_jh_ex1

D:\j_Iam_TEMP\_jh\_jh_ex1.wxmx

Conversion Factors

0.00001667 m3/s = 1 L/min
0.002228 ft3/s = 1 gal/min
0.0145 lb/in2 = 1 mbar
0.3048m = 1ft
2.54 cm = 1 in
3.281 ft = 1 m
4 qt = 1 gal
4.184 kJ = 1 kcal
4.448 N = 1 lb
6.894 kN/m2 = 1 lb/in2
7.48 gal = 1ft3
12 in = 1 ft
14.59 kg = 1 slug
25.4 mm = 1 in
60 min = 1 h
60 s = 1 min
100 cm = 1 m
100 kPa = 1 bar
101.3 kPa = 1 atm
144 in2 = 1 ft2
550 ft-lb/s = 1 hp
778ft-lb = l Btu
1000 N = 1 kN
1000L=lm’
1000 mm = 1 m
1000 Pa = 1 kPa
1728 in3 = 1 ft3
2000 lb = 1 ton
3600s=lh
4184 J = 1 kcal
5280 ft = 1 mile
86 400s = 1 day
1000 000N = 1MN
1 000 000 Pa = 1 MPa
1 0000000(X)N = 1 GN
1000 000 000 Pa = 1 GPa

quarter circle

_jh_ex1a.ai -----------------------------

Figure 1:D:\j_Iam_TEMP\_jh\_jh_ex1a.jpg
Diagram

Figure 2:D:\j_Iam_TEMP\_jh\_jh_ex1b.jpg
Diagram

(%i1)

kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i5)

R : 1 ; B : 2 ; ro : 1000 ; g : 9 . 81 ; H : R ;

\[\operatorname{ }1\]

\[\operatorname{ }2\]

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }1\]

(%i6)

P_x : integrate ( ro · g · ( H − h ) · B , h , 0 , R ) ;

\[\]\[rat: replaced 9810.0 by 9810/1 = 9810.0\]

\[\operatorname{ }9810\]

(%i8)

W_z : integrate ( ( sqrt ( R · · 2 − ( R − h ) · · 2 ) ) · B , h , 0 , R ) $ W_z , numer ;

\[\operatorname{ }1.5707963267948966\]

(%i9)

W : ( ( %pi · ( R · · 2 ) ) / 4 ) · B , numer ;

\[\operatorname{ }1.5707963267948966\]

(%i10)

P_z : W_z · ro · g , numer ;

\[\operatorname{ }15409.511965857935\]

(%i12)

phi_rad : atan ( P_z / P_x ) , numer ; phi_g : ( 180 / %pi ) · phi_rad , numer ;

\[\operatorname{ }1.0038848218538872\]

\[\operatorname{ }57.51836340947025\]

x_C - Center of gravity of body volume pressure (Центр ваги об'єма тіла тиску)

(%i13)

w : integrate ( ( sqrt ( R · · 2 − ( R − h ) · · 2 ) ) · B , h , 0 , R ) ;

\[\operatorname{ }\frac{\ensuremath{\pi} }{2}\]

(%i14)

mw : integrate ( ( sqrt ( R · · 2 − ( R − h ) · · 2 ) ) · B · ( ( sqrt ( R · · 2 − ( R − h ) · · 2 ) ) / 2 ) , h , 0 , R ) ;

\[\operatorname{ }\frac{2}{3}\]

(%i15)

x_C : mw / w , numer ;

\[\operatorname{ }0.42441318157838753\]

Numerical methods, K123 (Чисельні методи, K123)

Numerical calculation methods (Чисельні методи розрахунку)

(%i16)

kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i5)

R : 1 ; B : 2 ; ro : 1000 ; g : 9 . 81 ; H : R ;

\[\operatorname{ }1\]

\[\operatorname{ }2\]

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }1\]

P_x

(%i6)

dh : R / 10000 ;

\[\operatorname{ }\frac{1}{10000}\]

(%i8)

h : 0 ; P_x : 0 ;

\[\operatorname{ }0\]

(%i10)

for i : 1 while h < = R do ( Pi : ro · g · ( H − h ) · B · dh , P_x : P_x + Pi , h : h + dh ) ; P_x ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

\[\operatorname{ }9810.980999999996\]

(%i12)

h : 0 ; mP_x : 0 ;

\[\operatorname{ }0\]

(%i14)

for i : 1 while h < = R do ( mPi : ro · g · ( ( H − h ) · · 2 ) · B · dh , mP_x : mP_x + mPi , h : h + dh ) ; mP_x ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

\[\operatorname{ }6540.981032700002\]

(%i16)

h : 0 ; mP_x_down : 0 ;

\[\operatorname{ }0\]

(%i18)

for i : 1 while h < = R do ( mPi : ro · g · ( H − h ) · h · B · dh , mP_x_down : mP_x_down + mPi , h : h + dh ) ; mP_x_down ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

\[\operatorname{ }3269.9999672999975\]

(%i19)

h_D : mP_x / P_x ;

\[\operatorname{ }0.6667000000000005\]

(%i20)

h_D_down : mP_x_down / P_x ;

\[\operatorname{ }0.3332999999999999\]

(%i21)

h_D + h_D_down ;

\[\operatorname{ }1.0000000000000004\]

P_z

(%i26)

R : 1 ; B : 2 ; ro : 1000 ; g : 9 . 81 ; H : R ;

\[\operatorname{ }1\]

\[\operatorname{ }2\]

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }1\]

(%i28)

n : 10000 ; dh : R / n ;

\[\operatorname{ }10000\]

\[\operatorname{ }\frac{1}{10000}\]

(%i30)

h : 0 ; P_z : 0 ;

\[\operatorname{ }0\]

(%i33)

fB ( h ) : = ( sqrt ( R · · 2 − ( R − h ) · · 2 ) ) ; fB ( 0 ) ; fB ( R ) ;

\[\operatorname{ }\operatorname{fB}(h)\operatorname{:=}\sqrt{{{R}^{2}}\operatorname{-}{{\left( R\operatorname{-}h\right) }^{2}}}\]

\[\operatorname{ }0\]

\[\operatorname{ }1\]

(%i34)

fb : fB ( h ) ;

\[\operatorname{ }0\]

(%i36)

for i : 1 thru n step 1 do ( fb1 : fB ( h ) , dfb : fb1 − fb , Pi : ro · g · ( H − h ) · dfb · B , P_z : P_z + Pi , h : h + dh , fb : fb1 ) ; Pz : P_z , numer ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

\[\operatorname{ }15408.52519768357\]

(%i38)

h : 0 ; mP_z : 0 ;

\[\operatorname{ }0\]

(%i39)

fb : fB ( h ) ;

\[\operatorname{ }0\]

(%i41)

for i : 1 thru n step 1 do ( fb1 : fB ( h ) , dfb : fb1 − fb , mPi : ro · g · ( H − h ) · dfb · B · fB ( h ) , mP_z : mP_z + mPi , h : h + dh , fb : fb1 ) ; mPz : mP_z , numer ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

\[\operatorname{ }6545.153696629369\]

(%i42)

x_D : mPz / Pz ;

\[\operatorname{ }0.4247748316375749\]

Analytical calculations using the three-team method K123

Аналітичні розрахунки методом трьох команд К123

(%i43)

kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i5)

R : 1 ; B : 2 ; ro : 1000 ; g : 9 . 81 ; H : R ;

\[\operatorname{ }1\]

\[\operatorname{ }2\]

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }1\]

P_x

(%i6)

P : integrate ( rho · gi · ( Hi − h ) · Bi , h ) ;

\[\operatorname{ }\ensuremath{\mathrm{Bi}}\, \ensuremath{\mathrm{gi}}\, \left( \ensuremath{\mathrm{Hi}} h\operatorname{-}\frac{{{h}^{2}}}{2}\right) rho\]

