I’m struggling with this liverpool.mobius.clouda. Find the Laplace transform of f(t) = 15e6t (using the tablesgiven on Canvas).L{f(t)} =Psin (a)b. Find the inverse Laplace transform of g(s) =L-¹ {g(s)} =abPabsin (a)adasin (a)∞aƏra Ωc. Using Laplace transformations, solve the differential equationy"(t) + y(t) = -14,y (0) = -14,y' (0) = 9.y(t) =96(8-3)5a ΩαΩSubmit AssignmentBack Question MenumEQuit & SaveNext

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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EVE Online is a space-based multiplayer game, where players use spaceships to engage in combat, industry, exploration and other activities. Players can design their own ships, incorporating ship systems that affect a range of different critical variables. In combat situations, one such critical variable is ”capacitor recharge rate”: the capacitor stores energy used for activating both offensive and defensive ship systems. A spaceship that runs out of energy rarely survives for long. The capacitor recharge rate varies with how full the capacitor is currently. The recharge rate is determined by the differential equation dC/dt = 10 M/T [√(C/M) − C/M] where M is the capacitor’s overall capacity for holding energy (measured in gigajoules, GJ), and T is the time (measured in seconds, s) taken to recharge from zero to a standardised fraction of M. a) Using Rolle’s theorem, infer that there is a maximum value for dC/dt for some C ∈ (0, M). b) Treating M and T as constant, show that dC/dt is at…
3. A political toy company manufactures stuffed donkeys and elephants using cotton and polyester. At present, 40 units of cotton and 30 units of polyester are available. A donkey sells for $4 and requires 1 unit of cotton and 1 unit of polyester. An elephant sells for $5 and requires 2 units of cotton and 1 unit of polyester. Formulate an LP that will help the company maximize profit.
Fertilizer is sold in 100 pound bags labelled with the amount of nitrogen (N), phosphoric acid (P2O5), and potash (K2O) present. The mixture of these nutrients varies from one type of fertilizer to the next. For example, a 100 pound bag of Vigoro Ultra Turf fertilizer contains 29 pounds of nitrogen, 3 pounds of phosphoric acid, and 4 pounds of potash. Another type of fertilizer, Parker's Premium Starter, has 18 pounds of nitrogen, 25 pounds of phosphoric acid, and 6 pounds of potash per 100 pounds. Determine the total amount of nitrogen, phosphoric acid, and potash in the mixture of 200 pounds of Vigoro and 300 pounds of Parker's. The mixture contains pounds of potash. pounds of nitrogen, pounds of phosphoric acid, and
Preventing heart attacks: Medical researchers performed a comparison of two drugs, clopidogrel and ticagrelor, which are designed to reduce the risk of heart attack or stroke in coronary patients. A total of 6650 patients were given clopidogrel, and 6710 were given ticagrelor. Of the clopidogrel patients, 650 suffered a heart attack or stroke within one year, and of the ticagrelor patients, 580 suffered a heart attack or stroke. Can you conclude that the proportion of patients suffering a heart attack or stroke is less for ticagrelor? Let p, denote the proportion of patients suffering a heart attack or stroke with clopidogrel and p, denote the proportion of patients suffering a heart attack or stroke with ticagrelor. Use the a=0.01 level of significance and the critical value method. Part 1 of 5 State the null and alternate hypotheses. Ho: P1= P2 H: P1> P2 This hypothesis test is a right-tailed test. Part 2 of 5 Find the critical value(s). Round the answer(s) to two decimal places. If…
Freddy is the owner of Freddy’s fast fuel for Small Aircraft specializing in “Providing flight fit fantastic fuel” for small general aviation aircraft such as a Cessna 172. Freddy is experimenting with a fueling process involving new equipment and is trying to determine if the current process takes more time than the new process with the new equipment he is experimenting with. If the current process takes more time than the new process, Freddy will purchase some new, rather expensive fueling equipment to use across several small general aviation airports his company services. Freddy is comparing sample mean times to evaluate his hypothesis about the population (total number of aircraft fuel fill-ups). Over the period of a week, he took a random sample of fuel fill-up times using both the old and new processes. Using the information Freddy provided, you ran a t-test for independent samples. These are the results (α = .05). t-Test: Two-Sample Assuming Unequal Variance Current…
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Three competing brands of cerial are being sold in the school cafeteria. Brand z's weekly sales are affected by the sales of the other two proucts. For each $1 increase in brand æ's sales, there is a decrease $0.80 in sales of brand z. Similarly, each $1 increase in brand y's sales, there is a increase $0.10 in sales of brand z. If the current sales for brand z, y, and z are $45.00, $69.00, and $76.00 respectively, write an equation for z's sales in terms of a and y.
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Scenario“A car manufacturer produces two versions of its popular medium sized model: a hatchback aimed at the family market and a coupe designed to appeal to affluent single customers.Both are based on the same chassis and differ only in the body kit used to make up the cars. They are both produced at the same factory.There are 95,000 hours of manpower and 8,900 basic chassis units (one per vehicle) available each week. The hatchback takes 4 hours of assembly time while a coupe takes 6.5 hours.At least 1,000 coupe models should be produced per week.Production is also constrained by the fact that owing to problems with a supplier only 34,000 door handles are available per week. A hatchback uses ten of these handles while a coupe uses four.The profit to the factory on a hatchback model is estimated to be £3,450 while the profit on a coupe is £975.The market demand for the cars is high. It is known that demand will exceed production for time to come so they should be able to sell whatever…

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