<p> roots solve </p>

989bb9b1-113f-49b8-aeda-b5ff6410449b 3 4 5 decimal

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

1. concentration strong base [mol/L]
2. concentration strong acid [mol/L]
.....
3. ion product of water [mol/L]
4. Volume [mL] of acid solution being titrated cNaOH 0.05 : cHCl 0.1 : Kw 1014 -^: vHCl 50 : 41 sys

Titration curve before Equivalence point x ≤ [100 mL] pH1 x 11002 range : i 1 x rows range sol i el H Kw H / - vHCl cHCl * x i el vHCl + / - x i el cNaOH * x i el vHCl + / + 0 ≡ H 1 roots : for sol sol rows el 1107 -^* : x sol log10 vectorize - augment 41 line :

Titration curve beyond Equivalence point  x ≥ [100 mL] pH2 u 100.001 200101 range : i 1 u rows range sol i el OH Kw OH / - u i el cNaOH * u i el vHCl + / - vHCl cHCl * u i el vHCl + / + 0 ≡ OH 100 roots : for u 14 sol log10 vectorize + augment 31 line :

Titration curves ... from 300 roots canvas

pH1 pH2 2 1 sys

1007 + 10 black 15 mat

x pH1 H Kw H / - vHCl cHCl * x vHCl + / - x cNaOH * x vHCl + / + 0 ≡ H 1 roots : u pH2 OH Kw OH / - u cNaOH * u vHCl + / - vHCl cHCl * u vHCl + / + 0 ≡ OH 100 roots : 21 sys

1 x ≤ (x 100 ≤ (&

100 u ≤ (u 200 ≤ (&

<= pH 48 pH1 log10 - 14128 pH2 log10 + 21 mat 1.58 11.90 21 mat

Convivial roots on running canvas ...

γ 1.4 : (Air isentropic ≡ k 0.88128485 : (Pitot constant ≡ p static pressure ≡ qc dynamic pressure ≡ x Pitot dynamic ratio qc/P ≡ x qc p / ≡ (supersonic Pitot ratio ≡ 61 line

Observe the canvas solutions:

as 'x' in Supersonic(x) runs on the plot canvas,

the 'roots' solves and plots each canvas pixel result ...

each result on the basis of 96 ppi [pixel per inch].

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Plot limit x c 10 x ≤ (x 5 ≤ (& cases :

t0 1 time :

x Subsonic 2 γ 1 - / (x 1 + (γ 1 - γ /^1 - (* sqrt 0 x ≤ (x k ≤ (& Supersonic cases : x Supersonic U x 1 + (117 U 2^* / - (2.5^* sqrt / k - 0 ≡ U 1 roots k x ≤ Subsonic cases : 21 line

x Subsonic x Supersonic x c * k 1 + 20 black 1 5 mat 3 1 sys

1 time t0 - 71 s *

supersonic

5 Supersonic 2.07

subsonic