19d6a7a0-bf71-4811-acc3-77cef9c5741a 19 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

An 'n' stages system

n 3 :

T 1 :

XFR of 'n' multistage system of
=  Unit Time Constant [1] t xfr 1 t - T / exp 1 k! / t T / (k^* (k 0 n sum * - :

Reaction rate of the nth system t Laplace t n 1 - (^n 1 - (! / t - T / exp T n^/ * :

x xfr x Laplace 2 1 sys

Observe: 1. XFR(n,T,t) does not plot 2. XFR(n,T,x+zero) escapes the 0^0 "uncertainty" 3. For each set of [n, T], renew root argument.

n T t XFR 1 t - T / exp 1 k! / t T / (k^* (k 0 n sum * - :

00^#

n T 0 XFR #

zero 1017 -^:

n T zero XFR 0

1. The undocumented Smath 'root' w sol t xfr w - t root :

Some numerical inverse fncts

x asin x acos x atan x asinh x acosh 51 line

2.The 'root argument' is the reflexive solver w sol 61 - w + (* t - exp 321 t + (* t 2^+ (* t 3^+ (* + 6 / - t root

An inverse fnct solves 'x' given 'y'=f(x)

3. The solver "Reflexive-Generatrix" w t argument 61 - w + (* t - exp 321 t + (* t 2^+ (* t 3^+ (* + 6 / - :

The companions 'root' function inverser

4. Solving for (t), given (w)... Roots(range) => t,0,20 w t Sol w t argument 0 ≡ t 020 solve :

X 0.5 0.5 t Sol augment :

0.5 t Sol 3.67

X 0.5 3.672 12 mat

The Smath discrete inverser for plot view Inverse ω 1012 -^0.999 0.01 range : i 1 ω rows range sol i el ω i el t argument 0 ≡ t 020 solve : for ω sol augment 31 line :

Inverse Inverse :

Inverse X 2 1 sys

Solving for (w), given (t)... Roots(range)  => w,0,1.01
... this is  simply 'xfr(x)'. w t Sol w t argument 0 ≡ w 0 1.01 solve :

w 13.06 Sol 0.998998

13.06 xfr 0.998998