Please solve the following equation by using the frobenius method.

xy′′ − (3 + x)y ′ + 2y = 0

My apologies, the original image did not upload properly.

Unoccupied seats at the Cardinal’s football stadium causes the football team to lose revenue. The Cardinal’s owner wants to estimate the mean number of unoccupied seats per game over the past few years. To accomplish this, the records of 225 games are randomly selected and the number of unoccupied seats is noted for each of the sampled games. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats. x-=

Compute all possible cycles, length of the cycle, and number of cycles in the following cases:

(a) mult by 3 mod 17

(b) mult by 13 mod 17

(c) mult by 9 mod 17

(d) mult by 16 mod 17

A leading UK Chocolate Brand has seen a downturn in sales due to new competition in the

market. Analysis work has shown the need for a customer loyalty programme. You have been

tasked with designing the approach that your Partner will present to the Client.

One Page Project Summary including;

▪

The purpose of the assignment and the outline of the

task

▪

The core deliverables expected from the engagement

▪

The make up of your Consulting Delivery Team

One Page High

-

Level market summary, including;

▪

The market size

▪

Core competition in the market

▪

Challenges faced by the industry

One Page Solution Overview, including;

▪

Your proposed solution to the problem statement

▪

Your justification for your solution

▪

Expected outcomes / ROI if the Client goes ahead with

your suggestion

One Page Implementation Plan, including;

▪

A One Page Project Plan

▪

Your change management approach to ensure

seamless integration

Explain what is rule based system and the fuzzy expert system based on the following information. Here is what Amy will do. When the temperature is cold, she will wear a coat. When the temperature is moderate, she will wear a jumper. When the temperature is cold, she will stay indoor. When the temperature is moderate, she will go for shopping. Here is Amy’s consideration for the weather/temperature. It is cold when the temperature is below 16 degree. It is moderate when the temperature is between 16 – 22 degree.

The diagram shows a kite AFCE inside rhombus ABCD. Angle AFB = angle AED = 35degrees, angle ABF = angle ADE = 120degrees. Find the size of angle EAF.  

Let f be a differentiable function on the interval [0, 2π] with derivative f' . Show that there exists a point c ∈ (0, 2π) such that cos(c)f(c) + sin(c)f'(c) = 2 sin(c).

In this activity we have graphed the function y = sin(x). For this assignment, you will explore the changes that occur in the curve when we make simple changes to the function.

For each of the different parts below, create sketches and a description of the crucial properties of the periodic graphs including:

• Period
• Amplitude
• Maximum
• Minimum
• Axis of the Curve
• Zeros

Finally, in a few sentences, based on your findings describe how these changes in the function affect the properties of the curve.

For your sketches, you can scan hand-made sketches and email or fax these to your instructor. Alternately, you may use a simple drawing program like Windows Paint.

Consider the optimization problem of the objective function f(x, y) = 3x 2 − 4y 2 + xy − 5 subject to x − 2y + 7 = 0. 1. Write down the Lagrangian function and the first-order conditions. 1 mark 2. Determine the stationary point. 2 marks 3. Does the stationary point represent a maximum or a minimum? Justify your answer.

Find the particular integral of the differential equation

d²y/dx² + 3dy/dx + 2y = e ^−2x (x + 1). show that the answer is yp(x) = −e ^−2x ( 1/2 x² + 2x + 2) ]

Devonna and Jerry are making cookies for a bake sale at their daughters’ school. They decide to make chocolate chip cookies and iced sugar cookies. Respond to the following questions (make sure the final answers are proper fractions or mixed numbers and include the correct unit for each item).

Attempt History

Question 1

Davonna is going to mix up five times a single recipe of chocolate chip cookies. The recipe calls for:

• 1/2 c butter
• 1 c sugar
• 2 eggs
• 1 1/2 tsp vanilla
• 1 1/4 c flour
• 2 1/4 tsp salt
• 2 1/2 tsp baking soda
• 1 3/4 c chocolate chips

Calculate the total of each ingredient that Davonna needs for all her cookies.

Question 2

Jerry is going to mix up 2 1/2 times a single recipe of sugar cookies. The recipe calls for:

• 2 1/4 c flour
• 3/4 c sugar
• 1/4 tsp baking powder
• 1/2 tsp salt
• 1 1/4 c butter
• 2 eggs
• 1 1/2 tsp vanilla

Calculate the total of each ingredient that Jerry needs for all her cookies.

Question 3

Latisha also needs to make icing for her cookies. She decides to cut the recipe in 1/2. The recipe calls for:

• 2 egg whites
• 1/2 c sugar
• 1/8 tsp salt
• 1 1/2 tsp vanilla

Calculate the total of each ingredient that Latisha needs for her icing.

Question 4

Make a shopping list that includes the total ingredients necessary for Davonna and Latisha’s cookies.

Davonna needs:

• 2 ½ c butter
• 5 c sugar
• 10 eggs
• 7 1/2 tsp vanilla
• 6 1/4 c flour
• 11 1/4 tsp salt
• 12 1/2 tsp baking soda
• 8 3/4 c chocolate chips

Latisha needs for the cookies:

• 5 5/8 c flour
• 1 7/8 c sugar
• 5/8 tsp baking powder
• 1 1/4 tsp salt
• 3 1/8 c butter
• 5 eggs
• 3 3/4 tsp vanilla

Latisha needs for the frosting:

• 1 egg white
• 1/4 c sugar
• 1/16 tsp salt
• 3/4 tsp vanilla

Question 5

A bag of chocolate chips contains 2 c of chips.

• How many bags does Davonna need?  bags
• How much will be left over?  c

Question 6

One pound of butter is 2 cups.

• How many pounds of butter do the two women need for their cookies (they will need 5 5/8 c butter)?  lbs
• How many cups will be left over?  c

Constant Yield Harvesting. In this problem, we assume that fish are caught at a constant rate h independent of the size of the fish population, that is, the harvesting rate H(y, t) = h. Then y satisfies dy/dt = r(1 − y/K )y − h = f (y). (ii) The assumption of a constant catch rate h may be reasonable when y is large but becomes less so when y is small.

(a) If h < rK/4, show that Eq. (ii) has two equilibrium points y1 and y2 with y1 < y2; determine these points.

(b) Show that y1 is unstable and y2 is asymptotically stable.

(c) From a plot of f (y) versus y, show that if the initial population y0 > y1, then y → y2 as t → ∞, but if y0 < y1, then y decreases as t increases. Note that y = 0 is not an equilibrium point, so if y0 < y1, then extinction will be reached in a finite time.

(d) If h > rK/4, show that y decreases to zero as t increases regardless of the value of y0. (e) If h = rK/4, show that there is a single equilibrium point y = K/2 and that this point is semistable. Thus the maximum sustainable yield is hm = rK/4, corresponding to the equilibrium value y=K/2. Observe that hm has the same value as Y m in Problem 1

(d). The fishery is considered to be overexploited if y is reduced to a level below K/2.

(e) If h = rK/4, show that there is a single equilibrium point y = K/2 and that this point is semistable. Thus the maximum sustainable yield is hm = rK/4, corresponding to the equilibrium value y=K/2. Observe that hm has the same value as Y m in Problem 1(d). The fishery is considered to be overexploited if y is reduced to a level below K/2

*Using Matlab