Composite Program (CurveP - Accurate TVM - Hg vapour standard - RainGaugeCalP - Parallel resistances - Quadratic equation solve - Convert to Fraction - Solve a System of Linear Equations - EbikeMax - Bike Power - Bike Development - Function tests)

Description

J E Patterson - jepspectro.com - 20210329

This program works with the DM15C series of calculators by SwissMicros. The extended memory firmware should be installed. The hp15c Simulator by Torsten Manz can be used as well if the DM15C preferences are set to 229 registers. The programs are self-contained so they can be extracted as separate programs.

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CurveP J E Patterson - jepspectro.com - version 20191006

CurveP starts at line 1 and finishes at line 163.

The program fits data that may be linear at low x,y amplitudes but y falls off at higher x values.
This is a common issue in many physical systems. x1, y1 should preferably be on the linear part of the curve.
CurveP is not a regression. It assumes that the data is reasonably precise. Linear and power curves can be fitted, as well.

The equation used is y = scale*xorder + slope*x*e-factor*x. See Curve Fitting at jepspectro.com.


Originally chart recorders were used to obtain data which occupied the y axis, leaving interpreted results naturally plotted on the x axis, when graphed on the same paper.
Here we are using y as the equation output axis.

x is first normalised, the equation solved and un-normalised to get y.
The equation parameters, scale, order, slope and factor are found by entering some standard data.

y1 ENTER, y2 ENTER, y3 f A
x1 ENTER, x2 ENTER, x3 f B

Do not press ENTER after y3 or x3.
y3>y2>y1 and x3>x2>x1.
After normalisation y3 = x3 = 10 so x3 is not saved. y3 is used instead in the program.

The curve runs through the origin and three points (x1,y1) (x2,y2) (x3,y3).
The order of the upper part of the curve is displayed.

y input to GSB C to get x. This uses SOLVE to run GSB D - y until zero, the solution x is obtained.
x input to GSB D to get y.

If there is a blank value, enter it and subtract the answers.
Enter f USER to avoid the f key during data input.

Test [x,y] data sets [2,2 4,5 5,8] [1,1 2,4 3,9] [1,1 2,2 3,3] [20,3.69 30,8.64 47,22.16]
Enter y data in A and x data in B. eg. y1 ENTER y2 ENTER y3 GSB A, x1 ENTER x2 ENTER x3 GSB B.
The last data set relates an element's atomic number to its X-ray fluorescence k line energy in keV - see Moseley's Law.

In this update I have improved the starting values for the iteration and added a refined guess to the stack for Solve. A second guess is created by entering the first twice and multiplying by 1.1.

Order is limited to 10.

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TVM - Time Value of Money - Accurate TVM usage instructions - Jeff Kearns

TVM starts at line 164 and finishes at line 203.

1. Store 4 of the following 5 variables, using appropriate cash flow conventions as follows:

n STO 1 --- Number of compounding periods
i STO 2 --- Interest rate (periodic) expressed as a %
PV STO 3 --- Present Value
PMT STO 4 --- Periodic Payment
FV STO 5 --- Future Value

Store the appropriate value (1 for Annuity Due or 0 for Regular Annuity) as
B/E STO 6 --- Begin/End Mode. The default is 0 for regular annuity or End Mode.

2. Store the register number X containing the floating variable to the indirect storage register as X STO I.

3. f SOLVE E

Example from the HP-15C Advanced Functions Handbook - Page 145 and Page 151

"Many Pennies (alternatively known as A Penny for Your Thoughts):

A corporation retains Susan as a scientific and engineering consultant.
Her fee is one penny per second for her thoughts, paid every second of every day for a year.
Rather than distract her with the sounds of pennies dropping, the corporation proposes to deposit them for her into a bank account.
Interest accrues at the rate of 11.25 percent per annum compounded every second.
At year's end these pennies will accumulate to a sum

total = (payment) x ((1+i/n)^n-1)/(i/n)

where payment = $0.01 = one penny per second,
i = 0.1125 = 11.25 percent per annum interest rate,
n = 60 x 60 x 24 x 365 = number of seconds in a year.

Using her HP-15C, Susan reckons that the total will be $376,877.67.
But at year's end the bank account is found to hold $333,783.35 .
Is Susan entitled to the $43,094.32 difference?"

31,536,000 STO 1
(11.25/31,536,000) STO 2
0 STO 3
-0.01 STO 4
5 STO I
f SOLVE E

The HP-15C now gives the correct result: $333,783.35.

