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

A patient is ordered to receive sodium supplementation by intravenous infusion of a sodium phosphate dibasic solution [Na₂H PO₄ , MW=141.96 g/mol]. The patient is ordered to receive 0.5 mEq of Na + ions per hour.

A 500 mL intravenous bag is prepared that contains 47 mL of a 1% solution of sodium phosphate dibasic. What should be the infusion rate (in units of mL/min) necessary to produce the ordered dose of 0.5 mEq/hr of sodium?

(Note: Consider the total solution volume to be 500 mL. Also assume the sodium phosphate dibasic salt completely disassociates in solution. Please do not assume the specifics of this question are exactly clinically relevant due to the variability in this question.)

1. Considering the results you have shown your manager, they now want to know (out of the    companies you have shortlisted) the following:

1. The social and environmental performance growth of the companies (3 points)
2. Which company has made the best improvement in their social and environmental performance from 2014 to 2015 (1 point)
3. Has any company demonstrated a decline in its social and environmental growth in the two years? (1 point)
4. Considering all the information you have collected what would your suggestion be to your manager? Is the data and information gained from it sufficient to choose a company to invest in? If you decide the data provided is not sufficient, what other data would you suggest collecting to enhance the current data? (4 points, no more than 100 words)

2015 data

Let A = { a , b } A = { a , b } and B = P ( A ) . B = P ( A ) .

Prove that [ B ; ∪ , ∩ , c ] [ B ; ∪ , ∩ , c ] is a Boolean algebra.

Write out the operation tables for the Boolean algebra.

1. Calculating inflation using a simple price index

Consider a fictional price index, the College Student Price Index (CSPI), based on a typical college student’s annual purchases. Suppose the following table shows information on the market basket for the CSPI and the prices of each of the goods in 2017, 2018, and 2019.

The cost of each item in the basket and the total cost of the basket are shown for 2017.

Perform these same calculations for 2018 and 2019, and enter the results in the following table.

Suppose the base year for this price index is 2017.

In the last row of the table, calculate and enter the value of the CSPI for the remaining years.

Between 2017 and 2018, the CSPI increased by

. Between 2018 and 2019, the CSPI increased by

.

Which of the following, if true, would illustrate why price indexes such as the CSPI might overstate inflation in the cost of going to college? Check all that apply.

Professors required each student to buy eight textbooks, regardless of the price.

As the price of textbooks increased, more and more students turned to the used-book market or chose not to buy textbooks at all, instead using the copies on reserve in the library.

The quality and design of calculators improved dramatically from 2017 to 2019. For example, calculators made in 2019 accept memory cards, whereas those made in 2017 do not, but this quality change is hard to measure.

A new, safe method of memory enhancement became available for purchase.

Use the shell method to find the volume of the solid generated by revolving the region bounded by the line y equals 2x plus 3 and the parabola y equals x squared about the following lines. a. The line x equals 3 b. The line x equals minus 1 c. The​ x-axis d. The line y equals 9

3. A 6 inch personal pizza has 610 calories, with 240 of those from fat. A 16 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 16 inch pizza. ____Calories

Which of the following statements are true and which are false?

(a) Assume that we are implementing AES or a similar system on an RFID tag. When calculating the ASIC cost, one of the things we need to take into account is the key.

(b) Assume that we are implementing AES or a similar system on an RFID tag. When calculating the ASIC cost, one of the things we need to take into account is the internal state. (c) Assume that we are implementing AES or a similar system on an RFID tag. When calculating the ASIC cost, one of the things we need to take into account is the cryptographic signature.

(d) When studying how hard it is to break a cryptosystem, average-case complexity is more important than worst-case complexity. (e) The function n −5 is negligible.

(f) The function 5−n is negligible.

(g) The function log n is negligible.

(h) The function n − log n is negligible.