## Draining a shaped container from the top, and the ...

Hello everybody. Ive got some questions.

As the title states: Draining a shaped container from the top, and the amount of Joule it takes to do it. That is what the questions are about.

I did make the first one, and some attempts at the sphere questions b, and c. I left them out because i want to see what you guys come up with. I think ive got the right answers, but we will see if our answers compare. :)

The Dutch text translated: Calculate in questions a, b, and c the amount of work (joule, J) it takes to drain a tank filled with water from the top with a pump. Each question has a discription of the shape of the tank. Take for gravity g=9.81m/s^2. For water take rho=1000kg/m^3.

a.
A coneshaped tank, the topangle is down, with a height of 2.0meters and a radius of 0.5meters.

b.
A sphere with a radius of 1.0meters.

c.
The lower half of a sphere with a radius 2.0meters.

Greetings,

The Function.

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## How can I substitute an alias by a given expressio...

In the code above expression #1 contains the term D(Phi)(X): how can I replace the "abstract" function Phi by a "specific" one  phi = k*X(t) ?

```restart:
alias(X = X(t)):
alias(Phi=Phi(X(t))):
kin := 1/2*M*diff(X, t)^2 + 1/2*m*diff(Phi, t)^2;  #1

# attempt to replace Phi by phi=k*X(t))
alias(phi=k*X(t)):
eval(kin, Phi=phi);                                #2 ... I expected phi would replace Phi
```

The attached file  How_to_eval.mw contains a more detailed explanation and a more general situation.

## nth derivative of f evaluated at zero...

Dear all

I would like to compute the monomial polynomial in taylor series, I tried
f:=cos(t);

fn:=n->subs(diff(f(x),x\$n),x=0)/factorial(n);
but it is does not work

## Is it possible to export routines from a personal ...

Is there a way to export routines from a package. The reason I ask, I was answering a question here and I needed two routines I have, that I put together a couple of years ago in a package. I used showstat copied, pasted and edited. Worked, but not great and would utterly fail with anything complicated. e.g. In the two routines pasted  below SignedArea on line 3 c[1]  is c   [1] that caused a minor problem.

## Printing math expressions...

Hi,

Does anyone know how can I write this thing in a Maple script?
I have a problem with printing math expressions when there is an increment in the matrix power.

## Need help Homework ...

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 Homothety
 Rotation on x axis

Rotation of angle k

 (3.1)

Neige

Hi, i need some help for a homework.

Here is the statement

You must first animate a series of linear transformations on the polygon formed by the following couples: [5, 0], [6., 0], [6, 3], [10, 3], [7, 5], [9, 5], [7, 7], [8, 7], [5.5, 9], [3, 7], [4, 7], [2, 5], [4, 5], [1, 3], [5, 3] It will be necessary to make, at the same time, a rotation around a line making an angle k with the axis of x, a rotation of an angle k and a scaling of variable ratio (but equal to 3 at the end animation). The k animation parameter should range from 0 to 180. I suggest you use the color green for your polygon. Then you will need to create a second animation by entering these command lines: SnowPoints: = seq ([- 30 + i, 30 - j / 2 * sin (i + j)], i = 0 .. 60): snow: = animate (pointplot, [[PointsNeige], color = black], j = 0 .. 60, view = [-30 .. 30, 0 .. 30]) : Finally, you will have to roll both animations at the same time.

The GIF shows the results that I should get according to my teacher

Thanks for the help !

## problem using dsolve first oder ode...

Dear all

I solve a first order nonlinear ode, using dsolve but there is no solution obtained.

problem_dsolve.mw
How, can I get the exact solution.

## Why do you use Array instead of Vector and Matrix?...

In the obselote book programming examples it is using array's as data type

Is het easier to use A Vector or Matrix as datatype?

## Can maple solve an ode using asymptotic expansions...

Can Maple solve an ode by asymptotic expansions methods? series methods (power series or Frobenius series) work only on ordinary expansion point or removable singularity point. For non removable singularity (essential), Maple's dsolve with series method can't solve these. Also, if the RHS of the ode is not analytic at the expansion point, series method do not work.

The asympt command only applies to algebraic expressions.

Does Maple have something similar to Mathematica's AsymptoticDSolveValue  ?