Thanks to Thomas Klemm for debugging the routine.
The code has been edited to reflect his suggested changes.

Jeff Kearns

The hyperbolic sine in this program calculates ex-1 more accurately using 2.sinh(x/2).ex/2 from this reference by Thomas Klemm (Post #14).

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HgCalP - J E Patterson - jepspectro.com - version 20151017

HgCalP starts at line 204 and finishes at line 229.

The concentration of mercury vapour in air, above liquid mercury, depends on the temperature.
A good calibration curve can be obtained using a simplified Dumarey equation.
Reference: R. Dumarey, E. Temmerman, R. Dams, J. Hoste, Analyt. Chim. Acta 170, 337 (1985).

Enter the temperature in °C of the mercury calibration vessel, then GSB 1
The mercury vapour concentration in the calibration vessel is displayed in ng/ml

The equation is Hg ng/ml = 10(-3229/(T+273.16)+14.6 - Log(T +273.16)).
At 20°C mercury saturated air has a mercury concentration of 13.14 ng/ml

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RGCalP - J E Patterson - jepspectro.com - version 20151017

RGCalP starts at line 230 and finishes at line 252.

RAIN GAUGE calibration in mm per bucket tip, given the number of bucket tips, the diameter of funnel in mm and the calibration volume of water in ml.

Number of tips ENTER
Diameter of funnel in mm ENTER
Water volume in ml GSB 2
mm per tip is displayed.

A tipping bucket rain-gauge has a funnel diameter of 79 mm.
200 ml of slowly added water generates 81 tips.

8 1 ENTER
7 9 ENTER
2 0 0 GSB 2
The result in x = 0.50 mm of rain per tip.

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Parallel Resistances - J E Patterson - jepspectro.com - version 20151017

Parallel Resistances starts at line 253 and finishes at line 265.

First resistance, press ENTER, second resistance.
GSB 3 for parallel resistance result.
R/S returns first entry for the next try.
Enter a second value and press R/S for a new result.

R1 = 15 ohms and R2 = 10 ohms.
1 5 ENTER
1 0 GSB 3
The parallel resistance R = 6 ohms is displayed in x.

R/S returns R1=15 ohms to x.
1 2 R/S calculates R = 6.7 ohms.
R/S to return R1 = 15 ohms to x.
1 0 R/S calculates R = 6 ohms, etc.

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Quadratic Equation Solver program for the HP-15C - from Torsten Manz

This program starts at line 266 and finishes at line 359.

This program finds the roots of a quadratic equation of the form ax2 + bx + c = 0.
Push a, b, and c into the Z, Y, and X registers of the stack respectively, then press GSB 4.
The discriminant b2 - 4ac is displayed briefly.
If it is positive there are two real roots.
If is zero there is one real root.
If it is negative there are two complex roots.
The roots of the equation will appear in the X and Y registers.
Use X<>Y to view the second root.
If the "C" indicator appears then the roots are complex.
f (i) can be used to temporarily view the imaginary parts.
Press g CF 8 to clear this flag before running the routine again.

Example: a = 1, b = 2, c = 3.
1 ENTER
2 ENTER
3 GSB 4
Roots are in x and y.
x= -1 - √2i
press f (i) to view the imaginary part.
X<>Y
y = -1 + √2i
press f (i) to view the imaginary part.

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Convert to Fraction - Guido Socher

This program starts at line 360 and finishes at line 383.

Let's say you would like to know what 0.15625 as a fraction is.
You type: 0.15625.
GSB 5
The display shows "running" and then you see first 5, and then a second later, 32
The fraction is therefore 5/32 (numerator = 5 and denominator = 32).
32 remains in X (display) after the program finishes and 5 remains in Y.

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Solve a System of Linear Equations - J E Patterson - jepspectro.com - version 20170531

This program starts at line 384 and finishes at line 418.

N GSB 6 where N is the number of equations (8 or less).

A N N is displayed.
Matrix [A] has a dimension of NxN.

Enter the coefficients of xi where i has values from 1 to N
Press R/S after each is entered.

B N 1 is displayed.
Matrix [B] has a dimension of Nx1.

Enter the constants.
Press R/S after each is entered.

C N 1 is displayed.
Matrix [C] has a dimension of Nx1.

Values for xi are read out in turn by pressing R/S.

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EbikeMax - Ebike maximum speed from motor rpm - J E Patterson - jepspectro.com - version 20160210

The program starts at line 419 and ends at line 452

Enter motor rpm
Enter wheel size in inches or mm - the program works out if the units are inches or mm from the magnitude
GSB 7

The maximum speed at 36 volts is displayed.
Press R/S.
The maximum speed at 42 volts is displayed.

speed km/h = 4.79E-3 x motor rpm x wheel size in inches at 42 volts
25.4 x pi x 60 / E^6 = 4.79E-3.

Speed is proportional to the battery voltage and the wheel diameter.
Speed is limited by hills and wind.
For a 20 inch wheel the bike speed in km/h at 42 volts is approximately motor rpm/10.

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Bike Power - J E Patterson - jepspectro.com - version 20160119

This program starts at line 453 and ends at line 532

This program calculates the power required for a given bike speed.

Enter total weight W (kg), STO 1. This weight W includes the bike plus rider.
Enter the grade G (%) of the road, STO 2. For a flat road enter 0 STO 2
Enter V (km/h)
GSB 8
The required power P (watts) to reach a bike speed V (km/h) is displayed.

Enter a head wind speed in km/h. This is an optional step..
Press R/S
The power Pw required to maintain the same speed into the head wind is displayed.

Stored results:
R4 = Power required to overcome air drag resistance, Pd
R6 = Power required to overcome rolling resistance, Pr
R7 = Power required to overcome % grade G, Ps
R8 = The total required power, P = (Pd + Pr + Ps) * 1.0309
R9 = The power required into a head wind, Pw = (R4 * (Va/Vr)^2 + R6 + R7) * 1.0309

There are constants in the program:
1.0309 = 1/(1 - 3/100) compensates for a 3% drive-train loss.
0.2778 = 1000/3600 converts km/h to m/s
0.2626 = 0.5 x (Air Density (1.226) * Drag coefficient Cd (0.63) * Frontal area (0.68))
Reduce this constant in proportion for a more streamlined setup

0.0490 = g (9.8067) * Coefficient of rolling resistance Crr (0.005)
9.8067 = g acceleration due to gravity (m/s²)

Equations:
Pd = Vr * 0.5 * rho * Va^2 * Cd * A
Pr = Vr * m * g * cos(arctan(s)) * Crr
Ps = Vr * m * g * sin(arctan(s))
P = (Pd + Pr + Ps) * 1.0309

Va = Vr + head-wind speed (m/s)
Vr = Va in still air.
Pw = (R4 * (Va/Vr)² + R6 + R7) * 1.0309

Terms:
rho = air density = 1.226 kg/m³
Cd = drag coefficient 0.63
A = frontal area 0.68 m² - upright riding style
m = mass kg = W
g = acceleration due to gravity = 9.8607 m/s²
Crr = coefficient rolling resistance 0.005
s = slope = G/100
Vr = bike road speed (m/s)
Va = bike air speed (m/s)

References:
Bicycle Performance
Bike Calculator

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Bike Development - J E Patterson - jepspectro.com - version 20160210

This program starts at line 533 and finishes at line 572

Enter wheel diameter in inches or mm - the program works out if the units are inches or mm from the magnitude
Enter front sprocket teeth number
Enter rear sprocket teeth number

GSB 9 returns Gear-Inches
R/S returns Metres-Development
R/S returns Gain-Ratio for a 170 mm crank arm

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Function tests - J E patterson - jepspectro.com - version 20151017

This program starts at line 573 and ends at line 614

N STO 2
GSB 0 for N iterations.
N is the number of iterations required otherwise there is only one iteration.

The Simulator result is 3736036.572 with 10,000 iterations in 56 seconds.
The DM15 result is 3736036.611 with 100 iterations in 67 seconds.

