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Nov 10, 2019, 11:42:01 PM11/10/19

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On 11/10/2019 2:15 PM, Rainer wrote:

> Hi,

>

> I'm a student in high school and we're using MAPLE and GeoGebra in

> math classes.

>

> I've stumbled across something weird: I can't make MAPLE (2016) solve

> the following system of equations, but I can do so with GeoGebra

> (5.0.5). That can't be right.

>

> Is there a way to make MAPLE put out the numerical solution like

> GeoGebra does?

>

> Thank you for your help!

> Rainer

>

>

> MAPLE:

> =========

>> restart:S:=t->c*exp(-a*t)+18;

>

> S := t -> c*exp(-a*t)+18

>

>> sys:={S(2)=55,S(8)=36};

>

> sys := {c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}

>

>> solve(sys);

>

> {a = -1/2*ln(18/37*RootOf(18*_Z^3-37)^2), c = 37*RootOf(18*_Z^3-37)}

>

>

Try

restart:

S:=t->c*exp(-a*t)+18:

sys:={S(2)=55,S(8)=36}:

sol:=solve(sys):

evalf(sol)

{a = 0.1200910262, c = 47.04478235}

--Nasser

> Hi,

>

> I'm a student in high school and we're using MAPLE and GeoGebra in

> math classes.

>

> I've stumbled across something weird: I can't make MAPLE (2016) solve

> the following system of equations, but I can do so with GeoGebra

> (5.0.5). That can't be right.

>

> Is there a way to make MAPLE put out the numerical solution like

> GeoGebra does?

>

> Thank you for your help!

> Rainer

>

>

> MAPLE:

> =========

>> restart:S:=t->c*exp(-a*t)+18;

>

> S := t -> c*exp(-a*t)+18

>

>> sys:={S(2)=55,S(8)=36};

>

> sys := {c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}

>

>> solve(sys);

>

> {a = -1/2*ln(18/37*RootOf(18*_Z^3-37)^2), c = 37*RootOf(18*_Z^3-37)}

>

>

Try

restart:

S:=t->c*exp(-a*t)+18:

sys:={S(2)=55,S(8)=36}:

sol:=solve(sys):

evalf(sol)

{a = 0.1200910262, c = 47.04478235}

--Nasser

Nov 11, 2019, 4:19:33 PM11/11/19

to

Try :solve(sys); [allvalues(%)];

The following shows what you actually ask for:

Sys:=(expand(sys));

subs(exp(a) = sqrt(t), Sys); solve(%);

Or even better:

subs(exp(a) = sqrt(t), Sys); eliminate(%, c);

Then just solve exp(a) = sqrt(t) for a.

Likewise evaluate to numerical values.

So there are 3 solutions

PS: You may use http://www.mapleprimes.com/recent/all for questions.

It is alive instead of this usenet group.

On 10.11.2019 21:15, Rainer wrote:

> Hi,

>

> I'm a student in high school and we're using MAPLE and GeoGebra in

> math classes.

>

> I've stumbled across something weird: I can't make MAPLE (2016) solve

> the following system of equations, but I can do so with GeoGebra

> (5.0.5). That can't be right.

>

> Is there a way to make MAPLE put out the numerical solution like

> GeoGebra does?

>

> Thank you for your help!

> Rainer

>

>

> MAPLE:

> =========

>> restart:S:=t->c*exp(-a*t)+18;

>

> S := t -> c*exp(-a*t)+18

>

>> sys:={S(2)=55,S(8)=36};

>

> sys := {c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}

>

>> solve(sys);

>

> {a = -1/2*ln(18/37*RootOf(18*_Z^3-37)^2), c = 37*RootOf(18*_Z^3-37)}

>

>

> fsolve doesn't do the job, either:

>

>> fsolve(sys);

>

> fsolve({c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55},{a, c})

>

>

>

> GeoGebra:

> =========

> S(t):=c*exp(-a*t)+18

>

> S(t):=(c * e^(((-a) * t))) + 18

>

> system:={S(2)=55,S(8)=36}

>

> system:={(c * e^(((-2) * a))) + 18 = 55, (c * e^(((-8) * a))) + 18

> = 36}

>

> lsg:=NLöse(system)

>

> lsg:={a = 0.1200910257913, c = 47.04478235943}

>

> SS(t):=Numerisch(Ersetze(S(t),lsg))

>

> SS(t):=(47.04478235943 * ?^(((-0.1200910257913) * t))) + 18

>

The following shows what you actually ask for:

Sys:=(expand(sys));

subs(exp(a) = sqrt(t), Sys); solve(%);

Or even better:

subs(exp(a) = sqrt(t), Sys); eliminate(%, c);

Then just solve exp(a) = sqrt(t) for a.

Likewise evaluate to numerical values.

So there are 3 solutions

PS: You may use http://www.mapleprimes.com/recent/all for questions.

It is alive instead of this usenet group.

On 10.11.2019 21:15, Rainer wrote:

> Hi,

>

> I'm a student in high school and we're using MAPLE and GeoGebra in

> math classes.

>

> I've stumbled across something weird: I can't make MAPLE (2016) solve

> the following system of equations, but I can do so with GeoGebra

> (5.0.5). That can't be right.

>

> Is there a way to make MAPLE put out the numerical solution like

> GeoGebra does?

>

> Thank you for your help!

> Rainer

>

>

> MAPLE:

> =========

>> restart:S:=t->c*exp(-a*t)+18;

>

> S := t -> c*exp(-a*t)+18

>

>> sys:={S(2)=55,S(8)=36};

>

> sys := {c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}

>

>> solve(sys);

>

> {a = -1/2*ln(18/37*RootOf(18*_Z^3-37)^2), c = 37*RootOf(18*_Z^3-37)}

>

>

>

>> fsolve(sys);

>

> fsolve({c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55},{a, c})

>

>

>

> GeoGebra:

> =========

> S(t):=c*exp(-a*t)+18

>

> S(t):=(c * e^(((-a) * t))) + 18

>

> system:={S(2)=55,S(8)=36}

>

> system:={(c * e^(((-2) * a))) + 18 = 55, (c * e^(((-8) * a))) + 18

> = 36}

>

> lsg:=NLöse(system)

>

> lsg:={a = 0.1200910257913, c = 47.04478235943}

>

> SS(t):=Numerisch(Ersetze(S(t),lsg))

>

> SS(t):=(47.04478235943 * ?^(((-0.1200910257913) * t))) + 18

>

Jan 17, 2021, 11:27:42 AM1/17/21

to

restart:S:=t->c*exp(-a*t)+18;

S := t -> c*exp(-a*t)+18;

sys:={S(2)=55,S(8)=36};

sys := {c*exp(-8*a)+18 = 36., c*exp(-2*a)+18 = 55.};
S := t -> c*exp(-a*t)+18;

sys:={S(2)=55,S(8)=36};

solve(sys);

Jan 17, 2021, 10:56:31 PM1/17/21

to

restart;

S:=t->c*exp(-a*t)+18:

sys:={S(2)=55,S(8)=36}:

1/3 2/3

24642 24642

sol := {a = -1/2 ln(--------), c = --------}

37 18

evalf(%);

{a = 0.1200910257, c = 47.04478236}

Getting the three roots (of which two are nonreal, ie. complex) is similar,

solve(sys, explicit);

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