question 2 of my homework is actually abit more simple imo. i think i performed all the operations correctly but however my 3dplot shows just a flat plane. i dont think thats right. if someone could take a look at my code in reference to this question. it would be great.

Suppose that a baseball is hit from 5 feet off of the ground with an initial velocity of 40 feet per second at an angle of above the horizontal. Let the horizontal and vertical components of the position, velocity, and acceleration be denoted respectively by and . Assume that the only acceleration is due to gravity (i.e, ).

a) If , plot the parametric equations over the time period that the ball is in the air.

b) Clear in maple by typing theta:='theta'; Now, suppose that we write in Cartesian form by solving for t: t:=solve(rx=x,t); Typing in ry should now yield a function that involves only x and . Make a 3-dimensional plot of for , 

ax:=0;ay:=-32;
0
-32
vx:=int(ax,t)+C1;
C1
vy:=int(ax,t)+C2;
C2
v0:=40;
40
theta:=Pi/3;
1
- Pi
3
C1:=solve(subs(t=0,vx)=v0*cos(theta),C1);
20
C2:=solve(subs(t=0,vy)=v0*sin(theta),C2);
(1/2)
20 3
vx; vy;
20
(1/2)
20 3
rx:=int(vx,t)+C3;
20 t
ry:=int(vy,t)+C4;
(1/2)
20 3 t + 5
C3:=solve(subs(t=0,rx)=0,C3);
0
C4:=solve(subs(t=0,ry)=5,C4);
5

ry;
(1/2)
20 3 t + 5
plot([rx, ry, t = 0 .. infinity]);

Hi,

I have an ode like this

ODE:=(diff(T(x), x, x))+P*(S+a*(1-exp(-L*x))/L)*(diff(T(x), x))=0;

bcs:=T(0)=1,T(infinit)=0;

where P, S, L a, are all constants.

let assume that 

z=P/L^2*exp(-L*x);

subing z into the ode, we can have

ode1:=diff(T(z), z$2)+(1+z*a-P)*(diff(T(z), z)) = 0;

bcs1:=T(P/L^2)=1,T(0)=0;

Is it possible to find a closed form solution (T(x) in a compact form)?

I'm trying to display some flow lines for a vector field. The vector field I have is:

What I put into Maple is:

I've tried this with a number of points, but I always get an error message along the lines of:

"Error, (in Student:-VectorCalculus:-FlowLine) cannot determine if this expression is true or false: (2.*(1)(0)-4.)^2+(-2.+4.*(1)(0))^2 < 0.9e-9"

Could someone please shed some light as to what's going wrong for me? I would be very grateful for any help.

Thanks.

For the recursive equation

x_n − 10x_n−1 + 50x_n−2 = 0
n = 2, 3, ...
x₀ = 0
x₁ = 10

How do I calculate x_n in Maple? I'm wondering because n doesn't start at 0 but at 2, how will that make a difference?

Thanks in advance!

Hi, the display function in the simplex package gives us a nice breakdown of the form Ax<=b, but how do we extract the individual elements, i.e. the matrix A and vectors x and b? Normal indexing into the expression doesn't work, i.e. if for some set of constraints of the form 2x+3y<=21 we enter

res:=display(constraintSet);

this gives us a nice expression, but res[1] etc. doesn't work as we might hope (i.e. by returning the matrix A).

a := matrix(...);
b := Convert to hermit matrix from a;
Norm(MatrixMatrixMultiply(b, a), 2) = Norm(a,2)^2

i have tried, but not exactly equal
Norm(MatrixMatrixMultiply(b, a), 2) = 0.01
Norm(a,2)^2 = 0.1

Guess what matrix a is?

How to calculate colimit with only substitution and solve? Any simple example to show the steps.

run a command string in C# by calling maple

it can run in maple if copy into maple

however return input string was not in correct format

String commandstring = "restart;with(LinearAlgebra):with(ExcelTools): filename := "0257.HK";open3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "B2:B100");high3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "C2:C100");low3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "D2:D100");close3 := Import(cat(cat("C://Temp//HK//Transportation//",filename),".xls"), filename, "E2:E100");n := 30;Round := proc(x,n::integer:=1) parse~(sprintf~(cat("%.",n,"f"),x)); end proc: t:=1; gg :=Matrix(n+1,1); ggg :=Matrix(n+1,1); for k from 0 to n do InputMatrix3 := Matrix([[close3[t+1+k] , close3[t+k], close3[t+2+k]],[close3[t+k], close3[t+2+k],0],[close3[t+2+k],0 , 0]]): InputMatrix3b := Matrix([[close3[t+2+k], close3[t+1+k] , close3[t+3+k]],[close3[t+1+k] , close3[t+3+k],0],[close3[t+3+k],0 , 0]]): InputMatrix3c := Matrix([[close3[t+3+k] , close3[t+2+k], close3[t+4+k]],[close3[t+2+k], close3[t+4+k],0],[close3[t+4+k],0 , 0]]): Old_Asso_eigenvector := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3), InputMatrix3)): Old_Asso_eigenvector2 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3b), InputMatrix3b)): Old_Asso_eigenvector3 := Eigenvectors(MatrixMatrixMultiply(Transpose(InputMatrix3c), InputMatrix3c)): gg[k+1,1] :=Old_Asso_eigenvector[2][1,1]; od;Round(Re(gg[1,1][1,1]));";

alpha:= (1/2)*(-y*t2-x*t1-y*t3+sqrt(y^2*t2^2+2*y*t2*x*t1+2*y^2*t2*t3+x^2*t1^2+2*x*t1*y*t3+y^2*t3^2-4*x*t4*y*t9-4*x*t4*y*t8-4*x^2*t4*t7-4*y^2*t5*t9-4*y^2*t5*t8-4*y*t5*x*t7-4*y^2*t6*t9-4*y^2*t6*t8-4*y*t6*x*t7))/(x*t4+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g))));
g := (1/2)*(-x+sqrt(x^2-4*y*x-4*y^2))/(x+y);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g))));
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));

(g o f ) o alpha =g o (f o alpha)
restart;alpha := (1/2)*(-x-x*t1-y*t2-y*t3+sqrt(x^2+2*x^2*t1+2*x*y*t2+2*x*y*t3+x^2*t1^2+2*x*t1*y*t2+2*x*t1*y*t3+y^2*t2^2+2*y^2*t2*t3+y^2*t3^2-4*x*t4*y*t9-4*x^2*t4*t7-4*x*t4*y*t8-4*y^2*t9-4*y*x*t7-4*y^2*t8-4*y^2*t5*t9-4*y*t5*x*t7-4*y^2*t5*t8-4*y^2*t6*t9-4*y*t6*x*t7-4*y^2*t6*t8))/(x*t4+y+y*t5+y*t6);
g := -y/x;
f := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -1
g := (-x+sqrt(x^2-x*y-2*y^2))/(2*y+x);
f := x*y;
gof := subs(p=f,subs(q=f,subs(x=p,subs(y=q,g)))); # -(1/3)*(y/x+sqrt(-2*y^2/x^2))*x/y
lhsgofoalpha := subs(q= alpha,subs(p=alpha, subs(x=p,subs(y=q,gof))));
foalpha := subs(p= alpha,subs(q=alpha,subs(x=p,subs(y=q,f))));
rhsgofoalpha := subs(x= foalpha,subs(y= foalpha, g));
osys := lhsgofoalpha = rhsgofoalpha;
sys1 := subs(x=0, osys);
sys2 := subs(y=0, osys);
sys3 := subs(x=1, osys);
sys4 := subs(y=1, osys);
sys5 := subs(x=2, osys);
sys6 := subs(y=2, osys);
sys7 := subs(x=3, osys);
sys8 := subs(y=3, osys);
sys9 := subs(x=4, osys);
sys1 := subs(x=3,subs(y=2, osys));
sys2 := subs(x=5,subs(y=1, osys));
sys3 := subs(x=1,subs(y=5, osys));
sys4 := subs(x=1,subs(y=2, osys));
sys5 := subs(x=2,subs(y=5, osys));
sys6 := subs(x=5,subs(y=2, osys));
sys7 := subs(x=2,subs(y=1, osys));
sys8 := subs(x=3,subs(y=5, osys));
sys9 := subs(x=5,subs(y=3, osys));
res:=solve([sys1, sys2, sys3, sys4, sys5, sys6, sys7, sys8, sys9], {t1,t2,t3,t4,t5,t6,t7,t8,t9});
eval(osys,res);
simplify(%);
`~`[lhs](select(evalb, res));

I want to begin by saying hello! im new to the forums i hope some one can give me a push in the right direction with some of my maple homework. im sort of stuck on a few of these questions and would be greatfull for some help. 

Let .

a) Let g be the tangent line to f when x = c. Use Maple to find g as a function of c.

b) Use Maple to plot f and g(3) using view = [0..5, -25..100].

c) Define a function called plot_tan that plots both f and g(c) where f is blue and g(c) is red. Also use the same view as in part (b). Note that plot_tan is also a function of c.

d) Using your function plot_tan, the following all in one graph using the display command:

plot_tan(1), plot_tan(1.5), plot_tan(2), plot_tan(2.5), plot_tan(3), plot_tan(3.5), plot_tan(4), plot_tan(4.5), plot_tan(5).

e) Try using the option insequence = true in the display command. What does this option do? (You will need to click on the graph and play around with some buttons).

now it seems to me i have to use the point slope formula to get to a fuction g of c. thanks in advance! i hope you can help

Hello!

I am trying to create a Fortran routine that creates and populates a large 2D array, using Maple's codegen or CodeGeneration capabilities. I would like Maple to create the Fortran code so that the column-major ordering is respected: I would like Maple to populate mat(1,1), mat(2,1), mat(n,1) before moving on to mat(1,2)... Unfortunately, codegen and CodeGeneration seem to only produce row-major code.

Any idea on how to proceed, or an option of the code generation that I would have missed?

Thanks for your help!

Etienne

soslve('(cosh(C + cosh(C))/cosh(C) = 2') gives me a "Waning, solutions may have ben lost" message and no answer.

Write a procedure which inverts a given 2x2 matrix ie
Given a list of 4 numbers (a,b,c,d) return numbers (x,yz,w) such that
Matrix(a,b,c,d)(Matrix(x,y,z,w)) =Identity matrix

I want to find the area of the triangle ABC with the sides are a, b, c. I tried

a:=sqrt(91)/6:

b:=sqrt(17)/2:

c:=sqrt(13)/3:

p:=(a+b+c)/2:

s:=simplify(sqrt(p*(p-a)*(p-b)*(p-c)));

How can I get the result sqrt(523)/24?