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Program Resources

Labels

Name Description Name Description Name Description
 A CurveP - Enter y inputs  3 Parallel resistances .2 CurveP - RCL .5 1/x STO .5
 B CurveP - Enter x inputs  4 Quadratic equation solver .3 CurveP - GSB D-x =0 for SOLVE
 C CurveP - Enter y to get x  5 Convert to Fraction .4 Convert to fraction - loop and test
 D CurveP - Enter x to get y  6 Solve a System of Linear Equations .5 Linear equations - coefficients of xi storage loop
 E TVM SOLVE  7 Electric bike speed .6 Linear Equations - constant storage loop
 0 Function tests  8 Bike Power .7 Linear equations - result display
 1 Mercury - Enter temperature( (°C) for ng/l Hg in air  9 Bike development .8 Quadratic equation - subroutine
 2 Millimetres of rain per tip .1 CurveP - loop .9 Quadratic equation - subroutine

Storage Registers

Name Description Name Description Name Description
 0 Fraction, decimal input value  7 xscale, Ps .4 scale
 1 y1, N, °K, Funnel area, R1+R2, Result, Speed 36V,W,GI  8 yscale, Pt .5 temp1
 2 y2, I, Hg conc, Number of tips, R1, Count, Speed 42V,G,25.4  9 slope, Pw .6 temp2
 3 y3, PV, ml water used, V m/s, 25.4,front/rearT .0 absolute decimal number for fraction .7 temp3
 4 order, PMT, Pd, Wheel size in inches .1 x1 .8 xinput
 5 factor, FV,Tan-1(G/100) .2 x2 .9 yinput
 6 count, B/E 1/0, Pr .3 order first guess (i) Register of TVM value required

Flags

Number Description
8 Indicates, by showing "C" in the display, that the roots are complex numbers

