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Differential Equations and Linear Algebra (4th Edition)
- A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at timet (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt-and-water solution being poured into the tank alternately gets faster and slower. a) Show how the following differential equation describe the salt concentration s in the solution at any time t. Show full solution ds 0.2(1 + cos 2t)? dtarrow_forward3. a) Solve the following two equations. In(x – 2) – In(x + 3) = 1 i) ii) 4x-2 = 3x+3 b) An amount of OMR 1500 is deposited in a bank at an annual rate of 4% interest compounded continuously; find the number of years after which the amount will become OMR 1700.arrow_forwardUCLAium-1919 is a radioactive element with a half-life of 140 days. Suppose that 10 mg of the element are placed in a lead container. Let y(t) represent the number of mg present t days later. Give exact answers only for all parts. No decimals, no rounding. The equation that represents the number of mg present t days later is y(t) = How many mg will be present after 10 weeks? Answer = In how many days will it take for 70% of the original sample to decay? Answer =arrow_forward
- 4. The growth rate of a colony of ants is given by the formula 10t 2 (1+t²)² where t is measured in hours. If 100 ants are initially present then how many are present after 2 hours? The number of ants present after 2 hours isarrow_forwardThe pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.31T, where P, V, and I are all functions of time (in seconds). At some point in time the temperature is 310 K and increasing at a rate of 0.05 K/s and the pressure is 14 and increasing at a rate of 0.07 kPa/s. Find the rate at which the volume is changing at that time. L/Sarrow_forwardSolve the following the initial value problem x=11² x x(0) = = [2]arrow_forward
- Suppose a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.arrow_forwardA 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at time t (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt- and-water solution being poured into the tank alternately gets faster and slower. Determine which of the following differential equation describing the salt concentration S in the solution at any time t. O A. dS dt OB. dS dt OC. dS dt O D. dS dt = 0.2(1 + cos 21) ² = = = -0.2(1 + cos 21) ² 0.2 (1 + cos 21) ² 0.2 2 (1 + cos 21) ²arrow_forwardA 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at time t (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt-and-water solution being poured into the tank alternately gets faster and slower. If the tank is just meant to contain the solution, determine the concentration of salt, in kilograms, if the controller was only opened for half an hour. Express your answer accurate to four decimal places.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage