Wikipedia:Reference desk/Archives/Mathematics/2020 February 27

= February 27 =

Calculating min max values
Hello,

I'm slowly losing my mind over this issue. Say you have the following equation:

F% = a%.g%.h%

Both F and h are known empirically, and a and g can be estimated. Is there a way of calculating what the min/max values are of the a and g variables, if for example we calculate the F value based in the estimated a.g and observed h, which produces F(calculated) and comparing back to F(observed).

I've gotten as far as working out what the proportionality of a and g are:

y(a+x) =g.x with y being the decrease in g and x the increase in a, but can't seem to get any further.

Any help, or pointers in the right direction will be greatly appreciated. Apologies for any incorrect terminology, as you may guess, I'm not a mathematician by trade.

Couldbeanything (talk) 15:06, 27 February 2020 (UTC)


 * Can you explain the percentage signs? Do you mean the equation $F = agh$ – in words, $F$ equals the product of $a$, $g$ and $h$? If all involved quantities are positive, we can rewrite this as $ag = F/h$. If $F$ and $h$ are known, the right-hand side of that equation is a known value. Let us assume for concreteness that that value is $42$; the following holds equally for any other value. Now you can choose $a$ arbitrarily large; for example, pick $a = 10^{100}$. Then the equation is satisfied by setting $g = 42×10^{−100}$. So $a$ can be arbitrarily large; as $a$ gets larger, $g$ gets smaller. You can also choose $a$ arbitrarily close to $0$; for example, pick $a = 10^{−100}$. Now the equation is satisfied by setting $g = 42×10^{100}$. So $a$ can also be arbitrarily small (but still positive); as $a$ gets smaller, $g$ gets larger. Precisely the same story holds with the roles of $a$ and $g$ swapped. So there is no minimum constraint other than remaining positive, and no maximum constraint at all. --Lambiam 19:32, 27 February 2020 (UTC)
 * If F and h have the same +/- sign, then a and g also need to have the same sign. If they have different signs then a and g need to also have different signs. If you allow a and g to take negative values, then there are no constraints on negative values. If % means that these are percentage values and these values are supposed to be in some range as in between 0 and 1 (meaning 0% and 100%) then there are more constraints. 89.172.73.94 (talk) 00:16, 29 February 2020 (UTC)