Program

Line Display Key Sequence Line Display Key Sequence Line Display Key Sequence
000 205 2 2 410 42,26,13 f RESULT C
001 42,21,11 f LBL A 206 7 7 411 10 ÷
002 44 8 STO 8 207 3 3 412 42,16, 1 f MATRIX 1
003 33 R⬇ 208 48 . 413 42,21, .7 f LBL . 7
004 44 2 STO 2 209 1 1 414 31 R/S
005 33 R⬇ 210 6 6 415 u 45 13 USER RCL C
006 44 1 STO 1 211 40 + 416 22 .7 GTO . 7
007 45 8 RCL 8 212 44 1 STO 1 417 42,16, 0 f MATRIX 0
008 1 1 213 3 3 418 43 32 g RTN
009 0 0 214 2 2 419 42,21, 7 f LBL 7
010 44 3 STO 3 215 2 2 420 2 2
011 10 ÷ 216 9 9 421 5 5
012 44,10, 2 STO ÷ 2 217 16 CHS 422 48 .
013 44,10, 1 STO ÷ 1 218 45,10, 1 RCL ÷ 1 423 4 4
014 43 32 g RTN 219 1 1 424 44 3 STO 3
015 42,21,12 f LBL B 220 4 4 425 33 R⬇
016 44 7 STO 7 221 48 . 426 2 2
017 33 R⬇ 222 6 6 427 0 0
018 44 .2 STO . 2 223 40 + 428 0 0
019 33 R⬇ 224 45 1 RCL 1 429 34 x↔y
020 44 .1 STO . 1 225 43 13 g LOG 430 43,30, 7 g TEST x>y
021 45 7 RCL 7 226 30 431 45,10, 3 RCL ÷ 3
022 45 3 RCL 3 227 13 10ˣ 432 44 4 STO 4
023 10 ÷ 228 44 2 STO 2 433 33 R⬇
024 44,10, .2 STO ÷ . 2 229 43 32 g RTN 434 33 R⬇
025 44,10, .1 STO ÷ . 1 230 42,21, 2 f LBL 2 435 4 4
026 45 3 RCL 3 231 44 1 STO 1 436 48 .
027 45 2 RCL 2 232 33 R⬇ 437 7 7
028 10 ÷ 233 44 2 STO 2 438 9 9
029 43 12 g LN 234 33 R⬇ 439 26 EEX
030 45 3 RCL 3 235 44 3 STO 3 440 16 CHS
031 45 .2 RCL . 2 236 33 R⬇ 441 3 3
032 10 ÷ 237 45 2 RCL 2 442 45,20, 4 RCL × 4
033 43 12 g LN 238 2 2 443 20 ×
034 10 ÷ 239 10 ÷ 444 44 1 STO 1
035 44 4 STO 4 240 43 11 g 445 31 R/S
036 44 .3 STO . 3 241 43 26 g π 446 48 .
037 1 1 242 20 × 447 8 8
038 44 5 STO 5 243 44 2 STO 2 448 5 5
039 0 0 244 45 1 RCL 1 449 7 7
040 44 6 STO 6 245 45 2 RCL 2 450 10 ÷
041 45 1 RCL 1 246 10 ÷ 451 44 2 STO 2
042 45,10, .1 RCL ÷ . 1 247 45 3 RCL 3 452 43 32 g RTN
043 44 9 STO 9 248 10 ÷ 453 42,21, 8 f LBL 8
044 42,21, .1 f LBL . 1 249 26 EEX 454 48 .
045 1 1 250 3 3 455 2 2
046 44,40, 6 STO + 6 251 20 × 456 7 7
047 45 3 RCL 3 252 43 32 g RTN 457 7 7
048 45 4 RCL 4 253 42,21, 3 f LBL 3 458 8 8
049 43,30, 7 g TEST x>y 254 44 1 STO 1 459 20 ×
050 45 .3 RCL . 3 255 33 R⬇ 460 44 3 STO 3
051 44 4 STO 4 256 44 2 STO 2 461 3 3
052 45 3 RCL 3 257 44,40, 1 STO + 1 462 14
053 45 5 RCL 5 258 43 33 g R⬆ 463 48 .
054 45,20, 3 RCL × 3 259 20 × 464 2 2
055 16 CHS 260 45,10, 1 RCL ÷ 1 465 6 6
056 12 261 31 R/S 466 2 2
057 45,20, 3 RCL × 3 262 45 2 RCL 2 467 6 6
058 45,20, 9 RCL × 9 263 31 R/S 468 20 ×
059 30 264 22 3 GTO 3 469 44 4 STO 4
060 45 3 RCL 3 265 43 32 g RTN 470 45 2 RCL 2
061 45 4 RCL 4 266 42,21, 4 f LBL 4 471 26 EEX
062 43,30, 2 g TEST x<0 267 43, 6, 8 g F? 8 472 2 2
063 45 .3 RCL . 3 268 22 .9 GTO . 9 473 10 ÷
064 44 4 STO 4 269 44 3 STO 3 474 43 25 g TAN⁻¹
065 14 270 33 R⬇ 475 44 5 STO 5
066 10 ÷ 271 16 CHS 476 24 COS
067 44 .4 STO . 4 272 44 2 STO 2 477 48 .
068 45,10, 1 RCL ÷ 1 273 43 11 g 478 0 0
069 45 .1 RCL . 1 274 34 x↔y 479 4 4
070 45 4 RCL 4 275 2 2 480 9 9
071 14 276 20 × 481 0 0
