Hello,

I am working on a problem involving Newton's Law of Cooling in Maple, I want to:

1. Solve for the cooling constant k,
2. Find how long it takes for the pizza to cool to 300 F,

Here is the code I am currently using:

with(plots):

T__s := 75;  # Surrounding temperature
ode := diff(T(t), t) = k*(T(t) - T__s);

# General solution
general_solution := dsolve(ode, T(t));

# Initial condition: T(0) = 350
T := t -> 75 + exp(k*t)*c__1;
C := solve(350 = 75 + exp(0)*C__1, C__1);

# Solve for k using T(5) = 340
k := solve(340 = 75 + 275*exp(5*k), k);
k := evalf(k);

# Solve for time to reach T = 300
time_to_reach := solve(300 = 75 + 275*exp(k*t), t);
time_to_reach := evalf(time_to_reach);

# Define T(t) with solved constants
T := t -> 75 + 275*exp(k*t);

# Plot temperature over time
temp := plot(T, t = 0 .. 280, 75 .. 360, title = "Exponential Decay of Pizza Temperature", labels = ["t (minutes)", "T(t) (°F)"], color = blue);

# Plot T__s as a horizontal line
T__sur := plot(T__s, t = 0 .. 280, color = red, linestyle = dash);

# Combine and display plots
display([temp, T__sur]);

The code works, but I am wondering if there is a more efficient or genuine way.

I would greatly appreciate any advice or alternative approaches to solving and visualizing this in Maple.

Thank you in advance for your insights!

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params.mw

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Running solve() takes forever...I assume this is because Maple is trying to find the explicit form. I am not sure, but I have reasons to believe that a solution exists.

Questions:

1. Did I set up the three equations correctly? Is there a simpler or smarter way to set up my problem?
2. Is it okay for Maple that lambda[i] sometimes appears isolated and sometimes as a component of a vector?  
3. Is there a way to keep my quantities (except the lambda vector I guess, since it containts the lambda[i] component I need to solve for) undefined/implicit while making sure Maple correctly deals with matrices and dot products?
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Worksheet:

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Anybody else experiencing the same?

My interface seetings:

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Below is the code up until the error. Any help or guidance would be greatly appreciated.

Parameter_estimation.mw

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Here is the code

restart;
with(Physics);
g_[sc];
g_[];
_local(g_[]);
g_[1, 2] := 1;
g_[3, 3];
Physics:-g_[1, 1];
g_[1, 2];
Physics:-g_[1, 1];
g_[];
for x to 4 do
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g_[];

So the question is. How do you reverse a localalized metric back to being protected after you altered the metric ?

I am sure that this question must be answered. But when I do a search in the "Search" box, I always receive a page where it  is mentioned that there is an error of generating the page.  So this has been the case for more than a month, or maybe more. I don't know why this is happening.  So that is the reason why I ask a question here.

I would like to put an entry in the file maple.ini so that each time I do the command "plot", the size of the plot in the document will be a size=[300,300] in pixels.  That is supposed to give a plot of 8 cm by 8 cm.  So when I print the document, which will be the size of the plot on the printed page.  I want to do that because if I do not modify the size of the plot by default in the document, it takes up too much space in the page.  I want to do it in maple.ini so I don't have to do it manually each time I plot a function.

Thank you in advance for your help.

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