## Solving Critical Points on Maple?...

Hi,

Ive been trying to solve critical points for maple but i keep getting this werid equation:

(1/7)*RootOf(tan(_Z)^2+4*_Z*tan(_Z)+4*_Z^2+28*tan(_Z)-140*_Z-1176)+1+(1/14)*tan(RootOf(tan(_Z)^2+4*_Z*tan(_Z)+4*_Z^2+28*tan(_Z)-140*_Z-1176)).

What I have typed

f:=x->(7-x)*sin(x^2-7);

f1:=D(f);

When I try putting:

solve(f1(x)=0);

I get that werid equation

## Euler's Method on Aircraft...

Hi, I am working on an assignment and I am having difficulties with this Eurler method since I am working with vector.

The assignment:

If the aircraft's engine transmits power P to the air, the force of the propellar, Fp, satisfies P=Fpv. Since the force Fp acts in the direction of motion, it can be written in vector form as: (what I have so far)

with(linalg);

v:=Vector(2,1,[vx,vy]); velocity vector

nu:=v->Norm(Vector(v),2); (length of v)

Fd:=-1/2*C*rho*A*nu*v # air resistance

Fl:=1/2*Cl*rho*A*nu*v # liftforce in y direction here v=[-vy,vx]

Fp:=(P/nu^2)*v^2 # power from aircraft

All this adds up to:

F_T:=v->Vector(evalm(Fp/nu(v)^2*v+Fd*nu(v)*v+Fl*nu(v)*zip((x,y)->x*y,v([2,1]),Vector([-1,1]))+Vector(2,1,[0,-m*g]))); # I have tried it and it works

so up til here I am good. It is this next part that I can't seam to get.

Write a routine which uses Euler's method to solve the equation of motion numerically for velocity v(t):

m*dv/dt=F_T(v)

Test the program by trying a plane with intitial velocity [v0,0] such that it maintains this speed when the engines power is P=P0

We have been given an Esolve we can use:

Esolve:=proc(f::procedure,h,x0,y0,N::integer) # Calculates y(x0+n*h) for n=1..N given y0=y(x0) and f(x,y)

local n,y,x;

y[0]:=y0; # Start Value
x:=x0;

for n from 1 to N do
y[n]:= y[n-1]+h*f(y[n-1],x); # Euler's formula
x:=x+h; # Next x
end do;

y;

end proc;

If anyone could help me understand how it works and how to get this to work with vectors I would be very gratefull.

## math problem!! (Newton's method)...

 Consider the following function.f (x) = ( x3 − 442x2 + 65107x − 3196058) e1/x f:=x->(x^3-442*x^2+65107*x-3196058)*exp(1/x);
 Use Newton's method to find all 3 roots (correct to at least 6 decimal places) of f (x). (Note that you might have to increase the 'Digits' variable to 15, i.e., Digits:=15, in order to get the required accuracy.)

my answer are 143.2030067,143.2030339,143.2030610

but, it is wrong. can anyone tell me where is the wrong part?

## plot a 2D arc in a coordicates which is in 3D coor...

In a local coordivates frame {B}, an arc whith center "coc" ,radius "radius" and angle between “alpha1” and “alpha2” can be plotted in XY plane of {B}. The coord {B} is in a Ref frame {O}. The homogeneous transformation matrix is “H”. How can I plot this arc in coordinate {O}？

## How to use Verlet algorithm to derive the orbit of...

Derive the orbit of the Moon around the Earth by doing a Verlet algorith of Molecular Dynamics simulation. Use one hour for your step τ. Place the stationary Earth at the origin of the Cartesian system. For initial conditions, use the position and the speed of the Moon when it is at its apogee (furthest from Earth). Plot the orbit.

## How to solve Cauchy sequences...

(a) Show that if {an} ∞ n=1 is Cauchy then {a 2 n} ∞ n=1 is also Cauchy. (b) Give an example of a Cauchy sequence {a 2 n} ∞ n=1 such that {an} ∞ n=1 is not Cauchy

## How to compute direct exponentiation of the matrix...

Hi EveryOne!

