Differential Equations: Please try to computer type, if not possible be clear and organize. Thank you so much

Use an annihilator to solve the IVP: y’’’ – y ’= 2sinx, y(0)=0 , y’(0)=0 , y”(0)=1

Find the general solution y = C₁Y₁ + C₂ Y₂  + Y_p to the ODE

y'' + y' − 2y = − 2x + 4 y (0) = − 4, y' (0) = − 7

Y = ?

Please show your work step by step. Thank you!

The marketing department for BER Inc. has been struggling with how they will spend their advertising budget in the coming year. You have been requested to make a recommendation. You have been provided the monthly values for net sales (SALES), and advertising expenditures for mailings (MAIL), print(PRINT), and billboards (BB) along with their sum (TOTAL = MAIL+ PRINT + BB), in the file BER.JMP, covering the months from July 2014 through June 2020. Your assignment is to evaluate the effectiveness of each of the advertising components (mailings, print and billboards) with regards to net sales.

1. Determine an appropriate forecasting equation using regression analysis. (use the following page to show you work)

b. Final estimated equation

(State equation in the form Y_t =   bo + b₁ X₁   + b ₂    X₂   + b ₃ X ₃      + ......   )

c. What is your recommendation regarding where (what media) to spend additional advertising dollars? Justify your answer.

c. What is your recommendation regarding where (what media) to spend additional advertising dollars? Justify your answer.

     d. Make a forecast for July 2020. Assume that the amount to be spent on the three types of advertising (MAIL, PRINT and BB), for July 2020, are identical to what was spent in June 2020.

Model Building Problem 5

     d. Make a forecast for July 2020. Assume that the amount to be spent on the three types of advertising (MAIL, PRINT and BB), for July 2020, are identical to what was spent in June 2020.

Model Building Problem 5

Month Sales Print Mail BB Total

07/2014   577563   1565.00   336.45   5488.75   7390.20
08/2014   542948   2092.75   352.72   3634.50   6079.97
09/2014   499066   1590.75   290.59   3608.75   5490.09
10/2014   485132   2229.25   267.92   4923.50   7420.67
11/2014   511742   1458.00   304.23   4525.50   6287.73
12/2014   631313   1370.50   270.26   6218.00   7858.76
01/2015   529692   2257.00   384.13   3451.00   6092.13
02/2015   637138   1384.25   277.97   6231.75   7893.97
03/2015   481165   1302.00   370.73   3106.00   4778.73
04/2015   580945   2066.50   265.48   5647.00   7978.98
05/2015   891906   1466.00   326.28   5426.25   7218.53
06/2015   685383   1558.75   356.62   5714.00   7629.37
07/2015   611582   1460.50   331.90   4719.50   6511.90
08/2015   613348   2302.25   312.57   5768.00   8382.82
09/2015   483268   1883.75   368.41   2756.00   5008.16
10/2015   466770   1318.50   227.59   3757.25   5303.34
11/2015   402431   1275.25   185.93   3514.00   4975.18
12/2015   401063   1899.75   269.74   3461.00   5630.49
01/2016   459923   1884.00   208.35   4377.75   6470.10
02/2016   449089   1972.25   302.45   3599.25   5873.95
03/2016   527236   2101.25   237.71   4840.50   7179.46
04/2016   607349   1462.00   310.25   6173.25   7945.50
05/2016   1019440   1622.75   382.90   5827.50   7833.15
06/2016   692305   2194.75   361.40   5928.50   8484.65
07/2016   634111   1849.00   388.14   4992.25   7229.39
08/2016   663151   2448.75   380.32   6131.00   8960.07
09/2016   535825   1751.25   388.75   3414.00   5554.00
10/2016   458804   1672.75   324.81   3371.25   5368.81
11/2016   415963   1905.25   250.31   3565.50   5721.06
12/2016   416112   1952.50   253.94   3924.00   6130.44
01/2017   518759   2392.25   261.97   5210.75   7864.97
02/2017   506471   2095.25   298.46   3971.75   6365.46
03/2017   562210   1581.75   299.79   5609.50   7491.04
04/2017   629802   2303.50   311.84   5965.75   8581.09
05/2017   1002376   2001.25   370.22   5697.50   8068.97
06/2017   692552   2465.50   407.25   5984.50   8857.25
07/2017   626601   1453.50   425.41   4289.75   6168.66
08/2017   517671   1873.25   304.05   3055.00   5232.30
09/2017   555945   2165.75   233.85   5968.00   8367.60
10/2017   459841   1724.25   341.83   3857.25   5923.33
11/2017   575057   1768.50   333.82   5766.75   7869.07
12/2017   314564   2419.00   281.04   3639.50   6339.54
01/2018   308211   2424.25   293.47   4544.25   7261.97
02/2018   324154   2397.25   265.65   5392.00   8054.90
03/2018   395687   1824.25   344.61   5340.00   7508.86
04/2018   591948   2281.25   322.29   3931.75   6535.29
05/2018   961455   1895.75   318.26   5671.50   7885.51
06/2018   606309   1482.75   361.22   5345.75   7189.72
07/2018   551793   1277.25   379.22   3969.50   5625.97
08/2018   500598   2359.75   326.13   3801.25   6487.13
09/2018   517344   1495.75   262.42   5073.25   6831.42
10/2018   468414   2135.00   320.52   2921.75   5377.27
11/2018   397045   1845.25   257.48   3208.25   5310.98
12/2018   449809   2062.75   261.89   5032.75   7357.39
01/2019   572024   2099.25   274.75   5374.75   7748.75
02/2019   507434   1282.50   359.94   2796.75   4439.19
03/2019   447931   1802.75   248.67   3388.50   5439.92
04/2019   477764   1276.00   221.05   5217.75   6714.80
05/2019   860729   1721.75   338.66   4119.75   6180.16
06/2019   642444   1879.50   271.87   5999.00   8150.37
07/2019   571933   2488.50   358.47   4290.00   7136.97
08/2019   476864   1633.00   320.58   2773.50   4727.08
09/2019   535468   1268.50   239.17   5687.00   7194.67
10/2019   471865   2325.75   315.12   3747.00   6387.87
11/2019   607926   1566.00   307.19   5858.75   7731.94
12/2019   621473   1855.50   335.55   5997.25   8188.30
01/2020   636665   1918.75   405.20   4208.25   6532.20
02/2020   615563   1301.50   331.18   5448.25   7080.93
03/2020   469326   2438.00   355.10   2735.25   5528.35
04/2020   528467   1642.50   273.02   5150.50   7066.02
05/2020   821140   2360.00   287.62   4226.25   6873.87
06/2020   467031   1816.25   308.22   3757.75   5882.22

