For the following second-order process with numerator dynamics, solve for the time-domain output response to a step input change of magnitude Au at t=0. 8p(s) = k₂(TS+1) (7,5+1)(T2+1) For k₁ = 1°C/Lpm, T₁ = 3 min, t₂ 3 min, t₂ = 15 min, T, = 20 min find the peak tem- perature and the time that it occurs.

Some of the highest tides in the world occur in the Bay of Fundy on the Atlantic Coast of Canada. At Hopewell Cape the water depth at low tide is about 2.0 m and at high tide it is about 12.0 m. The natural period of oscillation is a little more than 12 hours and on June 30, 2009, high tide occurred at 6:45 a.m. This helps explain the following model for the water depth D (in meters) as a function of time t (in hours after midnight) on that day: D(t) = 6 + 7 cos(0.503(t - 6.75)). How fast was the tide rising (or falling) at the following times? a. 6:00 a.m. b. 2:00 p.m.

The concentration of acid in a battery is given as a function of time by dx/dz = 37.5 - 3.5x At the initial time, t = 0, battery concentration = 50g/L. Determine the battery concentration after three minutes utilizing Runge-Kutta fourth order method and a step size of, h=1.5min.

1/18 csc 9nt cot 9t dt /1/54

Assume that the dynamics of caffeine absorption are given by Ct+1 = 0.87Ct , where t is time in hours and Ct is the concentration of caffeine. If C0 = 1000, estimate the time needed for 80% of the caffeine to be eliminated from the body (i.e. 20% left). What if C0 = 500?

A tank contains 460 gallons of water and 45 oz of salt. Water containing a salt concentration of 1/7(1+1/4sint) oz/gal flows into the tank at a rate of 9 gal/min, and the mixture in the tank flows out at the same rate. The long-time behavior of the solution is an oscillation about a certain constant level. What is this level? What is the amplitude of the oscillation? Round the values to two decimal places. Plz correct solution.

The lost value of equipment over a period of time is called depreciation. The simplest method for calculating depreciation is straight-line depreciation. The annual straight-line depreciation D of an item that costs x dollars with a useful life of n years is D= (1/n)x. Find the depreciation for items with the given characteristics. %3D Cost is $15,957; life is 13 yr The annual straight-line depreciation is approximately $ per year. (Round to the nearest cent.) Enter your answer in the answer box. MacBook Air 80 888 esc F10 FI F2 F3 F4 FS F6 F7 @ 23 $ & 6 8 9 %3D 1 2 3 4 5 Q W E Y P tab 11 A S F G H. J K ock レレ

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6. As blood circulates through our bodies, at any given time we have some volume of blood within vital organs. A researcher measured the rate of change in the volume of blood (in liters) per minute flowing through a liver. She obtained the following relationship: V = 0.8+ sin(2t - 7), where at t = 0, V(t) = 0.75. Find the blood dV dt volume as a function of time.

If f'fl. 1.2 f(x) dx = 7.2 and X and [Rx) dx = 5.6, find [°F(x) dx. Enhanced Feedback Ic Ch Ch