I. For each DE, identify the type, give the order, degree and determine whether linear or nonlinear. If linear, indicate the variable where it is linear and if nonlinear, box the term/s that make/s the DE nonlinear DE 1. ay(5) (4) + x²y"" = 2yy' dz a²w 2. = y dx dy 3. (1-x-3)²+(sin x) y' - 3 xy = ln x(3+1) dx² 4. {√/(1+y″)² = [2x*y³² + (v²”*Ë 5. a³w a²w exdy <-2 +2y tan w = 0 TYPE ORDER DEGREE LINEARITY
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- In the area of Russia récords were kept on the relationship between the rain Fall in inches and the yield of wheat (bushels per acre ).the data for a 9 year period is as follow. Rain fall x 13.1,11.4,16.0,15.1,21.4,12.9,9.6,18.2,18.6. yield y : 48.5,44.2,56.8,80.4,47.2,29.9,74.0,74.0,76.8 the equation of the line of least squares is given as ^y= -9.12+4.38x. How many bushels of wheat peen acre can be predicted if it’s is expected that there will be 30 inches of rain?Obtain the general solution VARIATION OF PARAMETERSAs a result of urbanization, the temperatures in Paris have increased. In 1891 the average daily minimum and maximum temperatures were 5.8°C and 15.1°C, respectively. Between 1891 and 1968, these average temperatures rose 0.019°C/yr and 0.011°C/yr, respectively. Assuming the increases were linear, find the year when the difference between the minimum and maximum temperatures was 9C, and determine the corresponding average maximum temperature.
- A value of r close to _______ suggests at most a weak linear relationship between the variables.Jenny Company produces two types of pants: long pants and short pants. The cost of making a pair of short pants and a pair of long pants are RM 75 and RM 95 respectively.In one week, the company must produce at least 150 pants of each type. The minimum weekly production is 500 pants. The short pants is sold for RM 120 each and the long pants for RM 150 each. Using the graphical method, find:a) The number of short pants and long pants to be made in a week in order to minimize the total production cost.b) The profit made at the minimum weekly production cost.There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows:P1=(10,15), P2=(20,25) ve P3=(40,5)To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the2two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively.Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move simultaneously in both directions.…
- Solve min x1-x2-2x3 problem by means of Lagrange multipliers under the constraints of x1+x2+x3=5 and x12+ x22 =4. Explain what the values of Lagrange multipliers mean?Almaha Clothing store has requested a manufacturer to produce pants and sports jackets. For materials, the manufacturer has 750 m of cotton textile and 1000 m of polyester. Every pair of pants (1 unit) needs 1 m of cotton and 2 m of polyester. Every jacket needs 1.5 m of cotton and 1 m of polyester. The price of the pants is fixed at $50 and the jacket, $40. By using the Linear Programing Function, what is the number of pants and jackets that the manufacturer must sale to the stores so that these items obtain a maximum sale?A certain puppy when born weighs 8 pounds, and its weight increases linearly by 0.45 pounds per day for the first week. Construct a model for the puppy’s weight during the first week using the variables W for weight and d for days.
- A rectangular vault is to be constructed on an existing floor at a bank so as to enclose avolume of 485 cubic meters. The cost per square meter of materials is $2,000 for the ceiling,$9,000 for the wall with the door and $3,000 for the other three walls. The minimized costof the vault rounded to the nearest $1,000 dollars is:a. $964,000b. $971,000c. $982,000d. $993,000The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). Using the linear prediction equation and plugging in the actual x-values (social expenditure rates) provided above, find the predicted child poverty rates for the United States and for Denmark. The x-values for both of these countries are provided above in the description of the study. (Note: You do not need to convert the percentages into proportions before or after plugging them into the equation.) The predicted child poverty rate for the U.S.: The predicted child poverty rate for Denmark:A diesel engine uses type A filter and high-grade lubricating oil costing P55 per liter. With this filter, the oil and the filter have to be changed every 500hrs. of operation, and 5L of oil have to be added every 100hrs. This filter costs P1480 a piece. Eighty liters of oil fill the engine. Another type, filter B, costing of P1200 may be used with a lower grade of oil costing P48 per liter. However, if this filter is used, the oil and filter have to be changed every 300hrs and 10 liters are added after each 150hrs the engine is used. Hint: Consider the cost per hour.