I need answers as soon as possible

1.Rabbits are sawing a log. They made 10 cuts. How many blocks of wood did they get? (the answer is a number)

2.Friends are cutting a donut into sectors. They made 10 cuts. How many pieces of a donat did they get? (the answer is a number)

3.Rabbits are sawing several logs. They made 10 cuts and got 16 blocks of wood. How many logs did they saw in the beginning? (the answer is a number)


4.In the bag, there are balls of two colors: black and white. What is the minimum number of balls one should take out from the bag (not looking) to be sure to get balls of different colors? (the answer is a number)

5.John's cat always sneezes before the rain. The cat sneezed today. "It means it is going to rain" - thinks John. Is John right?

Transform the given system into a single equation of second-order:

x′₁ =−4x₁+9x₂

x′₂ =−9x₁−4x₂.

Then find x1 and x2 that also satisfy the initial conditions:

x₁(0) =8

x₂(0) =5.

1. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 65 degrees occurs at 4 PM and the average temperature for the day is 60 degrees. Find the temperature, to the nearest degree, at 6 AM.

------degrees

2. Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 62 and 88 degrees during the day and the average daily temperature first occurs at 10 AM. How many hours after midnight, to two decimal places, does the temperature first reach 72 degrees?

-----hours

3. A Ferris wheel is 20 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. How many minutes of the ride are spent higher than 20 meters above the ground?

------minutes.

a. For each of the following, answer correct to two decimal places

Find the area under the curve y=3x^3+2

Find the area between the curve y=2/x and the x-axis for x between -5 and -4

Find the area between the curve y=x^2-3x and the x-axis for x between 2 and 7

Find the area bounded by the curves y=6x^3+1 and y=6x+1

b. The birth rate in a certain city is described by the following function

. The city's death rate is given by . Here, t is measured in years, and t = 0 corresponds to the start of the year 1990. The birth and death rates are measured in thousands of births or deaths per year. At the start of 1990, the population of the city is 300 thousand. Answer the following correct to two decimal places.

Calculate the total number of births between the start of 1990 and the end of 1999. (in thousands)

Calculate the total number of deaths over the same period (in thousands)

What is the population of the city at the start of year 2000? (in thousands)

Considering just the period from the start of 1990 to the start of 2000, over what interval is the population increasing? (not the number of years since 1990)

Over what interval is the population decreasing?

Calculate the area between the curves y = b ( t ) and  y = d ( t ) for t between 0 and 10.

Find the General Solutions to the given differential equations y(t) =

a) 6y' +y = 7t^2

b) ty' − y = 9t²e^−9t,    t > 0

c) y' − 8y = 9e^t

d) y' + y/t = 6 cos 5t,    t > 0

Find first four non zero terms in a power series expansion about x=0 for a general solution to the given differential equation.

(x^2 +21)y''+y=0

What is different about SL(2,Z) and GL(2,Z) with regard to its action on the Farey treeing particular distinguished edge. (Geometric group theory.)

John’s Construction has three projects under way. Each project requires a regular supply of gravel, which can be obtained from three quarries. Shipping costs differ from location to location, and are summarized in the table.

Formulate a transportation model (but do not attempt to solve it) which could be used to determine the amount of gravel to be shipped from each quarry to the various job sites.

Consider the following model: maximize 40x1 +50x2 subject to: x1 +2x2 ≤ 40 4x1 +3x2 ≤ 120 x1, x2 ≥ 0 The optimal solution, determined by the two binding constraints, is x1 = 24, x2 = 8, OFV∗ = 1,360. Now consider a more general objective function, c1x1 + c2x2. Perform a sensitivity analysis to determine when the current solution remains optimal in the following cases: (i) both c1 and c2 may vary; (ii) c2 = 50, c1 may vary; (iii) c1 = 40, c2 may vary. Suppose the RHS of the second constraint increases by an amount ∆b. (It is now 120 + ∆b.) Solve the two equations for x1 and x2 in terms of ∆b, and hence determine its shadow price.