(%i7)

fP ( h ) : = B · g · ( R · h − ( ( h · · 2 ) / 2 ) ) · ro ;

\[\operatorname{ }\operatorname{fP}(h)\operatorname{:=}B g\, \left( R h\operatorname{-}\frac{{{h}^{2}}}{2}\right) \, \ensuremath{\mathrm{ro}}\]

(%i8)

fP_x ( B , g , R , ro , h ) : = B · g · ( R · h − ( ( h · · 2 ) / 2 ) ) · ro ;

\[\operatorname{ }\operatorname{fP\_ x}\left( B\operatorname{,}g\operatorname{,}R\operatorname{,}\ensuremath{\mathrm{ro}}\operatorname{,}h\right) \operatorname{:=}B g\, \left( R h\operatorname{-}\frac{{{h}^{2}}}{2}\right) \, \ensuremath{\mathrm{ro}}\]

(%i9)

fP_x ( 2 , 9 . 81 , 1 , 1000 , 1 ) ;

\[\operatorname{ }9810.0\]

(%i10)

plot2d ( fP_x ( 2 , 9 . 81 , 1 , 1000 , h ) , [ h , 0 , R ] ) ;

\[\operatorname{ }false\]

(%i11)

mP : integrate ( rho · gi · ( ( Hi − h ) · · 2 ) · Bi , h ) ;

\[\operatorname{ }\ensuremath{\mathrm{Bi}}\, \ensuremath{\mathrm{gi}}\, \left( \frac{{{h}^{3}}}{3}\operatorname{-}\ensuremath{\mathrm{Hi}} {{h}^{2}}\operatorname{+}{{\ensuremath{\mathrm{Hi}}}^{2}} h\right) rho\]

(%i12)

mP_d : integrate ( rho · gi · ( Hi − h ) · Bi · h , h ) ;

\[\operatorname{ }\operatorname{-}\left( \frac{\ensuremath{\mathrm{Bi}}\, \ensuremath{\mathrm{gi}}\, \left( 2 {{h}^{3}}\operatorname{-}3 \ensuremath{\mathrm{Hi}} {{h}^{2}}\right) rho}{6}\right) \]

(%i13)

fmP_x ( B , g , H , ro , h ) : = B · g · ( h ^ 3 / 3 − H · h ^ 2 + H ^ 2 · h ) · ro ;

\[\operatorname{ }\operatorname{fmP\_ x}\left( B\operatorname{,}g\operatorname{,}H\operatorname{,}\ensuremath{\mathrm{ro}}\operatorname{,}h\right) \operatorname{:=}B g\, \left( \frac{{{h}^{3}}}{3}\operatorname{-}H {{h}^{2}}\operatorname{+}{{H}^{2}} h\right) \, \ensuremath{\mathrm{ro}}\]

(%i14)

plot2d ( fmP_x ( 2 , 9 . 81 , 1 , 1000 , h ) , [ h , 0 , R ] ) ;

\[\operatorname{ }false\]

(%i15)

fmP_x ( 2 , 9 . 81 , 1 , 1000 , 1 ) ;

\[\operatorname{ }6540.0\]

(%i16)

fh_D : ( fmP_x ( 2 , 9 . 81 , 1 , 1000 , 1 ) ) / ( fP_x ( 2 , 9 . 81 , 1 , 1000 , 1 ) ) ;

\[\operatorname{ }0.6666666666666666\]

(%i17)

plot2d ( [ fP_x ( 2 , 9 . 81 , 1 , 1000 , h ) , fmP_x ( 2 , 9 . 81 , 1 , 1000 , h ) ] , [ h , 0 , R ] ) ;

\[\operatorname{ }false\]

