## 178 Reputation

17 years, 121 days

## Differentiation Applications...

Or, in the spirit of applied differentiation: restart: Since h = 6 - r by the constraint r + h = 6 we have V:=Pi*r^2*(6-r); as you have already given. If the max occurs on the open interval (0,6), then dV/dr = 0. A quick look at the plot: plot(V,r=-1..7); Solve dV/dr = 0 for r diff(V,r); solve(diff(V,r)=0,r); So the maximum V occurs when r = 4. MaxVol:=subs(r=4,V); Thomas

## Quantile...

Some additional information at wikipedia-quantile. Also, some reference to the theory regarding computation at Quantile_function linked to that same page at the bottom.

## Quantile...

Some additional information at wikipedia-quantile. Also, some reference to the theory regarding computation at Quantile_function linked to that same page at the bottom.

## Quantile...

Just luck, I had come across it by chance a few months ago. Mma uses the same term. In wonder how it works as well. However, that is a topic you are eminently more qualified to discuss than I am. So, if it takes place, I will just have to read along and learn.

## Quantile...

Just luck, I had come across it by chance a few months ago. Mma uses the same term. In wonder how it works as well. However, that is a topic you are eminently more qualified to discuss than I am. So, if it takes place, I will just have to read along and learn.

## Quantile...

with(Statistics): df := 29: chiSquare := RandomVariable(ChiSquare(df)): Quantile(chiSquare, .95); 42.55696751 CDF(chiSquare, 42.55696751); 0.950000000033921820

## Quantile...

with(Statistics): df := 29: chiSquare := RandomVariable(ChiSquare(df)): Quantile(chiSquare, .95); 42.55696751 CDF(chiSquare, 42.55696751); 0.950000000033921820

## Well, I just went back and...

Two comments: First, you are missing a multiplication operator. 3x^2 should be 3*x^2 Second, if you are going to use "implicit" plot you need a second variable that is an implicit function of x. g1:= implicitplot(y-3*x^2=0, x=0..10, y=0..300); display(g1); or more simply implicitplot(y-3*x^2=0, x=0..10, y=0..300); But this is unnecessary since you can just use "plot" without y. plot(3*x^2, x=0..10, y=0..300);

## Well, I just went back and...

Two comments: First, you are missing a multiplication operator. 3x^2 should be 3*x^2 Second, if you are going to use "implicit" plot you need a second variable that is an implicit function of x. g1:= implicitplot(y-3*x^2=0, x=0..10, y=0..300); display(g1); or more simply implicitplot(y-3*x^2=0, x=0..10, y=0..300); But this is unnecessary since you can just use "plot" without y. plot(3*x^2, x=0..10, y=0..300);

I think about or getassumptions makes it more clear. That is why I put them in above. getassumptions(S); {Pi::Pi, _B1::(OrProp(0, 1)), _Z1::integer} about(_Z1); Originally _Z1, renamed _Z1~: is assumed to be: integer about(_B1); Originally _B1, renamed _B1~: is assumed to be: OrProp(0,1) There is nothing to indicate that _Z1 and _B1 cannot both be 0. Maple gave the same solution regardless of whether or not I included x<>0. I only put that in because it had not been discussed in the previous posts and had been incorrectly included in the solution set. I suppose that one can infer that if it is input to solve directly then _Z1 and _B1 both equal to 0 is eliminated by the statement of the problem, but this is probably a stretch.

I think about or getassumptions makes it more clear. That is why I put them in above. getassumptions(S); {Pi::Pi, _B1::(OrProp(0, 1)), _Z1::integer} about(_Z1); Originally _Z1, renamed _Z1~: is assumed to be: integer about(_B1); Originally _B1, renamed _B1~: is assumed to be: OrProp(0,1) There is nothing to indicate that _Z1 and _B1 cannot both be 0. Maple gave the same solution regardless of whether or not I included x<>0. I only put that in because it had not been discussed in the previous posts and had been incorrectly included in the solution set. I suppose that one can infer that if it is input to solve directly then _Z1 and _B1 both equal to 0 is eliminated by the statement of the problem, but this is probably a stretch.

## Oops...

My apologies for giving the wrong information. I should have looked more closely at the original post. Thanks Jacques for the correction. Thomas

## Oops...

My apologies for giving the wrong information. I should have looked more closely at the original post. Thanks Jacques for the correction. Thomas

## 700...

Congratulations on 700, and thanks for putting that much time and effort into helping others at this site. It is greatly appreciated. Thomas

## Primes...

Daniel, I'm glad the links were helpful. I can't comment beyond that because I am not knowledgeable enough in these areas. Fortunately, Jacques was able to respond before I read your post. Thomas
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