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For questions involving nonhomogeneous linear differential equations, find the general solution.
For questions with enumerated functions, tell whether they are linearly dependent or linearly independent.
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- A machine shop has an order for 12,000 pcs. of a machine part that requires anti-corrosive properties. Chromium steel alloy that cost Php 95.00/ kg or Nickel steel alloy that cost Php 85.00 /kg may be used. The weight per piece, production per day and tool bit replacement cost for Cr-alloy are: 0.25 kg, 75 pcs and Php 1,600 every 400 pcs. Produced. The respective date for Ni-alloy are 0.3 kg, 50 pcs. And Php 1,800.00 for every 300 pcs. produced. If the charge for the labor and other operating cost is Php 450.00/day with all other expenses being the same, determine which material should be used.Solve x,y,z if ConsistentFind numbers a and b such that ax + by =(9, -1, 10), where x =(3, -1, 0) and y =(0, 1, 5). Is there more than one solution?
- your natural gas bill is calculated as sum of the fixed monthly cost and a rate per therm of natural gas used. given a usage of 183 therms with a bill of $116.05 for this month and a usage of 129 therms with a bill of $85.80 for last month, determind the fixed monthly cost and rate of your bill with appropriate units.A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 8 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/hr and run 8 km/hr, where should he land to reach B as soon as possible? (Assume that the speed of the water is negligible compared with the speed at which the man rows)A diet is to contain at least 10 ounces of nutrientP, 12 ounces ofRand 20 ounces ofS. These nutrients are to beobtained from foodsA, BandC. Each pound ofAcosts 3 cents and contains Three ounces ofP, Two ounces ofRand Zero ounce ofS. Each pound ofBcosts 6 cents and contains one ounce ofP, Three ounces ofRand Threeounce ofS. Each pound ofCcosts 7 cents and contains Zero ounce ofP, one ounces ofRand five ounce ofS. Howmany pounds of each foods should be purchased if the stated dietary requirements are to be met at minimum cost ?[Do not use SIMPLEX method to solve this problem. Show all of your calculations in detail
- A high school dietician is planning menus for the upcoming month. Anew item will be spaghetti with sauce. The dietician wants each serving tocontain at least 10 grams of protein and at least 40 grams of carbohydrates.Spaghetti contains 5 grams of protein and 32 grams of carbohydrates per cup,and the sauce contains 4 grams of protein and 5 grams of carbohydrates percup. For aesthetic reasons, the dietician wants a ratio of spaghetti to sauce to be4:1.Spaghetti costs $0.30 per cup to buy and prepare, and the sauce $0.40 per cupto buy and prepare. The dietician wants to minimize the cost per serving andkeep the calories per serving 330 or less. The sauce contains 100 calories percup, and spaghetti contains 160 calories per cup.Formulate a linear programming model for this problem.Can u plz provide its solution?. A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants to reach point B, 8 km downstream on the opposite bank, as quickly as possible. He could row his boat directly across the river to point C and then run to B, or he could row directly to B, or he could row to some point D between C and B and then run to B. If he can row 6 km/h and run 8 km/h, where should he land to reach B as soon as possible? (We assume that the speed of the water is negligible compared with the speed at whichthe man rows.)
- d,e only Last 2 parts ,plz asap will definitely upvoteA production process produces and packages soap in boxes weighing 140 grams. Owing to inspection carried out by several large municipalities, the penalty for placing, on the average, less than 140 grams in a box can be severe. Likewise it would also be wasteful for the company if they place, on the average, more than 140 grams in a box. Hence, the machine was adjusted to put 140 grams of soap in a box. After a year, the company wants to check if there is a need to readjust the machine. The company wishes to perform a test of hypothesis at 0.01 level of significance using the following data collected from a random sample: (photo attached). • State Ho and Ha.• Write the formula of the test statistic to be used.• State the decision rule at 0.01 level of significance.• Compute for the value of the test statistic.• Is there sufficient evidence at 0.01 level of significance for the company to conclude that mean weight of soap packaged in a box is not anymore 140 grams so that there is a need…A grocery store is holding a 10% discount promo for purchasing all items without certain conditions. Dona, Dini and Dina shop at the store. Dona y 2 kg of cooking oil, 5 kg of rice, and 2 kg of eggs, must pay IDR 133,200.00. Then Dini, who bought 1 kg of cooking oil, 3 kg of rice and 2 kg of eggs, had to pay IDR 97,200.00. Meanwhile, Dina, who bought 2 kg of cooking oil, 4 kg of rice and 1 kg of eggs, also had to pay eggs before the discount! IDR 97,200.00. Determine the price of 1 kg of cooking oil plus 1 kg of rice plus 1 kg of.. A. IDR 50,000.00 B. IDR 52,000.00 C. IDR 54,000.00 D. IDR 56,000.00 Please with an explanation! E. IDR 58,000.00