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Differential Equations: An Introduction to Modern Methods and Applications
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- This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.If a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as the following. Therefore, when t = 5, the rate at which the water drains is V'(5)arrow_forwardSome diseases are lethal; not every individual infected by the disease will recover; some will die. Assume that in one unit of time a fraction m of infected individuals will die (m is called the mortality rate). We will moreover assume that the habitat this population lives in is at its carrying capacity. If no individuals die, then no reproduction occurs. However, if individuals die, then resources are freed up and more individuals will be born. Assume that individuals are born at a rate that exactly equals the rate at which individuals are lost due to the disease. In the given problem you will analyze models for lethal diseases. In the given problem you should assume that infants are initially uninfected by the disease but are also not immune to it, so new individuals added to the population are all in the susceptible class. In this problem we will determine the stability of equilibria in an SIRS model that includes mortality. Consider a population of size N = 400. The SIRS model…arrow_forwardA museum contains a large pendulum. Due to air resistance and friction, each swing of the pendulum is a little shorter than the previous one. Suppose the first swing of the pendulum has a length of 25,000 mm and each return swing loses 4% of its length until eventually the pendulum comes to a complete stop. Answer parts A, B, C, and D and if necessary, round to the nearest tenth of a millimeter. A. Let 'n' be defined as the number of swings the pendulum travels. Define 'a1' and 'r' (these are used in the explicit formula.) Write a geometric sequence in summation (Sigma) notation to express the total distance that the pendulum will have traveled after 30 swings. Sigma notation will have a lower limit, an upper limit, and an explicit formula. Do not compute the sum. B. Use the summation formula to find the total distance the pendulum swings. C. Using information from part A, write a geometric series in summation (Sigma) notation to express the total distance that the pendulum will have…arrow_forward
- How many days would a 67-unit construction activity lasts if this activity have a parameter of 0.9manhours per unit would last and that there's only 9hrs per day allotted to construction work. Neglect any additional allowances for overtime.arrow_forward2. Theorem LF = LD = G 63 Earrow_forwardIf an antibiotic is taken orally, only a fraction of the antibiotic is actually absorbed in the bloodstream. This fraction is called bioavailability of the dose. Suppose that for a specific antibiotic, when a mg is taken orally, only 50% of the dose is absorbed, that is the bioavailability can be expressed as 2 I. Now, if h mg of antibiotic enters the bloodstream, the amount eventually absorbed at the site of the infection 4h is g(h) = mg. h+ 4 !! Finally, if g mg is absorbed into the site of the infection, the number of surviving bacteria is given by 3000 f(9) = CFU (colony forming units). %3D 9+g? a) If a dose of 8 mg is given orally, compute the amount of antibiotic absorbed at the site of infection. An er: mg. Round to 1 decimal place as needed. b) If an amount of 7 mg enters the bloodstream, compute the amount that is eventaully absorbed at the site of the infection. Answer: mg. Round to1 decimal place as needed. c) If a dose of 6 mg is injected directly into the bloodstream…arrow_forward
- A pasta company with a blue box produces 1,400 tons of semolina pasta per day. The pasta is fed into a machine as a large, loose dough and then squeezed through a bronze die to form a desired shape. As the pasta is squeezed through the die, the volume of space it takes up decreases while the mass remains constant, and thus the resulting shape is more dense. If m is the constant mass of the pasta in grams and V is the volume of the pasta in mL, then the density p is given by p= - m (a) If the mass remains constant while the volume changes with time, find dp dt (b) Suppose the mass of the pasta is 80g, the density is 0.8 g/mL, and the volume is decreasing at a rate of 400 mL/sec. How fast is the density of the pasta changing at that moment? mL · secarrow_forwardSuppose that each year, 80% of residents living in state A stay in state A, while 20% of them move to state B. Also, 70% of the residents living in state B stay in state B, while 30% of them move to state A. Further, assume at t = 0 years, there are 2 million residents living in state A and 5 million residents living in state B, and let xn and yYn represent the populations (in millions) of the states A and B, respectively, at time t = n years. Given that (:) - (: )() Xn a b Yn d 5 find the value of the number h.arrow_forwardshow full and complete procedurearrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning