## Sunday, March 28, 2021

### Fun With the Casio fx-3650P (March 28 Edition)

Fun With the Casio fx-3650P (March 28 Edition)

Square Root Simplification

This program attempts to simplify the square root √D  to M√A, where D, M, and A are positive integers.

Program:  (68 bytes)

? → D : 2 →  M : Lbl 0 : D ÷ M ² → A : Fix 0 : Rnd : Ans →B : Norm 1 : A - B = 0 ⇒ Goto 1 : 1 M+  : M √ D ⇒ Goto 2 : Goto 0 : Lbl 2 : 1 → M : D →B : Lbl 1 : M ◢ B

Example:

D = 188.  Result:  M = 2, B = 47.   √188 = 2√47

D = 775.  Result:  M = 5, B = 31.   √775 = 5√31

Present Value of a Growing Annuity

Calculate the present value of an annuity where the payments grow X% of each period, where the Y% is the interest rate of the annuity.

Variables:

A = PV

X = periodic growth rate, G%

Y = periodic interest rate, R%

B = payment

C = number of periods, N

Programs:  (77 steps)

? → B : ? → X : ? → Y : ? → C : 0 → A : 1 → M : Lbl 0 : A + ( 1 + .01 X ) ^ ( M - 1 ) ÷ ( 1 + .01 Y ) ^ M → A : 1 M+ : M > C ⇒ Goto 1 : Goto 0 : Lbl 1 : A B → A

Examples:

1.  B = 1000.00 (PMT), X = 3 (G%), Y = 5  (R%), C = 10

Result:  A = 8747.596154 (\$8,747.60)

2.  B = 1000.00, X = 8, Y = 5, C = 10

Result:  A = 10846.42231  (\$10,846.42)

Smoke:  Front Velocity and Time for a Corridor to Fill

This program estimates:

*  The front velocity of the smoke (how quickly the smoke fills a corridor)

*  The time it takes for smoke to fill the corridor.

The program uses SI units (meters, seconds, kilograms).

Program:  (44 bytes)

? → A : ? → B : ? → Y : ? → X : √ ( 9.80665 Y ( 1 - A ÷ B ) ) ÷ 2 → C  ◢ X ÷ C → D

Variables:

Inputs:

A: Ambient Temperature, °C

B:  Gas Temperature, °C

Y:  Height, m

X:  Length, m

Outputs:

C:  Velocity, m/s

D:  Time, s

Example:

Inputs:

A: Ambient Temperature = 28°C

B:  Gas Temperature = 38°C

Y:  Height = 2.95 m

X:  Length = 4.18 m

Results:

C:  Velocity = 1.379588456 m/s

D:  Time = 3.029889081 s

Source:

Lawson, J.R. and Quintiere, J.G. "Slide Rule Estimates of Fire Growth".  Fire Technology, Vol 21., No. 4, November 1985, pg. 267

Sailing:  Distance by Bearings

This program calculates the distance off the abeam for either one or two bearings on the bow.  The variable C is the choice variable.  For one bearing, enter 1 for C.  For two bearings, enter 2 for C.  The fx-3650P is set to Degrees mode.

Distance Using One Bearing

D = X * sin A / cos A = X * tan A

A = angle off the bow, X = run,  D = distance off the abeam

Distance Using Two Bearings

D = (X * sin A) / (sin abs(A - B))

A = first angle, B = second angle

Program: (60 bytes)

Deg : ? → C : ? → X : ? → A : C = 2 ⇒ Goto 2 : X tan A → D : Goto 3 : Lbl 2 : ? → B : √ ( ( A - B ) ² ) : X sin A ÷ sin Ans → D : Lbl 3 : D

Example:

1 Angle:   X = 150 ft, A = 15°.   Enter 1 for C.   Result:  D = 40.192378886 ft

2 Angles:  X = 150 ft, A (first) = 15°, B (second) = 19°.  Enter 2 for C.  Result:  D = 556.5484418 ft

Source:

Shufeldt, Henry H. and Newcomer, Kenneth E.   The Calculator Afloat:  A Mariner's Guide to the Electronic Calculator  United States Naval Institute.  Annapolis, Maryland. 1980.

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Saturday, March 27, 2021

### HP 17BII+: Actuary and Finance Formulas

HP 17BII+:  Actuary and Finance Formulas

Simple Interest

Simple Interest is different from compound interest.   In simple interest, the interest is calculated only on the base principal amount, no matter how much time passes.   In compound interest, the interest is calculated each period (typically monthly or annually) on both the amount of current principal and accumulated interest.  The time value of money (TVM) keys on financial calculators deal work on compound interest.

The formula to calculate future value on a base amount (no annuity) based on simple interest is:

FV = PV * (1 + I%) * N

where the formula to calculate the future value on a base amount (no annuity) compound interest is:

FV = PV * (1 + I%)^N = PV * (1 + I%)N

HP 17BII+ formula:

SIMPLE: FV=PV×(1+0.01×I%×YEARS)

Note:

*  The percent sign (%) is just a character in the HP 17B's solver.

*  I%  =  periodic interest, YEARS = number of years

Example:

1.  Find the future value of a 6% simple interest loan of \$150.00.  The loan last 90 days on a 365-day year.

PV = 150.00, I% = 6, YEARS = 90/365 (90 [÷] 365 [=] in ALG mode, 90 [ENTER] 365 [÷] in RPN mode)

Result: FV = 152.22

(Note that the cash flow convention is not followed here)

2.  Find the simple interest rate if you made an auto business loan of \$1,750.00 for 6 months (1/2 year) and received \$1,790.00.

PV = 1,750.00, FV = 1,790.00, YEARS = 0.5

Result:  I% = 4.90  (about 4.9%)

Ordinary Growing Annuity

The following formula calculates the present value of a growing annuity:  with R% the interest rate of the annuity and G% the growth of each payment.  Note that both R% and G% are both periodic rates.

HP 17BII+ formula:

GROWING: PV=PMT×∑(K:1:N:1:(1+.01×G%)^(K-1)÷(1+.01×R%)^K)

Examples:

1.  Find the present value of a growing annuity with base payment of \$1,000, if each payment grows 5% each period for 12 periods.  The interest rate of the annuity is 4%.

PMT = 1,000.00, G% = 5, R% = 4, N = 12

Result:  PV = 12,168.66

(Note that the cash flow convention is not followed here)

2.  Same situation as Example 1 except the payment grows 3%.

PMT = 1,000.00, G% = 3, R% = 4, N = 12

Result:  PV = 10,947.40

3.  What is the required growth rate if the present value is \$12,000.00?

PMT = 1,000.00, R% = 4, N = 12, PV = 12,000.00

Result: G% = 4.74  (4.73859628349)  (after some time)

Present Value or Payment of a Annuity of Variable Interest Rate

This formula calculates the present value of an annuity of constant payment that varies in interest rate per period.

1.  Create a SUMS list named LIST.   This will be the list of each interest rate from Period 1 to Period N.

2.  Go to the Solver, enter the required parameters (PMT or PV) and solve (for either PMT or PV).

HP 17BII+ formula:

PVVARI%: PV=PMT×∑(I:1:SIZES(LIST):1:(1+ITEM(LIST:1)×.01)^(-I))

Example:

What is the annual payment of a loan of \$5,000.00 loan with a variable interest rate:

Years 1-3:  5.0%

Years 4-6:  4.0%

Year 7:  4.5%

LIST  = {5, 5, 5, 4, 4, 4, 4.5}

PV = 5,000.00

Result:  PMT = 843.86

Solve for Interest and Number of Periods Given Present Value Annuity Factor and Future Value Annuity Factor

Given the present value of annuity factor (PVAF) and the future value of annuity factor (FVAF), we can solve the periodic interest rate and number of periods are:

I% = (1/PVAF - 1/FVAF) * 100

N = ln(FVAF/PVAF) / ln(1 + I%*.01)

HP 17BII+ formula:

IF(S(I%):L(I:INV(PVAF)-INV(FVAF))×100-I%:LN(FVAF÷PVAF)÷LN(1+G(I))-N)

Solve for I% first, then for N.

Example:

PVAF = 12, FVAF = 18

Result:  I% = 2.78, N = 14.8

Source:

Finan, Marcel B.  A Basic Course in the Theory of Interest and Derivatives Markets:  A Preparation for the Actuarial Exam FM/2   Arkansas Tech University, 2017.

Note:  This is the first post done with a Chromebook using the editor in both Blogger and Google Docs, and eventually make diagrams using Sketchpad or an applicable Google/Android app. For the better part of three years, I used Windows based application WordPad and Paint.  I miss having a laptop, being able to visit favorite local coffee shops and being able to do work there.   I can't wait until the world opens up again.  Time's are a changing.

Special gratitude to all the nurses and doctors who have and continually to be on the front lines in the COVID-19 crisis.

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Sunday, March 21, 2021

### HP Prime: Testing Random Normal Distribution Generators

HP Prime:  Testing Random Normal Distribution Generators

Introduction

The HP Prime's randNorm generates random numbers to fit a normal distribution curve.  The Box-Muller Method is used, and calls for the use of the formula:

x1 = √(-2 * ln u1) * cos(2*π*u2)

where

u1 and u2 came from random generated numbers which takes the values in the range [0, 1).

The Box-Muller Method also includes a second formula, which isn't used by the calculator:

x2 = √(-2 * ln u1) * sin(2*π*u2)

I imply that the radians mode is used in this calculation.

What about using the direct normal distribution function?

(I)  y = 1/√(2*π) * e^(-x^2/2)

Where y represents the probability and the maximum value y can take is when x=0:

(II)   y = 1/√(2*π)

Solving (I) for x returns the solution:

(III) x = ± √(-2*ln(y*√(2 * π)))

Can (III) be a generator of random numbers that fit a normal distribution?

TESTBX uses the cosine portion of the formula to generate random numbers:

x = √(-2 * ln u1) * cos(2*π*u2)

While TESTND uses the following formula to generate random numbers:

x = u2 * √(-2*ln(u1*√(2 * π)))

where: u1 a random number between [0, 1) and u2 is either -1 or 1 chosen at random.  To accomplish the -1 or 1 choice, I use a wide range of random integers.

The programs generate a list of 300 data points and I used a histogram plot of four samples to see whether the sample fits a normal curve.  While this isn't a rigorous proof, the plots give an idea of what the results would look like.

HP Prime Program: TESTBX

EXPORT TESTBX()

BEGIN

// Box-Muller, 300 points

// EWS 2021

HAngle:=0;

LOCAL u1,u2,i,x,l;

l:={};

FOR i FROM 1 TO 300 DO

u1:=RANDOM();

u2:=RANDOM();

x:=√(−2*LN(u1))*COS(2*π*u2);

l:=CONCAT(l,{x});

END;

RETURN l;

END;

HP Prime Program: TESTND

EXPORT TESTND()

BEGIN

// Normal Dist, 300 points

// EWS 2021

HAngle:=0;

LOCAL u1,u2,i,x,l,m;

l:={};

FOR i FROM 1 TO 300 DO

// maximum

m:=1/√(2*π);

u1:=m*RANDOM();

u2:=SIGN(RANDINT(−100,101));

x:=u2*√(−2*LN(u1*√(2*π)));

l:=CONCAT(l,{x});

END;

RETURN l;

END;

As you can see, the four samples match nowhere near a normal distribution curve.  Clearly, the Box Muller transform does a better job.

Sources:

"Box-Muller transform" Wikipedia.  Last edited December 27, 2020.  https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform  Retrieved January 20, 2021.

"Which formula does randNorm use?"  Thread.  The Museum of HP Calculators.  Last edited October 31, 2017.  https://www.hpmuseum.org/forum/thread-9403.html  Retrieved January 21, 2021.

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Saturday, March 20, 2021

### Testing The Accuracy of LN and EXP Approximations

Testing The Accuracy of LN and EXP Approximations

Introduction

Today we are testing an approximation polynomial for two common scientific functions.  I used a TI-84 Plus CE in testing.   The values take a range from x = 0.5 to x = 11.

Approximating e^x

Approximation used:

e^x ≈ 1 + x * (1 + x/2 * (1 + x/3 * (1 + x/4 * (1 + x/5 * (1 + x/6)))))

(fractions are simplified, see source)

TI-84 Plus CE Program:  EXPTEST

"EWS 2021-01-19"

Disp "e^(X) TEST","JON M. SMITH"

Disp "RANGE, MIN. 0.5"

Input "START? ",A

Input "INCREMENT? ",I

Input "NO STEPS? ",N

seq(X,X,A,A+I*N,I)→L₁

e^(L₁)→L₂

1+L₁*(1+L₁/2*(1+L₁/3*(1+L₁/4*(1+L₁/5*(1+L₁/6)))))→L₃

abs(L₂-L₃)→L₄

iPart(log(L₄))→L₅

Disp "L₁:X, L₂:EXP, L₃:APPROX","L₄:ABS ERROR","L₅:PLACES"

SetUpEditor L₁,L₂,L₃,L₄,L₅

Disp "PRESS STAT, 1. EDIT"

Test: x range:  0.5 to 11, increments of 0.5

Approximating ln x

Approximation used:

ln x ≈ y * (1 + y/2 * (1 + 2y/3 * (1 + 3y/4 * (1 + 4y/5))))

where x ≥ 0.5

and y = (x - 1)/x

(see source)

TI-84 Plus CE Program:  LNTEST

"EWS 2021-01-19"

Disp "ln(X) TEST","JON M. SMITH"

Disp "RANGE, MIN. 0.5"

Input "START? ",A

Input "INCREMENT? ",I

Input "NO STEPS? ",N

seq(X,X,A,A+I*N,I)→L₁

ln(L₁)→L₂

(L₁-1)/L₁→L₆

L₆*(1+L₆/2*(1+2*L₆/3*(1+3*L₆/4*(1+4*L₆/5))))→L₃

abs(L₂-L₃)→L₄

Disp "L₁:X, L₂:LN, L₃:APPROX","L₄:ABS ERROR"

SetUpEditor L₁,L₂,L₃,L₄

Disp "PRESS STAT, 1. EDIT"

Test: x range:  0.5 to 11, increments of 0.5

Final Thoughts

The approximation for ln x hold much better than e^x as x increases.   I would not recommend the following approximations for values above 5.

Source:

Smith, Jon M.  Scientific Analysis on the Pocket Calculator John Wiley & Sons: New York. 1975

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Sunday, March 14, 2021

### Retro Review: Radio Shack EC-21 (Blackjack Calculator)

Retro Review: Radio Shack EC-21 (Blackjack Calculator)

Welcome to my birthday blog.  44 years today (March 14, 1977).

Quick Facts:

Models:  EC-21
First Manufactured: 1978
Memory Register:  1 independent memory
Battery:  3 AAA

The Calculator and The Game

The Radio Shack EC-21 is a dual-purpose calculator:  a 10-digit calculator and full blackjack game.

The Calculator

The calculator is a 10 digit, four function calculator with something extra:  a parenthesis [ ( ) ] key.   The parenthesis key allows the user to put certain calculations in higher priority.   The calculator operates in chain mode, the order of operations is not taken into consideration.

Example:

2 x (3 + 9) = 24

Keystrokes:  2 [ x ] [ ( ) ] 3 [ + ] 9 [ ( ) ] [ = ]

The calculator has a square root function, but it does not have a memory register.

The Game:  Blackjack

In GAME mode, the EC-21 is a one player blackjack game.  It is you against the house.  The house stands on 17 - 21.

Enter a bet and press the [ √ ] (BET) key.   You are not limited in bankroll.  Once you place the bet, the screen shows all zeroes as the calculator shuffles a deck of 52 playing cards.  Kings, queens, jacks, and tens are shown on the display as an F (face card).  Aces, shown by an A, count as either 1 or 11.  The ace is counted to the player's best benefit.

If you get a blackjack (Ace and a Face card) you automatically win, the payout is 3:2.

The game keys are:

[ = ] (HIT): Hit: The player takes a hit.  Be careful, going over 21 will cause you to bust and lose the game.

[ - ] (INS):  Insurance:  If the Dealer's up card is an Ace, you can take insurance, which is half of your bet.  If you take Insurance and the Dealer has a blackjack (Ace and a Face card), you lose only half your bet.

[ + ] (STD):  Stand.   Press this key when you decide to take no more cards.

[ ÷ ] (SPL):  Split.  If you are dealt a pair, you can split your cards into two hands.  If you split aces, you only get one more card per ace.   In this case, any 21 pays off at 1:1.

[ × ] (DBL):  Double Down.  If you have strong starting hand, such as a 10 or 11 against a Dealer's favorable up card, you can double your bet for one more card.

After each hand, press the total key ( [ ( ) ] (TOL) ) to check your earnings.

Keyboard

The keyboard has a solid feel.  However, the keys require a firm press to register.  I have the best luck of holding the calculator in my hand.  In my experience, laying the keyboard down flat did not allow me to register all the keys, particular the zero key.  If wish the keys were not hard to press.  It may be the luck of the draw when I made the purchase.

I love the colors:  green for the number keys, red of the clear keys, blue for the function keys.

Verdict

The calculator is stored in a beautiful leather case, and the green display is awesome.  I also like the two-in-one calculator/game.  I wish the keyboard is better, but buying it is not expensive, and I am happy to have this in my collection.

Source:

Flow Simulation, Ltd.  "Radio Shack EC-21 (Blackjack 21)"  Retrieved January 22, 2021.  https://americanhistory.si.edu/collections/search/object/nmah_334462

National Museum of American History Behring Center.  "Radio Shack EC-21 Handheld Electronic Calculator, Blackjack"  Washington D.C. Retrieved January 23, 2021.  https://americanhistory.si.edu/collections/search/object/nmah_334462

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Saturday, March 13, 2021

### Retro Review: Texas Instruments Personal Banker

Retro Review:   Texas Instruments Personal Banker

Quick Facts:

Models:  Personal Banker

Company:  Texas Instruments

Years:  1987 - 1988

Memory Register:  1 independent memory, 5 financial registers

Battery:  Solar

Finance in a Clamshell Calculator

The Texas Instruments Personal Banker is a basic solar financial calculator.   The calculator opens up like a book.  The gray case gives the calculator a professional look.

On the left side, we have the arithmetic functions with the memory functions (M+, M-, MRC).   There are three keys of note:

[ AC ]:  The key clears everything, resets the format to 2 decimal fixed mode, clear the memory register, and the financial register.

[ CE/C ]:  Clear the last entry but keeps everything in the memory register and financial registers intact.

[ DEC ]:  This sets the fixed decimal format.  The default is 2 places.  [ DEC ] [ . ] (decimal point) sets the Personal Banker to floating mode.

On the right side are the Time Value of Money keys:

[ 1st Amt ]:   Present Value  (PV)

[ # Pmts ]:  Number of Payments (n)

[ Int Rate ]:  Interest Rate per Period (i%)

[ Pmt Amt ]:  Payment (PMT)

[ Final ]:  Future Value (FV)

The [ Solve ] and [ Recall ] keys work exactly the way you expect.

The cash flow convention (positive for inflows, negative for outflows) is followed.

It is very simple.  A four function calculator with a full time value of money solver.

To help the user, included with the Personal Banker are four cards:

Blue Car Symbol:  Loans & Mortgages

Red Dollar Symbol:  Savings with Periodic Deposits

Gold Stock Graph Symbol:  Investments

Green House Symbol:  Loans & Mortgage with a Balloon Payment

Keyboard

The feel of the keys are solid.  However, the keys take a small fraction of a second for the key to register, so make sure the key registers before typing the next key.

Verdict

The Personal Banker is a basic financial calculator.  I really like the folding design on this calculator and how the keys work.  Unfortunately, the high price point of \$50 (see source) and it's basic set of functions (arithmetic, percent, time value of money, but no cost-sell-margin solver, amortization, statistics, logarithms, or exponents) did not help sales of the Personal Banker.

