For Problems 31-34, sketch the given function and determine its Laplace transform.
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EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- Repeat the previous exercise to find the formula forthe APY of an account that compounds daily. Usethe results from this and the previous exercise todevelop a function I(n)for the APY of any accountthat compounds n times per year.arrow_forwardKind the haplace transform of f(t)=78(t-½) Cost.arrow_forwardA tank contains 1000-gallon of pure water. Starting at time t = 0, a solution containing 0.2 lb of salt per gallon enters 10 gallons per minute and the well-stirred solution is withdrawn at a rate of 5 gallons per minute. Set up the initial value problem for the amount of salt, Q(t), in the tank as a function of t. Sove for Q(t).arrow_forward
- I need the answer as soon as possiblearrow_forwardIn the previous Problem Set question, we started looking at the position function s(t)st, the position of an object at time tt . Two important physics concepts are the velocity and the acceleration. If the current position of the object at time tt is s(t)st, then the position at time hh later is s(t+h)st+h. The average velocity (speed) during that additional time hh is (s(t+h)−s(t))hst+h−sth . If we want to analyze the instantaneous velocity at time tt, this can be made into a mathematical model by taking the limit as h→0h→0, i.e. the derivative s′(t)s′t. Use this function in the model below for the velocity function v(t)vt. The acceleration is the rate of change of velocity, so using the same logic, the acceleration function a(t)at can be modeled with the derivative of the velocity function, or the second derivative of the position function a(t)=v′(t)=s′′(t)at=v′t=s″t. Problem Set question: A particle moves according to the position function s(t)=e5tsin(7t) Enclose…arrow_forwardanswer quickly as soon as possiblearrow_forward
- Consider the following function. √x, (1, 1) (a) Find an equation of the tangent line to the graph of f at the given point. y = (b) Use a graphing utility to graph the function and its tangent line at the point. 2- y 1- -1 FK KE 2- y 1- 3 4 5 -1 0 1 O -1 -1 y y 3 2 1- 0 2- 1 2 1 2 2 3 4 4 5arrow_forwardFind the libraries toon L(x) of the functions at a.arrow_forwardAccording to Newton's Law of Cooling, the temperature T of an (as a function of time t) is given by T(t) = T, + D,e, where k is a positive constant, and D, is the difference between T(0) (the temperature at time t = 0) and T, (the temperature of the surroundings). If a bowl of soup with temperature 210 degrees Fahrenheit is set down in a room with temperature 65 degrees, after how many minutes will the soup's temperature reach 100 degrees? = 0.05] 10. [for this soup, assume karrow_forward
- Q3. Define the function shown in figure as f(t) and then take Laplace transform. 1arrow_forwardA clock is hung on a wall so that the center is 20 cm below the ceiling. The minute hand is 10 cm long, and the hour hand is 6 cm long. Find a function h(t) that gives the distance the tip of the hour hand is from the ceiling as a function of minutes past midnight. The function should have the form h(t)=Asin(Bt−C)+Darrow_forwardA. Find the Laplace transform of each given expression, all letters except a, t, and 6 are constant. You may use the table. (1) t3 + 8(t-3)+ sin(wt) (2) + x +t sin (3t), where x= x(t), a function of time with initial conditions (0) = x(0) = 0arrow_forward