In the the answer of the question "How to find k^th root of the given matrix over finite field (at URL: http://www.mapleprimes.com/questions/203997-How-To-Find-Kth-Root-Of-The-Given-Matrix#comment215683). Carl Love helped to find k^th root of the given matrix M over GF(2m)/f(x).

Now, I need to compute direct exponentiation of the given matrix M in finite field. (If M = [mi,j], we say Direct Exponent (element-wise exponent matrix), Mdk of M is a matrix whose each element is the result of exponentiation of corresponding elements of M. If k=2, then we say Md2 is a direct square matrix of M )

## sequence convergence and limit...

Determine wether the sequence below converges or diverges, and if it converges, find the limit.

and,

Thanks

## varying initial conditions...

Restrict calculation to real numbers.

Using y' = u, express the oscillator equation: y" + 3y' + 2y = cos(t) as a first order system.

Plot an approximate solution curve for the specified initial conditions.

[x0=5, y0=1],[x0=-2, y0=-4],[x0=0, y0=.1],

This is what i have so far but i am not sure if its correct.

Eulers modified method:

with(RealDomain);

x[0] := 0;

y[0] := 5;

t[0]=0

h := .1;

for n to 100 do

x[n] := x[n-1]+h*(x[n-1]+y[n-1]);

k1 := x[n-1]+y[n-1];

k2 := h*k1+x[n]+y[n-1];

k := 1/2*(k1+k2);

y[n] := h*k+y[n-1]

end do;

data := [seq([x[n], y[n]], n = 0 .. 100)];
G1 := plot(data, style = point, color = "blue");
G1;

## how do you find the horizontal asymptotes?...

1. Work with the function

f(x) = 5x^2-125/x^2-16

1. Find the horizontal asymptotes
2. Draw the graph of the function.  Show all horizontal and vertical asymptotes on your graph.  Edit the domain and the range to get a “good window” that clearly shows the shape of the function and all the important features, such as zeros, intercepts, maxima and minima, horizontal and vertical asymptotes.

## Maple Help ASAP...

I am new to maple and I need help.

Let x=x(t) and y=y(t) be functions in t. Suppose that x'=2x−5y+t and y'=4x+9y+sint such that x(0)=y(0)=0. Find y(1).

How do I go about doing this question?

Thanks

## How to find k-th root of the given matrix over fin...

Hi EveryOne!

In the the answer of the question "How to find roót of polynomial in finite field and extension finite field (at URL: http://www.mapleprimes.com/questions/203977-How-To-Find-Roots-Of-Polynomial-In-Finite#answer215097). Carl Love helped compute eigenvalues (x1,x2,...,xn)and eigenvectors of the given matrix M over GF(28)/(y^8+y^4+y^3+y+1).

I need to do:

1. Get matrix D from these eigenvalues (x1,x2,...,xn), with D[i,i] = xi and D[i,j≠i] = 0 (D will be diagonalizable matrix. Some xi may be in extension finite field  GF((28)2))

2. Get matrix P from eigenvectors corresponding to the above eigenvalues, compute P-1

3. Compute matrix B = P x D1/4 x P-1 in  extension finite field  GF((28)2).

## Mathematical model of time-variant temperature dis...

My task is to develop a mathematical model of time-variant temperature
distribution in a bar with Maple.
The bar is made of aluminum. The length is 202 mm and the diameter
is 8mm.
Heat is supplied from the kitchen lighter where the flame burns on butane.
The height of the flame is about 4 mm.
Your model should be able to answer how long the time it takes to reach
a certain value of temperature at the distance of 10 cm from the heat source.

anyone can help to answer this? im totally new to maple.. hopefully some1 can help me to answer this..

## MultiCalc Optimization ...

Please see attached document.

The 2 bits of data I am working with are a Constraint Function and Objective Function:

I need some pointers on how to do this. I keep getting solutions of

and I am ont receving an x value for some reason and leaving me unable to continue with the problem.

If anyone can send me some code I would be grateful. If anyone would like to send the correct full working code so I can see how to do this and review it I would be grateful.

Code I had so far was:

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