It is a good collector item, since vintage solar-powered Texas Instruments financial calculators yield premium prices.

Source

Woerner, Joerg.  "Texas Instruments TI-2600 Personal Banker"  Datamath.  Updated July 22, 2002.  Retrieved January 23, 2021.  http://www.datamath.org/Sci/Modern/PersonalBanker.htm

On Sunday, we'll take another trip back in time.

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Sunday, March 7, 2021

### Fun with the TI-73 Part II: Rolling Two Dice, Numerical Derivative, Rectangular/Polar Conversions

Fun with the TI-73 Part II: Rolling Two Dice, Numerical Derivative, Rectangular/Polar Conversions

TI-73 Program:  TWODICE - Rolling Two Dice

Introduction:

The program TWODICE will roll two regular dice and give the sum of those dice in three lists:

L_1: die 1

L_2: die 2

L_3: total

If there are seven rolls or less, the program displays the rolls.  In any case, the results are stored in the above lists.

Access L_1 by pressing [ 2nd ] [ STAT ] (LIST), 1

Access L_2 by pressing [ 2nd ] [ STAT ] (LIST), 2

Access L_3 by pressing [ 2nd ] [ STAT ] (LIST), 3

Program:

"EWS 2021"

Disp "ROLL THE DICE"

Input "ROLLS? ",X

dice(X)→L_1

dice(X)→L_2

L_1+L_2→L_3

If X≤7

Then

ClrScreen

For(A,1,X)

Output(A,1,L_1(A))

Output(A,3,L_2(A))

Output(A,6,L_3(A))

End

Pause

End

ClrScreen

Disp "L_1 = DIE 1","L_2 = DIE 2","L_3 = TOTAL"

Pause

TI-73 Program:  DERIVY1 - Numerical Derivative of y1(x)

The simple program DERIVY1 calculates the numerical derivatives of the equation stored in Y_1.

Access Y_1 by pressing [ 2nd ] [ APPS ] (VARS), 2, 1

Program:

"EWS 2021"

Disp "D/DX Y_1"

Prompt X

10^(-8)→H

(2*H)^-1*(Y_1(X+H)-Y_1(X-H))→D

Disp "APPROX D/DX"

Pause D

Example:

Y_1 = (X^2-3)^2 + 1

Derivative at x = 0.95, Result:  -7.9705

Derivative at x = 2, Result:  8

Y_1 = e^(X^3/4)

Derivative at x = 0.46, Result: 0.16261

Derivative at x = 1.55, Result:  4.571295

TI-73 Program: RECPOL - Rectangular/Polar Conversion

This program has two conversions:

1.  >RECT:  Polar (r, θ) to Rectangular (x, y)

2.  >POLAR:  Rectangular (x, y) to Polar (r, θ)

This program works in either Degree or Radian mode.

I take a different approach to calculate angle than the atan2 method.  Approached this as calculating the angle between the vectors [ x, 0 ] and [ x, y].  The angle between vectors v1 and v2 is:

θ = acos( dot(v1, v2) / ( norm(v1) * norm(v2) ) = acos( x / √(x^2 + y^2))

The angle is negative if y<0.

Like the argument and angle conversions, the point (0,0) is defined to have an angle of 0.

Since there is no theta character (θ) on the TI-73, I use the variable A instead.

Program:

"EWS 2021"

Lbl 0

Lbl 1

Input "R? ",R

Input "ANG? ",A

R*cos(A)→X

R*sin(A)→Y

Disp "X= ",X,"Y= ",Y

Pause

Goto 0

Lbl 2

Input "X? ",X

Input "Y? ",Y

√(X^2+Y^2)→R

If X=0 and Y=0

Then

0→A

Else

cos^-1(X/√(X^2+Y^2))→A

If Y<0

-A→A

End

Disp "R=",R,"ANG=",A

Pause

Goto 0

Lbl 3

Examples:

Examples are in Degree mode.