072 20 × 277 44 1 STO 1 482 20 ×
073 44 .5 STO . 5 278 45,20, 3 RCL × 3 483 45,20, 1 RCL × 1
074 1 1 279 2 2 484 45,20, 3 RCL × 3
075 43,30, 8 g TEST x<y 280 20 × 485 44 6 STO 6
076 32 .2 GSB . 2 281 30 486 45 5 RCL 5
077 1 1 282 42 31 f PSE 487 23 SIN
078 45 .5 RCL . 5 283 43,30, 2 g TEST x<0 488 45,20, 1 RCL × 1
079 30 284 22 .8 GTO . 8 489 45,20, 3 RCL × 3
080 43 12 g LN 285 11 √x̅ 490 9 9
081 16 CHS 286 44 0 STO 0 491 48 .
082 45,10, .1 RCL ÷ . 1 287 45,40, 2 RCL + 2 492 8 8
083 44 5 STO 5 288 45,10, 1 RCL ÷ 1 493 0 0
084 45,20, .2 RCL × . 2 289 45 2 RCL 2 494 6 6
085 16 CHS 290 45,30, 0 RCL 0 495 7 7
086 12 291 45,10, 1 RCL ÷ 1 496 20 ×
087 45,20, .2 RCL × . 2 292 43 32 g RTN 497 44 7 STO 7
088 45,20, 9 RCL × 9 293 42,21, .8 f LBL . 8 498 45 4 RCL 4
089 45 .4 RCL . 4 294 43, 4, 8 g SF 8 499 45,40, 6 RCL + 6
090 45 .2 RCL . 2 295 11 √x̅ 500 45,40, 7 RCL + 7
091 45 4 RCL 4 296 42 30 f Re↔Im 501 1 1
092 14 297 45,10, 1 RCL ÷ 1 502 48 .
093 20 × 298 44 .0 STO . 0 503 0 0
094 40 + 299 45 2 RCL 2 504 3 3
095 44 .6 STO . 6 300 45,10, 1 RCL ÷ 1 505 0 0
096 45 2 RCL 2 301 42 25 f I 506 9 9
097 45,10, 3 RCL ÷ 3 302 42 30 f Re↔Im 507 20 ×
098 3 3 303 45 2 RCL 2 508 44 8 STO 8
099 0 0 304 45,10, 1 RCL ÷ 1 509 31 R/S
100 20 × 305 45 .0 RCL . 0 510 48 .
101 45,10, 6 RCL ÷ 6 306 16 CHS 511 2 2
102 11 √x̅ 307 42 25 f I 512 7 7
103 45,20, .6 RCL × . 6 308 43 32 g RTN 513 7 7
104 45 .6 RCL . 6 309 42,21, .9 f LBL . 9 514 8 8
105 45,30, 2 RCL 2 310 44 3 STO 3 515 20 ×
106 10 ÷ 311 42 30 f Re↔Im 516 45 3 RCL 3
107 15 1/x 312 44 .3 STO . 3 517 40 +
108 1 1 313 33 R⬇ 518 45,10, 3 RCL ÷ 3
109 40 + 314 16 CHS 519 43 11 g
110 44 .7 STO . 7 315 44 2 STO 2 520 45 4 RCL 4
111 45,20, 4 RCL × 4 316 42 30 f Re↔Im 521 20 ×
112 44 4 STO 4 317 16 CHS 522 45,40, 6 RCL + 6
113 45 .7 RCL . 7 318 44 .2 STO . 2 523 45,40, 7 RCL + 7
114 1 1 319 42 30 f Re↔Im 524 1 1
115 30 320 11 √x̅ 525 48 .
116 43 16 g ABS 321 34 x↔y 526 0 0
117 1 1 322 2 2 527 3 3
118 26 EEX 323 20 × 528 0 0
119 16 CHS 324 44 1 STO 1 529 9 9
120 6 6 325 42 30 f Re↔Im 530 20 ×
121 43,30, 8 g TEST x<y 326 44 .1 STO . 1 531 44 9 STO 9
122 22 .1 GTO . 1 327 42 30 f Re↔Im 532 43 32 g RTN
123 45 4 RCL 4 328 45 3 RCL 3 533 42,21, 9 f LBL 9
124 43 32 g RTN 329 45 .3 RCL . 3 534 10 ÷
125 42,21,14 f LBL D 330 42 25 f I 535 44 3 STO 3
126 44 .8 STO . 8 331 20 × 536 20 ×
127 45,10, 7 RCL ÷ 7 332 2 2 537 44 1 STO 1
128 45 3 RCL 3 333 20 × 538 2 2
129 20 × 334 30 539 5 5
130 44 .8 STO . 8 335 42 31 f PSE 540 48 .
131 45 4 RCL 4 336 42 30 f Re↔Im 541 4 4
132 14 337 42 31 f PSE 542 44 2 STO 2
133 45,20, .4 RCL × . 4 338 42 30 f Re↔Im 543 2 2
134 45 5 RCL 5 339 11 √x̅ 544 0 0
135 45,20, .8 RCL × . 8 340 44 0 STO 0 545 0 0
136 16 CHS 341 42 30 f Re↔Im 546 45 1 RCL 1
137 12 342 44 .0 STO . 0 547 45 3 RCL 3
138 45,20, .8 RCL × . 8 343 45,40, .2 RCL + . 2 548 10 ÷
139 45,20, 9 RCL × 9 344 42 30 f Re↔Im 549 43,30, 7 g TEST x>y
