where h is the height of the water, t is time (in sec) and g is gravitational acceleration = 9.8 m/sec?. Find the level of the water in the tank at t = 3 sec using Ralston's %D method with 2 iterations.

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A: Given,

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A: To determine the value of r so that the population of fish remains constant.

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Q: Lets assume that y(t) represents how many fish are harvested in month t. Solve dy/dt =1/(y+yt2) with…

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Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: Suppose The problem of intial values y = log (x+y), y(a) = 2 How often is. The modified Euter method…

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Q: A 80-kg cyclist on a 19-kg bicycle starts coasting on level ground at 30 m/sec. Use v = vo e (-k/m)t…

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Q: Q5; Use three iteration of Picard's method to solve = 3x+ y' when x=0.1, given that y 1 dx for x=0.

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Q: new fast-rood firm predicts that the number or anchises for its produc Will grow at the rate dn =…

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Q: You bail out of a heicoptor and immediately pull the ripcord of your parachute. Your downward…

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Q: For a given function ƒ, explain the steps used to solve the initialvalue problem F '(t) = ƒ(t), F(0)…

A: Consider the following differential equation: F't=ftdFtdt=ftdFt=ftdt Integrate the above equation:…

Q: When a switch is closed in a circuit containing a battery E,a ersistance R and an inductance L,the…

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Q: The concentration of pollutant bacteria e in a lake decreases according to c = 70 e 1.5t + 25…

A: Given c = 9, then 9 = 70e-1.5t+25e-0.075t, we can rewrite it as f(t) = 70e-1.5t+25e-0.075t-9

Q: Q2: Use Runge-Kutta (fourth order) for two iterations to find the solution of the initial value…

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Q: Find the temperature u(x,t) from the heat equation in a laterally insulated copper bar 80cm cm long…

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Q: A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall…

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Q: (c) Suppose instead that we have a rectangular tank containing the same volume of water (pictured…

A: c Volume of cube =8m×1.5m×3m=36m3 volume of water =12×3×3×8=36m3 Volume of water is equal to volume…

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: Apply Newton’s method twice to approximate 7^(1/3) . Use the initial approximation x0 = 2

A: We have to find the approximation of the expression 713 and we have to use the Newton Raphson method…

Q: The velocity v of a falling parachutist is given by gm v = C where, g = 9.8 m/s². For a parachutist…

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Q: If a baseball is thrown upward with a velocity of 45 m/s, its height in meters t seconds later is…

A: We know that, Average velocity          = change in position/time elapsed.

Q: You ARE TESTING A DECRSTINE CLOCK, TO POSSIBLY BE MANUFACTURED BY YOUR CONSUMER ELECTRONICS…

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Q: A population of E. coli bacteria will grow at a rate given byw′(t) = (3t + 2)1/3,where w is the…

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Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y() is the solution of the problem ₁…

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Q: A 400 - V, 10 h.p (metric), 3 - phase synchronous armature resistance and a synchronous reactance of…

A: Solution...

Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

A:

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: A 32-lb weight stretch a spring 2ft. At t = 0, the mass is released 1 ft above the cquilibrium…

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Q: Solve y”+2y’+y=e^t using a power series

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Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A:

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: The number of franchises for its products will grow at the rate  dndt=4t+1 where t is the number of…

Q: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

A: The number N(t) of supermarkets throughout the country that are using a computerized checkout system…

Q: Given the acceleration of a particle is a(t) = . If the initial velocity is v(0) = , find the…

A:

Q: The population of a city (in millions) at time t (in years) is P(t) = 2.4e0.007t When will the…

A: find the value of t when population is double from what it is when time is zero.substitute value of…

Q: An oil storage tank ruptures at time t =0 and oil leaksfrom the tank at a rate of r(t)  = 100e-0.01t…

A: Given: Oil leaks from the tank at the rate r(t)= 100e-0.01t liters per minute. we have to find how…

Q: Q2 The rate of heat transfer of a body can be express as: dT = -k(T – Ta) dt where T= temperature of…

A: Using Euler's method we can find the solution, the initial values are t0 = 0 and T0 = 90°C The…

Q: Q2: Use Runge-Kutta (fourth order) for two iterations to find the solution of the initial value…

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Q: The bacteria concentration in a reservoir varies as C 3e-1.4t + e-0.2t Using Newton- %D Raphson…

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Q: (a) Integrate x ln(x + 1)dx analytically; and numerically using (b) trapezoidal rule with iterations…

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Q: A 50-gal barrel is filled completely with pure water. Saltwater with a concentration of 0.3 Ib/ga…

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Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

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Q: Suppose that a change in biomass B(t) at time t during the interval [0,5] follows the dB equation…

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Q: Find the fourth iteration value of an extremum (maximum/minimum value) of 3 f (x) =acos (bx) +cx+d…

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Q: 3 Q2. Find an approximation to V11 using 4 steps Newton's method.

A:

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.