(%i18)

plot2d ( [ fmP_x ( 2 , 9 . 81 , 1 , 1000 , h ) / fP_x ( 2 , 9 . 81 , 1 , 1000 , h ) ] , [ h , 0 , R ] ) ;

\[\]\[expt: undefined: 0 to a negative exponent. \]\[plot2d: expression evaluates to non-numeric value somewhere in plotting range.\]

\[\operatorname{ }false\]

P_z

_jh_ex1c.ai -----------------------------

Figure 3:D:\j_Iam_TEMP\_jh\_jh_ex1c.jpg
Diagram

Figure 4:D:\j_Iam_TEMP\_jh\_jh_ex1d.jpg
Diagram

(%i19)

kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i5)

R : 1 ; B : 2 ; ro : 1000 ; g : 9 . 81 ; H : R ;

\[\operatorname{ }1\]

\[\operatorname{ }2\]

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }1\]

(%i7)

P_x : integrate ( ro · g · ( H − h ) · B , h , 0 , R ) ; P_x / 9 ;

\[\]\[rat: replaced 9810.0 by 9810/1 = 9810.0\]

\[\operatorname{ }9810\]

\[\operatorname{ }1090\]

(%i10)

fB ( h ) : = R − sqrt ( R · · 2 − h · · 2 ) ; fB ( 0 ) ; fB ( R ) ;

\[\operatorname{ }\operatorname{fB}(h)\operatorname{:=}R\operatorname{-}\sqrt{{{R}^{2}}\operatorname{-}{{h}^{2}}}\]

\[\operatorname{ }0\]

\[\operatorname{ }1\]

(%i11)

P_z : integrate ( fB ( h ) · B · ro · g , h , 0 , R ) , numer ;

\[\]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 1.0 by 1/1 = 1.0 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 2.0 by 2/1 = 2.0 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 1.5 by 3/2 = 1.5 \]\[rat: replaced 2.0 by 2/1 = 2.0 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.21460183660255128 by 5844813/27235615 = 0.21460183660255147\]

\[\operatorname{ }4210.48803414206\]

(%i12)

mP_z : integrate ( fB ( h ) · B · ro · g · ( R − fB ( h ) / 2 ) , h , 0 , R ) , numer ;

\[\]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced 0.16666666666666666 by 1/6 = 0.16666666666666666 \]\[rat: replaced 0.16666666666666666 by 1/6 = 0.16666666666666666\]

\[\operatorname{ }3270.0\]

(%i16)

x_C : mP_z / P_z ; x_C_ : R − x_C ; 295 · 0 . 22336793894575135 ; 295 · 0 . 7766320610542486 ;

\[\operatorname{ }0.7766320610542486\]

\[\operatorname{ }0.22336793894575135\]

\[\operatorname{ }65.89354198899665\]

\[\operatorname{ }229.10645801100335\]

(%i18)

W_test : integrate ( fB ( h ) · B , h , 0 , R ) , numer ; P_z_test : W_test · ro · g ;

\[\operatorname{ }0.42920367320510294\]

\[\operatorname{ }4210.488034142059\]

(%i19)

W_test : ( R · · 2 − ( ( %pi · ( R · · 2 ) ) / 4 ) ) · B , numer ;

\[\operatorname{ }0.42920367320510344\]

(%i21)

P_z_test : W_test · ro · g ; P_z_test / 9 ;

\[\operatorname{ }4210.488034142065\]

\[\operatorname{ }467.83200379356276\]

(%i23)

P : sqrt ( P_x · · 2 + P_z · · 2 ) ; P / 9 ;

\[\operatorname{ }10675.406759728337\]

\[\operatorname{ }1186.156306636482\]

(%i25)

phi_rad : atan ( P_z / P_x ) , numer ; phi_g : ( 180 / %pi ) · phi_rad , numer ;

\[\operatorname{ }0.40542580169731124\]

\[\operatorname{ }23.229187342963783\]

----------------------------------------------

(%i26)

kill ( all ) ;

\[\operatorname{ }\ensuremath{\mathrm{done}}\]

