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pik1432

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6 years, 123 days
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These are replies submitted by pik1432

Thank you!...

pik1432 245
February 04 2021
0 0

@nm, tomleslie: Thank you for your answers! I was able to see how they worked in the attached worksheet. 



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/q20210204_answers.mw .
 

Download q20210204_answers.mw
 

 

Thank you!...

pik1432 245
February 04 2021
0 0

@Carl Love : Thank you for the valuable information in your message.

I re-walked through and was able to see what you meant in a clearer manner. 


Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Q20210127_CarlLove.mw .
 

Download Q20210127_CarlLove.mw

Thank you!...

pik1432 245
February 03 2021
0 0

@dharr : Thank you for the comment. Yes, I agree that the 'trivial' answer (0,0) might not be the answer to the original equations. Is there any chance to ask what you mean by 'convert all your floats to rationals'? I want to try it to see if I can come down to the same conclusion as yours, i.e., solving the equations would become the issue of finding the roots of a quadratic. 

 

Thank you!...

pik1432 245
February 02 2021
0 0

@Georgios: Thank you for your attention and answer to the question. 

The order of the equations is 3, not 2. If both sides of the equations are multiplied by the denominator of the last term of each equation, 'VRi^2 + VRr^2', then probably it would become obvious. 

Then, when I tried to use the 'solve' command, it came up with 3 sets of solutions, which was expected. The new one was (0,0) which might have been considered trivial, but I don't know. 



Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/implicitplotSol_m2.mw .
 

Download implicitplotSol_m2.mw

 

Thank you!...

pik1432 245
February 01 2021
0 0

@Kitonum Thank you for your answer! I tried the software from the website (1-month subscription), but what I was able to see from there was not that much. Probably it would take time before I begin to see the better part of it. 

 

 

 

Thank you!...

pik1432 245
February 01 2021
0 0

@nm Thank you for introducing a way to see more regarding the intermediate steps. 

Thank you!...

pik1432 245
January 28 2021
0 0

@Kitonum You are absolutely correct. The number of unknowns is 9, while the number of equations is 3. 

Thank you!...

pik1432 245
January 04 2021
0 0

@Kitonum Thank you for showing another way of sloving the issue. 

 

Thank you!...

pik1432 245
January 03 2021
0 0

@tomleslie Thank you, it worked indeed.

 

Thank you!...

pik1432 245
January 03 2021
0 0

@acer I checked and saw that the both ways worked. Thank you!

Thank you for the clear answer....

pik1432 245
December 08 2020
0 0

@acer Thank you! I did not know that the 'evala()' can do the work. 

 

The answers are highly appreciated!...

pik1432 245
December 08 2020
0 0

@Kitonum Thank you for your answers!

Thank you for the furtuer step...

pik1432 245
December 08 2020
0 0

@nm Thank you for your answer. Probably you already noticed that those expressions were from a book which I'm reading now. The 'Desired' expression was given as a simplification, no further. 

 

Thank you for all the answers....

pik1432 245
December 08 2020
0 0

Here is the recap of the answers from 'Acer' and 'Kitonum':

Q20201208_w_answers.mw
 

> 

restart;
> 

eq9_30 := T__e_n = 2*(s/s_hat) / ((1+r*s/s_hat)^2+(s/s_hat)^2);

T__e_n = 2*s/(s_hat*((1+r*s/s_hat)^2+s^2/s_hat^2))

 (1)
> 

eq9_31 := solve(diff(rhs(eq9_30), s)=0,s);

s_hat/(r^2+1)^(1/2), -s_hat/(r^2+1)^(1/2)

 (2)
> 

eq9_32a :=  T__e_np = simplify(subs(s=eq9_31[1] , rhs(eq9_30))) assuming r::real;

T__e_np = (r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

 (3)
> 

Desired := T__e_np = 1/(sqrt(r^2 + 1) + r);

T__e_np = 1/((r^2+1)^(1/2)+r)

 (4)
> 

#20201208 from Acer
> 

restart;
> 

eq9_30 := T__e_n = 2*(s/s_hat) / ((1+r*s/s_hat)^2+(s/s_hat)^2);

T__e_n = 2*s/(s_hat*((1+r*s/s_hat)^2+s^2/s_hat^2))

 (5)
> 

eq9_31 := solve(diff(rhs(eq9_30), s)=0,s);

s_hat/(r^2+1)^(1/2), -s_hat/(r^2+1)^(1/2)

 (6)
> 

T__e_np := simplify(subs(s=eq9_31[1] , rhs(eq9_30))) assuming r::real;

(r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

 (7)
> 

evala(T__e_np);

(r^2+1)^(1/2)-r

 (8)
> 

1/evala(1/T__e_np);
 

1/((r^2+1)^(1/2)+r)

 (9)
> 

#There is also this (but it's easier to let evala figure it out.
> 

factor(T__e_np, sqrt(r^2 + 1));

(r^2+1)^(1/2)-r

 (10)
> 

1/factor(1/T__e_np, sqrt(r^2 + 1));

1/((r^2+1)^(1/2)+r)

 (11)
> 

#20201208 from Kitonum

> 

restart;        
> 

eq9_30 := T__e_n = 2*(s/s_hat) / ((1+r*s/s_hat)^2+(s/s_hat)^2);

T__e_n = 2*s/(s_hat*((1+r*s/s_hat)^2+s^2/s_hat^2))

 (12)
> 

eq9_31 := solve(diff(rhs(eq9_30), s)=0,s);

s_hat/(r^2+1)^(1/2), -s_hat/(r^2+1)^(1/2)

 (13)
> 

eq9_32a :=  T__e_np = simplify(subs(s=eq9_31[1] , rhs(eq9_30))) assuming r::real;

T__e_np = (r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

 (14)
> 

simplify(algsubs(r^2+1=t^2,eq9_32a)) assuming t>0;

T__e_np = 1/(r+t)

 (15)
> 

subs(t=sqrt(r^2+1), %);
 

T__e_np = 1/(r+(r^2+1)^(1/2))

 (16)
> 

T__e_np := sqrt(r^2+1)/(r^2+sqrt(r^2+1)*r+1);

(r^2+1)^(1/2)/(r^2+(r^2+1)^(1/2)*r+1)

 (17)
> 

numer(T__e_np)*sqrt(r^2+1)/expand(denom(T__e_np)*sqrt(r^2+1));

(r^2+1)/((r^2+1)^(1/2)*r^2+r^3+r+(r^2+1)^(1/2))

 (18)
> 

simplify(%);

1/(r+(r^2+1)^(1/2))

 (19)
> 

 


 

Download Q20201208_w_answers.mw

 

 

The answer is appreciated!...

pik1432 245
December 06 2020
0 0

@Kitonum Thank you!

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