## 1490 Reputation

17 years, 322 days

```--------------------------------------
Mario Lemelin```
```Maple 14.00 Win 7 64 bits
Maple 14.00 Ubuntu 10,04 64 bitsmessagerie : mario.lemelin@cgocable.ca
téléphone :  (819) 376-0987```

## Don't need to explain, I found out!...

mario.lemelin@cgocable.ca

## Could you explain......

the command

`M[1..-1,1]`

mario.lemelin@cgocable.ca

## Yes, but here a more practical .......

... way so you can use the output

```> primeCol := proc (m::integer, n::integer)
```
```local L, V;
```
```L := select(isprime, [seq(m .. n)]);
```
```V := convert(L, Vector);
```
```RETURN(V)

end proc;
```
```
> Vec := primeCol(1, 20);

```

mario.lemelin@cgocable.ca

## Here is how I did it...

for #1

The list "L" must be define before running showCol.

> showCol := proc (L::list)
local x;
for x in L do
print(L[x]);
end do;
end proc;

> showCol(L);

for #2

> primeCol := proc (m::integer, n::integer)
local L, i;
L := select(isprime, [seq(m .. n)]);
for i to nops(L) do
print(L[i]);
end do;
end proc;

> primeCol(1, 100);

Have you find a shorter way to do it?

mario.lemelin@cgocable.ca

## Just for pretty printing...

```Table := proc () local i, x1, T1, y1, h, Tx1;
h := solve(x1*exp(T)-1, T);
Tx1 := unapply(h, x1);
printf(` T1    y1 \n`);
for i to 10 do x1 := i;
y1 := 3*Tx1(x1);
printf(` %+04.10E %+04.10E`, Tx1(x1), y1); printf(`\n`):
end do:
end proc:```

Table()

> Table();
T1                                      y1
+0.0000000000E+00  +0.0000000000E+00
-6.9314718060E-01     -2.0794415420E+00
-1.0986122890E+00    -3.2958368670E+00
-1.3862943610E+00    -4.1588830840E+00
-1.6094379120E+00    -4.8283137360E+00
-1.7917594690E+00    -5.3752784070E+00
-1.9459101490E+00    -5.8377304470E+00
-2.0794415420E+00    -6.2383246250E+00
-2.1972245780E+00    -6.5916737340E+00
-2.3025850930E+00    -6.9077552790E+00

mario.lemelin@cgocable.ca

## A modest but interested opinion...

```> Y := ((1/2)*x)^(2/3);

1  (1/3)  (2/3)
Y := - 2      x
2
> eq1 := sqrt(1+(diff(Y, x))^2);

(1/2)
/     (2/3)\
1 |    2     |
eq1 := - |9 + ------|
3 |     (2/3)|
\    x     /
>A:= int(eq1, x);

(1/2)
/   (2/3)    (2/3)\
1  |9 x      + 2     |       (1/3) /   (2/3)    (2/3)\
A:=    -- |-----------------|      x      \9 x      + 2     /
27 |      (2/3)      |
\     x           /

```

Now you can see a problem at x = 0.  But if you rewrite this way

```> B := (1/27)*(9*x^(2/3)+2^(2/3))^(3/2);

(3/2)
1  /   (2/3)    (2/3)\
B := -- \9 x      + 2     /
27

```

and you do

```> subs(x = 2, B)-subs(x = 0, B);

20   (1/2)   2
-- 10      - --
27           27

```

You have the anwser.  It seem to me (and that my modest opinion) that Maple is giving hypergeom because it cannot simplify to B.  Since I more interested in the pedagogical use of Maple, I was not able to pass from A to B with Maple but  had to do it by hand, which sometime is OK cause student has to do some work  too  :-)

mario.lemelin@cgocable.ca

## I forgot to add that......

```> eq1 := sqrt(1+(diff(Y, x))^2);

1            (1/2)
eq1 := - (64 + 18 x)
8
> int(eq1, x = 0 .. 2);

61
--
27
> evalf(%);

2.259259259

```

So for the student, this would be the right answer?????

mario.lemelin@cgocable.ca

## Wich is really right?...

Form Jakubi,

```> eval(%, u = 2);

2    20   (1/2)
- -- + -- 10
27   27

evalf(%,5)
2.2683

```

From Joe,

```> subs({A = 0, B = 2}, len);

8    (1/2)   25    (1/2)
- -- 64      + -- 100
27           54
```
```evalf(%,5)
2.2592

```

too close for confort.  I, for my part, need a little more explanation since the plot show a very simple curve.

mario.lemelin@cgocable.ca

## Just a little start...

mario.lemelin@cgocable.ca

## Correct me if I am wrong...

but I think the problem is more interesting if we stay with exact solution.  So if you have the following:

```> eq := a*x^3+x^2-a*x+1;

3    2
eq := a x  + x  - a x + 1

```

solve(eq=0,x)

you will have the first solution that is interesting in the fact that if you look under the square root, you need to satisfy (for a real solution)

> eq1 := -3*a^4+33*a^2+3 > 0;

4       2
eq1 := 0 < -3 a  + 33 a  + 3

```> solve(%, a);

/    /                    (1/2)\      /                  (1/2)\\
|    |  1 /         (1/2)\     |      |1 /         (1/2)\     ||
RealRange|Open|- - \22 + 10 5     /     |, Open|- \22 + 10 5     /     ||
\    \  2                      /      \2                      //

```

you need to stay in the range -3.3302..< x < 3.3302.... If you look with the plot builder with "a" ranging between -5 to 5  you see that in the fonction has one real root an two complex one inside this range.  Outside that range, the  function has 3 real roots.

If I had to ask that problem to my students, that's the point I would want to see them talked about.  That is my modest opinion.

mario.lemelin@cgocable.ca

## Wow! very nice.......

Thanks.

mario.lemelin@cgocable.ca

## Forget my preceding posting...

My problem is that the Excel separate the decimal with a comma instead of a point.  Now I have been able to import with ImportData or readdata.  Sorry for the trouble.....

mario.lemelin@cgocable.ca

## Cannot make it work!...

Here is my *.txt file created in Excel

1    10,9    118,81
2    12    144
3    15    225
4    17,8    316,84
5    21,2    449,44
6    35,4    1253,16

The separator is the Tabulation.  When I want to import it in Maple, here is what I get:

```> readdata("D://Data//Data6//Data_plot1.txt", float, 3);

[[1., 10.], [2., 12., 144.], [3., 15., 225.], [4., 17.], [5., 21.], [6., 35.]]

```

As you can see, even if I tell Maple that they are floating numbers and that there is 3 columns, I get that strange result.

Any ideas?

mario.lemelin@cgocable.ca

## Here is how...

```> z := 9-5*I;

z := 9 - 5 I
> abs(z);

(1/2)
106
> Im(z);

-5
> argument(z);

/5\
-arctan|-|
\9/
> evalf(%);

-0.5070985044
> convert(%, degrees);

91.27773079 degrees
- -------------------
Pi
> evalf(%);

-29.05460409 degrees

```

where evalf mean to have the answer in decimal.  % tell Maple to use the last output and the := is to make an assignment to z so each time you une as argument the letter z, it mean for Maple 9-5*I (capital I is for the imaginary part).  Remember that Maple works in radian, not in degree so that's the reason I had to convert to have an idea of the angle.

Hope it help?

mario.lemelin@cgocable.ca

## OUPS! Still a problem...

According to the text I am reading, the tension in the rope is still wrong.  Look at my new file:

mario.lemelin@cgocable.ca

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