(%i1)

S : 300 ;

\[\operatorname{ }300\]

(%i6)

R : 1 ; B : 2 ; ro : 1000 ; g : 9 . 81 ; H : R / 2 , numer ;

\[\operatorname{ }1\]

\[\operatorname{ }2\]

\[\operatorname{ }1000\]

\[\operatorname{ }9.81\]

\[\operatorname{ }0.5\]

(%i7)

P_x : integrate ( ro · g · ( R − h ) · B , h , 0 , H ) ;

\[\]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.375 by 3/8 = 0.375\]

\[\operatorname{ }7357.5\]

(%i8)

mP_x : integrate ( ro · g · ( R − h ) · B · ( R − h ) , h , 0 , H ) ;

\[\]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.2916666666666667 by 7/24 = 0.2916666666666667\]

\[\operatorname{ }5722.5\]

(%i11)

h_D : mP_x / P_x ; ( R − h_D ) ; ( R − h_D ) · S ;

\[\operatorname{ }0.7777777777777778\]

\[\operatorname{ }0.2222222222222222\]

\[\operatorname{ }66.66666666666666\]

(%i12)

fB ( h ) : = sqrt ( R · · 2 − ( R − h ) · · 2 ) ;

\[\operatorname{ }\operatorname{fB}(h)\operatorname{:=}\sqrt{{{R}^{2}}\operatorname{-}{{\left( R\operatorname{-}h\right) }^{2}}}\]

(%i13)

P_z : integrate ( ro · g · ( R − h ) · ( fB ( h ) ) · B , h , 0 , H ) , numer ;

\[\operatorname{ }4247.854605562666\]

(%i14)

P : sqrt ( P_x · · 2 + P_z · · 2 ) ;

\[\operatorname{ }8495.70921112534\]

(%i16)

phi_rad : atan ( P_z / P_x ) , numer ; phi_g : ( 180 / %pi ) · phi_rad , numer ;

\[\operatorname{ }0.5235987755982983\]

\[\operatorname{ }29.999999999999964\]

(%i17)

P_z : integrate ( fB ( h ) · B · ro · g , h , 0 , H ) , numer ;

\[\]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.5 by -1/2 = -0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 1.0 by 1/1 = 1.0 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.25 by -1/4 = -0.25 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced -0.125 by -1/8 = -0.125 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 1.0 by 1/1 = 1.0 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.25 by 1/4 = 0.25 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5\]

\[\operatorname{ }19620.0 \left( 0.25 \ensuremath{\pi} \operatorname{-}0.4783057387452591\right) \]

(%i18)

mP_z : integrate ( fB ( h ) · B · ro · g · ( fB ( h ) / 2 ) , h , 0 , H ) , numer ;

\[\]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 0.5 by 1/2 = 0.5 \]\[rat: replaced 1.0 by 1/1 = 1.0 \]\[rat: replaced -0.3333333333333333 by -1/3 = -0.3333333333333333 \]\[rat: replaced 0.20833333333333334 by 5/24 = 0.20833333333333334\]

\[\operatorname{ }2043.75\]

(%i20)

x_C : mP_z / P_z , numer ; S · x_C ;

\[\operatorname{ }0.3392029835468756\]

\[\operatorname{ }101.76089506406268\]

-->

----------------------------------------------

(%i23)

x : 600 ; y : 150 ; x2 : x / 2 ;

\[\operatorname{ }600\]

\[\operatorname{ }150\]

\[\operatorname{ }300\]

(%i25)

sr : 0 . 4244 ; sr_1 : 1 − sr ;

\[\operatorname{ }0.4244\]

\[\operatorname{ }0.5756\]

(%i28)

z_c : x2 · sr ; z_c_1 : x2 · sr_1 ; z_c + z_c_1 ;

\[\operatorname{ }127.32\]

\[\operatorname{ }172.68\]

\[\operatorname{ }300.0\]

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