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Contrast the behavior of functions and expressions by performing the following commands.
a)Define a function f equal to x^3 and Define an expression g equal to x^3
b) Evaluate f and g at 2.
c) Evaluate f and g at y.
d )Assign the value 2 to x. Evaluate f and g.

I want to solve following PDE question with forward difference method inn Maple. Can you help me please?


du/dt=d^2u/dx^2, 0<x<2, t>0


u(0,t)=0, u(2,t)=0


Use h=0.4 and k=0.1. and compare your answers at  t=0.5 to the exact solution u(x,t)=exp(-4*pi^2*t)*sin(2pi*x). Then use h=0.4 and k=0.05,and compare the answers. 

Three families grow vegetables in their backyards,and agree to form a small closed economy by sharing their produce. family andrews grow artichokes, family brown grows beans and family Cuthbert grows corn.Family Andrews receives 70% of its artichokes, 30% of the beans and 30% of the corn.Family Brown receives 20% of the artichokes,60% of the beans and 10% of thr corn.Family Cuthbert receives the remainder of the vegetables.

a) Write down the exchange matrix A.

b) If production is measured in doolars ,define the variables
 of the production vector X.

c) Find all solution of the Leontief closed with matrix equation (I-A)^-1¤X=0.

d) If family Cuthbert produces $100 worth of corn, how much will familes Andrews and Brown need to produce (in dollars) in order foe the economy to be in equilibrium?


Please respond me by email, thanks.


Here is the original question , replaced by the questioner.  She/he must not do such things.





The differential equation dy/dt = t / (2-y), y(0)=1 fails the tests in section 5.1 at y=2. [ f(t,y) is undefined at y=2 and the y-partial derivative of f(t,y) is also undefined there. ] If a solution stays away from y=2, there is no problem at all. Try a few different initial conditions and summarize your findings. Use the Runge-Kutta order 4 method with a fixed step size.

Hint: You may find Maple's solution of the differential equation helpful:

s1 := dsolve({diff(y(t),t)= t/(2-y(t))}, y(t)); 

In the solution _C1 is a constant to be determined using the initial conditions.

An economy consists of service and food sectors. Assume that to produce $1 worth of service consumes 50 cents worth of service and 20 cents worth of food,and to produce $1 worth of food consumes 40 cents worth of serives and 20 cents worth of food. Assume that there is an external demand for $2 million worth of serices and $12 million worth of food.

a)Determine the comsumption matrix C for this economy.

b)In order to satisfy the demand, how much of each must be produce?(Find the production vector that will satisfy the demand.)

c)For this production vector, what is the value of serices that is consumed internally by the food industry ?


I'm in desperate need for help!! For an assignment, we were asked to "write out our first and last names" in maple, using correct upper and lower case letters. I am clueless on how to approach the assignment. Is there anyone that could help me?

when a user liked a particular photo for the first launch of a mobile app, and the time different where by the event started and stoped was k seconds which is at constant (does not change). At this constant thus triggered the like application operation or function that was connected to the application server. Then later the user unlike the photo and the same event and operation was carried out at of (k + 2) seconds. The time variation that was carried out during the sequential or running loop event carried out by 2 seconds.

check if this derived equation is correct first f(Xn) = en(Xn + Xn+ 1) . if its correct do the second question.

what is the rate at which the operation will be finish given an equation f(Xn) = en(Xn + Xn+ 1) 

[A restatement, from my memory, of the essential detail of the original, deleted, question.--Carl Love as moderator]

1) a) Compute a primitive 4th root of unity modulo 29. Note that the command numtheory:-rootsofunity(p,r) will not work for this.

1) b) Compute the inverse of the root found in (a).

2) Letting omega be the root found in 1 (a), compute the matrix of the Discrete Fourier Transform DFT[omega] and the matrix of the inverse transform DFT[omega^(-1)]. Show that the product of these matrices is 4I (I being the identity matrix).

[A restatement of the essential details of the original, deleted, question from my memory.--Carl Love as moderator]

1) Compute the square root of 2 mod 3^8.

2) Compute the cube root of 2 mod 625.

Hi, I have encountered a difficult question.


My answer is A=151,B = 47.

Could anyone tell me whether this answer is correct?


The question is as follow:

Pi=∑((120n2+An+B)/(16n((512n4 + 1024n3 + 712n2 + 194n + 15))  (n starts from 0 to infinity)


Thanks in advance.

Need help with starting this question. Thanks!

If a sequence is defined by X0=0, X1=1, X2=2 and Xn=n(Xn-3+Xn-2+Xn-1), n>=3

How many digits will X2013 have?

I have no idea how to start to answer this question. Please help Thanks!

Let G(x) denote the no. of ways of representing n as the sum of two prime numbers.

For eg, G(10)=2: where 10=3+7=5+5

           G(20)=2: where 20=3+17=7+13

           G(30)=3: where 30=7+23=11+19=13+17

How do you find G(10 000 000)?

I'm having problem dealing with this question on Maple and would appreciate any help possible.

If f(x) = x/2, if x is even
   f(x) = 3x-1, if x is odd

which sequence will 2013^1102 fall in


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