How do I make x the subject of this function?

Question

Zaraleena Adamson 2024-9-6，15:23

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https://ww2.mathworks.cn/matlabcentral/answers/2150794-how-do-i-make-x-the-subject-of-this-function

评论： Zaraleena Adamson 2024-9-6，22:19

What code do I use MATLAB to make x the subject in the function below?

Y = [D^2 * acos(1-(2x/D)]- [squareroot(x(D-x) * (D-2x)] / [pi*(D^2)]

Where D=0.05m

x=unknown

y=0.2170535

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Answer 1

Piyush Kumar 2024-9-6，17:35

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在 MATLAB Online 中打开

@Zaraleena Adamson,

You can use symbolic variables and solve function.

I found this example on the same page -

syms a b c x

b = 2;

c = 3;

x = 3;

eqn = a*x^2 + b*x + c == 0

eqn =

S = solve(eqn, a)

S =

I tried for your case, but it is unable to find explicit solution -

syms x D y

% D = 0.1;

% y = 0.2;

% Define the function

Y = (D^2 * acos(1 - (2*x/D))) - (sqrt(x * (D - x) * (D - 2*x)) / (pi * (D^2)));

% Solve for x

solution = solve(Y == y, x);

Warning: Unable to find explicit solution. For options, see help.

% Display the solution

disp(solution);

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Piyush Kumar 2024-9-6，17:45

在 MATLAB Online 中打开

I also tried with fzero to find the roots of the function -

D = 0.05;
y = 0.2170535;
% Define the function
f = @(x) (D^2 * acos(1 - (2*x/D))) - (sqrt(x * (D - x) * (D - 2*x)) / (pi * (D^2))) - y;
% Find a root near an initial guess
initial_guess = D / 2;
solution = fzero(f, initial_guess);
Exiting fzero: aborting search for an interval containing a sign change
    because complex function value encountered during search.
(Function value at 0.0257071 is -0.21306-0.11966i.)
Check function or try again with a different starting value.
disp(solution);
   NaN