Problem 6.5 Find the Hamilton-Jacobi-Bellman equation for the sys- tem i1(t) = x2(t) &2(t) = -202(t) – 3.x3(t) + u(t) with the performance index as 1 J : rtf dt.

Q: Suppose that  dP dt  = 0.19P(t)  represents a mathematical model for the growth of a…

A: The objective of the question is to find the rate of growth of the cell culture when the size of the…

Q: 4. The acceleration of a particle is modeled by the function a(t) = t³ – 61² – 37t – 30 where t is…

A: Please see the answer below.

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Q: Suppose A = A(t) represents the amount of money in a bank account where t is time in years Given dA…

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Q: Example 10.14. Apply Runge's method to find an approximate value of y when x= 0.2, given that dy/dx…

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Q: In 2 I = t-2 e(-1/t) dt

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Q: Evaluate the following: a. [₁₂ (6 + e ²¹) 8(t - 4) dt = [ b. ₁ (6 + e ²¹) 5(t− 8) dt = [ c. L₁ (6 +…

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Q: M₁ = -0.85-fe`·a·b· (d-2) 200 106 = 0.9.0.85-20.7. a 300-480- 2)

A: Sol:- Let  f(a)=0.9⋅0.85⋅20.7⋅x⋅300(480-a2)-200⋅106∴f'(a)=4750.65⋅(480-a2)-2375.325aLet ; a0=951st…

Q: Calculate the following anti derivatives

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Q: Solve this problem on separate paper. Show all supporting work and include units on your solutions.…

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Q: Biologists are modelling the population of an endangered species of fish in a river system. The…

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Q: 1. A hot metal object is submerged in a large tank of water held at temperature 25° c. Let y(t) be…

A: SOLUTION-

Q: he projected world population (in billions of people) t years after 2000 is modeled by the function…

A: To find: The value of r if the expected population for the year 2012 is 7 billion. Given: The…

Q: Suppose that dP/dt = 0.19P(t) represents a mathematical model for the growth of a certain cell…

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Q: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation…

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Q: The gas equation for one mole of oxygen relates its pressure, P (in atmospheres), its temperature, T…

A: We need to find T and dT.

Q: Show by change of variables that T(x) ₁²²-1₁-²² = 2√₁ 1²²-¹6-²³ dt = 1²e²¹e²" du. Love ехи ее u

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Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: •1 1 g(x) = dt 2x In(t + 1)

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Q: 3. A hot coffee with temperature 90° C is placed in living room with temperature 26°C. After 5…

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Q: At any time t 2 0, in hours, the rate of growth of a population of bacteria is given by dy/dt =…

A: A differential equation of the form dydt=ky can be solved by separation of variables. This equation…

Q: Solve the problem. The population P of elephants in a wild animal preserve changes with time (in…

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Q: Exercise 1.4.4: Solve y' + xy = x.

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Q: If the position of a moving particle at any time t' is defined by s(t) = t - 2t2 + 13. Then the…

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Q: A body whose temperature is 180°C is cooled by immersing in a liquid at 60°C. In one minute, the…

A: The given rate of change in temperature (T) at time t is: dTdt=-kT-60 Also, it is given that the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.