Here is an example. This is an ode with RHS not analytic (has no Taylor series) at x=0

```ode:=diff(y(x),x)+y(x)=1/x;
dsolve(ode,y(x),'series',x=0)```

No solution.  While in Mathematica

```ode = y'[x] + y[x] == 1/x
AsymptoticDSolveValue[ode, y[x], {x, 0, 6}]```

Here is another example of ode where the coefficient of y(x) is not analytic at x=0

```ode:=diff(y(x),x)+sqrt(x)*y(x)=0;
dsolve(ode,y(x),'series',x=0)```

No solution. In Mathematica

```ode = y'[x] + Sqrt[x] y[x] == 0
AsymptoticDSolveValue[ode, y[x], {x, 0, 6}]```

Does there exist a package in Maple that can do this? Will this functionality be added in Maple in the future if currently there is no support? ( I searched and could not find anything so far).

One possible workaround I found is to solve the ODE using normal methods (non-series), then apply the asympt command on the solution. But one needs to remove the constant of integration first, Here is the above example done this way

```ode:=diff(y(x),x)+sqrt(x)*y(x)=0;
sol:=dsolve(ode);
Order:=8;
sol:=eval(sol,_C1=1);
asympt(eval(rhs(sol),x=1/y),y);
eval(%,y=1/x)

```

Mutliplying the above back by the constant _C1 gives same answer as Mathematica's.

Is the above how one is supposed to do it in Maple? It worked on the above simple example, but need to see if it will work for other examples. it will be better if this was more directly supported. i.e. if asympt will work directly on ode's (or a new command or a new option to dsolve similar to 'series' but call 'asympt').

## Is it possible to disable the automatic conversion...

Greetings!

For factorization and computing times purposes, I'd like Maple to not perform this automatic conversion.

gives

while gives

Alternatively, a way to factorize into could do the trick.

Here's a list of the functions I've already tried:

• factor
• collect (so coeff too)
• combine/expand

Any ideas?

Thank you!

## Please fix my Explore plot...

Hi. I can't seem to get my Explore plot to work. Maple gives me a cryptic error message (IMHO).

Rectangle_within_circle_gen.mw

## Invalid substitution simplification?...

I want to simplify the following expression to 2a-2bk+k(n+6). But the following command is invalid.

algsubs(n2+n1=n+6,a+(n1-b)*k+a+(n2-b)*k);

However, the above expression can be simplified when k is fixed to a number, such as k=2.

algsubs(n2+n1=n+6,a+(n1-b)*2+a+(n2-b)*2);

I wonder what went wrong.

It seems to be recognized only if n1+ n2 is combined.

algsubs(n1+n2=n+6,simplify(a+(n1-b)*k+a+(n2-b)*k))

## OpenMaple for Java: Memory Access Error running sa...

Error occurred running sample test.java (at new EngineCallBackDefault()):

# A fatal error has been detected by the Java Runtime Environment:
#
#  EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x00007ffd66e7345a, pid=1740, tid=7716
#
# JRE version: Java(TM) SE Runtime Environment (11.0.1+13) (build 11.0.1+13-LTS)
# Java VM: Java HotSpot(TM) 64-Bit Server VM (11.0.1+13-LTS, mixed mode, tiered, compressed oops, g1 gc, windows-amd64)
# Problematic frame:
# C  [maplec.dll+0x345a]
#
# No core dump will be written. Minidumps are not enabled by default on client versions of Windows
#
# If you would like to submit a bug report, please visit:
#   http://bugreport.java.com/bugreport/crash.jsp
# The crash happened outside the Java Virtual Machine in native code.

## Determine whether a point with known coordinates i...

Hello

Imagine you have an irregular polygon as follows:

restart; with(plottools):with(plots):

display(polygon([[0,0],[200,0],[200,300],[250,400],[500,300],[500,500],[0,500]]),color=yellow,linestyle=solid,thickness=2);

with vertices that can be easily defined, and that you have an arbitrary point P(x,y) with coordinates of (x) and (y). I want Maple to check whether the point P(x,y) is inside or outside the polygon. In Matlab, the command (inpolygon) can be used for such a task. Is there a similar readily available command in Maple.

Thank you very much for your help and support.

## how to use arctan on complex number?...

I can't seem to figure out how to use arctan on a complex number in Maple.  I expect arctan(a+jb) assuming a and b are real to return atan(b/a).  Instead, returns arctan(a+Ib).  How do I do this?

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test out how to use arctan....

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