I reduced the order of two nonlinear equations and solved them numerically in this way. Why are the two results obtained the same?
directdsolve919.mw

I have the function  and derivate with respect to ν and make the change variable ν=1/t it seems it doesn’t work. I put the derivate of 1/t => -1/t² by hand  (could it be done by “dchange” the hole transformation ?)

I want to approximate the value of the integral. It seems that the solution of the equation and plot in 2 situations for low-frequency ν < 10¹⁴  and for high frequency so  when the exponential is dominated.

Thus plot the whole function E2 in the two situations. Could it be done with a series?

For value h := 6.62607015*10^(-34); c := 299792458; T := 273 + 24; k := 1.380649*10^(-23);

ec := 1.602176634*10^(-19); ν1 :=10¹² ; ν2 := 10¹⁷ ;Tq := 1.765358264*10^(-19);

Could it be merged E2 into one plot for ν = 10¹² .. 10¹⁷? 

PPh1.mw

Hi everyone, I wrote a complex 3D curve expression and wanted to calculate its length (0..Pi), but Maple was always calculating and could not get the answer. The code and worksheet are attached.
The idea came from: https://www.mapleprimes.com/questions/239065-Curve-Length-2d-3d

Download length_of_3d_curve.mw

Hi

How we can reduce run time for Cases III and IV ? (Maple 2016)

Thanks alot

Formula_II.mw

Good morning, I am trying to graph the length of the curve but Maple gives me an error. Please if someone can tell me how I can graph the curve in 2d and 3d.

plot([t*sin(t), t*cos(t), (2*sqrt(2))/3*t^(3/2),t, t = 0 .. Pi]) -> error

Just one more small geometry task to get to know Maple a little better:
In the 1st quadrant, point A is on the y-axis and points B, D, C are at a positively increasing distance from the origin on the x-axis. Let BD = DC = s/2 and angle ADB = 45°. Point D is therefore the center of BC. The area of ​​triangle ABC is 60, line AD = x and the length of AC = 19. We are looking for the length of line AB = y.

A student wakes up at the end of the lecture and just catches the professor saying:
"... and the roots form an arithmetic sequence."

On the board there is a 5th degree polynomial as homework, but unfortunately the student only manages to write down
x^5 - 5x^4 - 35x^3 +
before the professor wipes the board.

But the student still finds all the roots of the polynomial.

And the roots now have to be calculated.

I have a list

mylist := [[sqrt(-5*x^2 - 5*x - 1) = -4*x - 1, {-1/3, -2/7}], [sqrt(-5*x^2 - 5*x - 1) = x + 1, {-1/2, -2/3}], [sqrt(-5*x^2 - 5*x - 1) = 4*x + 3, {-2/3, -5/7}], [sqrt(-5*x^2 - 5*x + 4) = -5*x + 3, {1/2, 1/3}], [sqrt(-5*x^2 - 4*x + 2) = -5*x + 2, {1/3, 1/5}], [sqrt(-5*x^2 - 4*x + 2) = -2*x + 1, {-1/3, 1/3}]]

I tried
latex(mylist) and get
 

\left[\left[\sqrt{-5 x^{2}-5 x -1} = -4 x -1, \left\{-{\frac{2}{7}}, -
{\frac{1}{3}}\right\}\right], \left[\sqrt{-5 x^{2}-5 x -1} = x +1, 
\left\{-{\frac{2}{3}}, -{\frac{1}{2}}\right\}\right], \left[
\sqrt{-5 x^{2}-5 x -1} = 4 x +3, \left\{-{\frac{5}{7}}, -{\frac{2}{3}}
\right\}\right], \left[\sqrt{-5 x^{2}-5 x +4} = -5 x +3, \left\{{\frac
{1}{2}}, {\frac{1}{3}}\right\}\right], \left[\sqrt{-5 x^{2}-4 x +2} = 
-5 x +2, \left\{{\frac{1}{3}}, {\frac{1}{5}}\right\}\right], \left[
\sqrt{-5 x^{2}-4 x +2} = -2 x +1, \left\{-{\frac{1}{3}}, {\frac{1}{3}}
\right\}\right]\right]

How can I get  a latex like this?

