)

2. Let G be a bipartite graph with 10^7 left vertices and 20 right vertices. Two vertices u, v are called twins if the set of neighbors of u equals the set of neighbors of v (triplets, quadruplets etc are defined similarly). Show that G has twins. Show that G has triplets. What about quadruplets, etc.?

3. Show that there exists a bipartite graph with 10^5 left vertices and 20 right vertices without any twins.

4. Show that any graph with n vertices and δ(G) ≥ n/2 + 1 has a triangle.

Consider a multiple-choice examination with 50 questions. Each question has four possible answers. Assume that a student who has done the homework and attended lectures has a 65% chance of answering any question correctly. (Round your answers to two decimal places.)

(a) A student must answer 43 or more questions correctly to obtain a grade of A. What percentage of the students who have done their homework and attended lectures will obtain a grade of A on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question. %

(b) A student who answers 35 to 39 questions correctly will receive a grade of C. What percentage of students who have done their homework and attended lectures will obtain a grade of C on this multiple-choice examination? Use the normal approximation of the binomial distribution to answer this question. %

(c) A student must answer 28 or more questions correctly to pass the examination. What percentage of the students who have done their homework and attended lectures will pass the examination? Use the normal approximation of the binomial distribution to answer this question. %

(d) Assume that a student has not attended class and has not done the homework for the course. Furthermore, assume that the student will simply guess at the answer to each question. What is the probability that this student will answer 28 or more questions correctly and pass the examination? Use the normal approximation of the binomial distribution to answer this question.

Siblings Dana, Dan, and Doug have inherited 50 acres of pasture land from their Uncle Bob. They plan to start ranching but cannot agree on what type of animals they should raise. They decide to build three adjoining rectangular pens of the same size. One pen will be Dana to use, one pen for Dan to use, and one pen for Doug to use. They have 1000 yards of chain link fence to build the adjoining pens.

Part 1:

1. Solution: What is the maximum size - area that each pen could be?

Include all of the following:

• draw a picture
• use calculus, show formula used
• write a sentence answer
• articulate why this particular approach was chosen to solve the problem and explain the context of the solution.

2. Recommendation: Do some research on the Internet and recommend what kind of animal they should raise.

Your recommendation should include:

• the animal that you are recommending to raise
• two reason why you recommend that animal
• two websites (URL) that support your recommendation. Give a brief description of each web site.