R = 19, ANG = 87.3°

Result:  X = 0.8950225635, Y = 18.97890762

X = -11.5, Y = 2.4

Result:  R = 1.74776575, ANG = 168.2118167

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

## Saturday, March 6, 2021

### Fun with the TI-73 Part I: Logarithmic Regression, Percent, Square Root Simplification

Fun with the TI-73 Part I: Logarithmic Regression, Percent, Square Root Simplification

TI-73 Program:  LNREG - Logarithmic Regression

Introduction:

The program LNREG fits the data to the equation:

y = a * ln x + b

The lists used are:

L_1:  x list

L_2:  y list

Access L_1 by pressing [ 2nd ] [ STAT ] (LIST), 1.

Access L_2 by pressing [ 2nd ] [ STAT ] (LIST), 2

You can edit lists by pressing [LIST].

The lower case a and b are from the VARS, Statistics, EQ menu.

Program:

"EWS 2021"

Disp "FIT Y=A LN X +B","USES X=L1,Y=L2:

ln(L_1) → L_1

LinReg(ax+b) L_1,L_2

a → A

b → B

Output(4,1,"A=")

Output(4,5,A)

Output(5,1,"B=")

Output(5,5,B)

Output(6,5,r²)

e^(L_1) → L_1

Pause

Lbl 1

PlotsOff

FnOff

"A*ln(X)+B"→Y_1

Plot1(xyLine,L_1,L_2,□)

ZoomStat

Lbl 2

Example:

X:  L_1 = {1, 2, 3, 4, 5, 6}

Y:  L_2 = {-1.26, 2.1018, 4.0683, 5.4635, 6.5458, 7.43}

Results:

y = A ln x + B

A = -1.259978557

B = 4.849985251

r^2 ≈ 1

TI-73 Program: PERCENT - Percent Calculations

Introduction:

The program gives the users four options:

2.  Subtracting tax (minus percent)

3.  Percent Change

4.  Percent Total

The percent key divides the amount by 100.  Example:  5% turns to 0.052.

Program:

"EWS 2021"

Lbl 1

Prompt N

Input "X% ",X

N*(1+X%)→Y

Pause Y

Stop

Lbl 2

Prompt N

Input "X% ",X

N*(1-X%)→Y

Pause Y

Stop

Lbl 3

Input "OLD=",O

Input "NEW=",N

(N-O)*100/O→Y

Pause Y

Stop

Lbl 4

Input "PART=",P

Input "WHOLE=",W

100*P/W→Y

Pause Y

Stop

Example:

N: 19.95, X%:  15

Result:  22.9425

TAX-:  Subtract 15% from 19.95

N:  19.95, X%:  15

Result:  16.9575

%CHG:  Old (O):  11700, New (N):  15420

Result:  31.79487179

%TOT:  Part (P):  11700, Whole (W):  15420

Result:  75.7548638

TI-73 Program: SQROOT - Simplification Square Root

This program tries to factor √N to A√B.  N, A, and B are integers.

Program:

"EWS 2021"

Disp "√(N)->A√(B)"

Prompt N

iPart(√(N))→X

While X≠0

If fPart(N/X^2)=0

Then

X→A

N/X^2→B

Goto 1

Else

X-1→X

End

End

Lbl 1

Disp "A=",A,"B=",B

Pause

Examples:

N = 88;   √88 = 2√22

N = 1225;  √1225 = 35√1

Notes:

*  There is no ALPHA key for the TI-73 (family).   Text is entered by use of the [ 2nd ] [ MATH ] (TEXT) key sequence.  Letters are selected by using the arrow keys and selecting them with the ENTER key.

*  The underscore character ( _ ) acts like a space.

*  The TEXT has the letters A-Z, _, <, =, >, ≤, ≠, ≥, and the logic functions and, or.  For the question mark character, ?, press [ 2nd ] [ PRGM ] (CATALOG) [ ↑ ] [ ENTER ].

* The programming language of the TI-73 is the robust as the TI-83 family (TI-83, TI-83 Plus, TI-84 Plus family, TI-82).

* The main difference is that results are shown on a separate screen for output.   When a program terminates, the TI-73 returns to the Home screen.  It is necessary to include a Pause at the end to keep the results on the screen.

Stay tuned tomorrow for more programs for the TI-73.

Eddie

All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

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