\documentclass[12pt,a4paper]{article}
\usepackage[left=1.5cm, right=1.5cm, top=2cm, bottom=2cm]{geometry}
\usepackage{fouriernc}
\usepackage{enumitem}
\usepackage{amsmath}
\begin{document}
	Solve the following equations:
	\begin{enumerate}[label=\arabic*)]
		\item $\sqrt{-5 x^{2}-5 x -1} = -4 x -1.$ \hfill Answer: $\left\{-{\dfrac{2}{7}}, -{\dfrac{1}{3}}\right\}.$
		\item $\sqrt{-5 x^{2}-5 x -1} = x +1.$ \hfill Answer: $\left\{-{\dfrac{2}{3}}, -{\dfrac{1}{2}}\right\}.$
		\item $\sqrt{-5 x^{2}-5 x -1} = 4 x +3.$ \hfill Answer: $\left\{-{\dfrac{5}{7}}, -{\dfrac{2}{3}}\right\}.$
		\item $\sqrt{-5 x^{2}-5 x +4} = -5 x +3.$ \hfill Answer: $\left\{{\dfrac{1}{2}}, {\dfrac{1}{3}}\right\}.$
		\item $\sqrt{-5 x^{2}-4 x +2} = -5 x +2.$ \hfill Answer: $\left\{{\dfrac{1}{3}}, {\dfrac{1}{5}}\right\}.$
	\end{document}

Loop is not executing all values just considerinng 1st value of tau0 =0.3.

Also how to plot a 2D graph from the loop result

Attaching sheet with questions in the sheet:
for_loop_question_rec.mw

I have some lecture notes and examples that suddenly appears to be corrupted. I am getting the following error code when trying to open the file: "There was a problem in the loading process, you worksheet may be incomplete."

I've tried the following trouvleshooting:

- Close and reopen Maple

- Restarting computer

- Tried different computer

note: I have no backup files as I do not have autosave switched on.

I have also tried looking into the solution posted on a previous question on this site (https://www.mapleprimes.com/questions/235363-How-To-Fix-Corrupted-Maple-File), i.e.  changing the file format to.xml and making changes but with no luck :(

Is anyone able to help me fix it and un-corrupt this file:

Lecture_2_-_notes.mw

I cannot find an explanation why a boolean evaluation with higher Digits is not the same

RealRange seems to be evaluated differently.
Any explanation for that?

(expression extracted from an error message)

Download eval_of_range_in_ln.mw

Dear Maple user

I want to add caption for all four graphs with a,b,c,d at the bottom centre of each graph that should be arrange in 2X2 array and the array bottom caption as Figure 6, also i want to save the output of the array graphs in desktop with jpeg format. sample graph i have uploaded.

restart:
with(plots):
A1:= plot(sin(x), x = -Pi .. Pi,title = "Graph at M^2=1",caption = "Fig a"):# This caption is at the centre bottom of first graph and the title of A1 is M*M (M^2)should be display
A2:= plot(cos(x), x = -Pi .. Pi,caption = "Fig b"):# This caption is at the centre bottom of second graph
A3 := plot3d(1.5^x*sin(y), x = -3 .. 3, y = -3 .. 3,caption = "Fig c"):# This caption is at the centre bottom of Third graph
A4 := plot3d(1.3^x*sin(y), x = -1 .. 2*Pi, y = 0 .. Pi,caption = "Fig d"):# This caption is at the centre bottom of forth graph
display(Array(1 .. 2, 1 .. 2, [[A1, A2], [A3, A4]]), aligncolumns = [1],caption = "Fig 6"):# This caption at the bottom centre of array graphs 

I have and input parameter to a procedure called shift:=05. It sets the position of test between to points.

this particular procedure has two potential sets of text one in Q and the other in vec.
Can Q and vec have the own individual values for shift?

I have shown the input to the procedure and what it outputs. The procedure itself to too long and akward to the post.

Also given is the input definiton of the procedure and how I could possibly find a shift in a list.

Download 2024-09-18_Select_name_and_Value_from_List.mw