140 40 + 345 45,40, 2 RCL + 2 550 45,10, 2 RCL ÷ 2
141 45,20, 8 RCL × 8 346 45 1 RCL 1 551 45 3 RCL 3
142 45 3 RCL 3 347 45 .1 RCL . 1 552 20 ×
143 10 ÷ 348 42 25 f I 553 44 3 STO 3
144 43 32 g RTN 349 10 ÷ 554 45 2 RCL 2
145 42,21,13 f LBL C 350 45 2 RCL 2 555 20 ×
146 44 .9 STO . 9 351 45,30, 0 RCL 0 556 44 1 STO 1
147 36 ENTER 352 45 .2 RCL . 2 557 45 2 RCL 2
148 36 ENTER 353 45,30, .0 RCL . 0 558 10 ÷
149 1 1 354 42 25 f I 559 31 R/S
150 48 . 355 45 1 RCL 1 560 45 1 RCL 1
151 1 1 356 45 .1 RCL . 1 561 43 26 g π
152 20 × 357 42 25 f I 562 20 ×
153 42,10, .3 f SOLVE . 3 358 10 ÷ 563 26 EEX
154 43 32 g RTN 359 43 32 g RTN 564 3 3
155 42,21, .2 f LBL . 2 360 42,21, 5 f LBL 5 565 10 ÷
156 45 .5 RCL . 5 361 43 16 g ABS 566 31 R/S
157 15 1/x 362 44 0 STO 0 567 45 1 RCL 1
158 44 .5 STO . 5 363 1 1 568 3 3
159 43 32 g RTN 364 44 1 STO 1 569 4 4
160 42,21, .3 f LBL . 3 365 42,21, .4 f LBL . 4 570 0 0
161 32 14 GSB D 366 33 R⬇ 571 10 ÷
162 45,30, .9 RCL . 9 367 15 1/x 572 43 32 g RTN
163 43 32 g RTN 368 44,20, 1 STO × 1 573 42,21, 0 f LBL 0
164 42,21,15 f LBL E 369 36 ENTER 574 2 2
165 44 24 STO (i) 370 43 44 g INT 575 36 ENTER
166 45 2 RCL 2 371 30 576 36 ENTER
167 26 EEX 372 4 4 577 4 4
168 2 2 373 16 CHS 578 14
169 10 ÷ 374 13 10ˣ 579 15 1/x
170 36 ENTER 375 43 10 g x≤y 580 11 √x̅
171 36 ENTER 376 22 .4 GTO . 4 581 12
172 1 1 377 45 0 RCL 0 582 13 10ˣ
173 40 + 378 45 1 RCL 1 583 43 11 g
174 43 12 g LN 379 43 44 g INT 584 43 12 g LN
175 34 x↔y 380 20 × 585 43 13 g LOG
176 43 36 g LSTx 381 42 31 f PSE 586 43 14 g %
177 1 1 382 43 36 g LSTx 587 43 15 g Δ%
178 43,30, 6 g TEST x≠y 383 43 32 g RTN 588 43 16 g ABS
179 30 384 42,21, 6 f LBL 6 589 16 CHS
180 10 ÷ 385 43, 5, 8 g CF 8 590 23 SIN
181 20 × 386 42,16, 0 f MATRIX 0 591 24 COS
182 45,20, 1 RCL × 1 387 36 ENTER 592 25 TAN
183 36 ENTER 388 42,23,11 f DIM A 593 43 25 g TAN⁻¹
184 12 389 42,16, 1 f MATRIX 1 594 43 24 g COS⁻¹
185 45,20, 3 RCL × 3 390 45,16,11 RCL MATRIX A 595 43 23 g SIN⁻¹
186 34 x↔y 391 42 31 f PSE 596 15 1/x
187 2 2 392 42,21, .5 f LBL . 5 597 42,22,23 f HYP SIN
188 10 ÷ 393 31 R/S 598 42,22,24 f HYP COS
189 42,22,23 f HYP SIN 394 u 44 11 USER STO A 599 42,22,25 f HYP TAN
190 43 36 g LSTx 395 22 .5 GTO . 5 600 43,22,25 g HYP⁻¹ TAN
191 12 396 45,23,11 RCL DIM A 601 43,22,24 g HYP⁻¹ COS
192 20 × 397 42,16, 1 f MATRIX 1 602 43,22,23 g HYP⁻¹ SIN
193 2 2 398 1 1 603 1 1
194 20 × 399 42,23,12 f DIM B 604 0 0
195 45,20, 4 RCL × 4 400 45,16,12 RCL MATRIX B 605 40 +
196 26 EEX 401 42 31 f PSE 606 42 0 f Χ !
197 2 2 402 42,21, .6 f LBL . 6 607 44 1 STO 1
198 45,10, 2 RCL ÷ 2 403 31 R/S 608 1 1
199 45,40, 6 RCL + 6 404 u 44 12 USER STO B 609 44,30, 2 STO 2
200 20 × 405 22 .6 GTO . 6 610 45 2 RCL 2
201 40 + 406 3 3 611 43,30, 1 g TEST x>0
202 45,40, 5 RCL + 5 407 45,16,12 RCL MATRIX B 612 22 0 GTO 0
203 43 32 g RTN 408 42 31 f PSE 613 45 1 RCL 1
204 42,21, 1 f LBL 1 409 45,16,11 RCL MATRIX A 614 43 32 g RTN