Casio fx-3650P Program Bank

Casio fx-3650P Program Bank

Economic Order Quantity

The program calculates three business parameters:

*  EOQ:  Economic Order Quantity: this is the optimum number of units to order in a single of order of items to be sold.  Each single inventory item has its on economic order quantity.   The calculation assumes every order will be available when needed.  This number of units is theoretical.  The calculation takes the estimated annual sales of units into account.  

*  The estimated amount of orders needed in a year.

*  The estimated annual cost of inventory.

Note that no amounts are rounded in this algorithm, all results are based on the theoretical values.

Formulas:

EOQ = √(2 × A × B ÷ (C% × D))

where:

A = cost to  place an order

B = annual sales of units

C = holding costs percentage 

D = cost per unit

EOQ is stored in X.

Orders per Year = B ÷ EOQ

The result is stored in Y. 

Estimated Annual Cost = A × amount of orders per year

Estimated annual cost is stored in M.

Program Code:  (47 steps)

(spaces are included for clarity)

Fix 2 : ? → A : ? → B : ? → C : ? → D : 

√ ( 2 A B ÷ 100(^-1) C × D → X ◢

B ÷ X → Y ◢

A Y → M ◢

Norm 1

Example:

Inputs:

A = cost to  place an order = $ 79.36

B = annual sales of units = 100,000

C = holding costs percentage = 24%

D = cost per unit = $ 1.20

Outputs:

X = EOQ ≈ 7,423.69

Y = Orders per Year ≈ 13.47

M = Estimated annual cost ≈ $1,069.01

Source:

Hewlett Packard.   Step-by-Step Solutions For Your HP Calculator: Marketing and Sales:  HP-17B, HP-19B, HP-27S.   Hewlett Packard.  Edition 1.  January 1988. 

Banker's Rounding

We will focus on rounding positive numbers to integers.   

Banker's rounding is similar to regular rounding except, when the number has a fraction part of 0.5, the number is rounded to the nearest even integer.

For example:  both 17.5 and 18.5 would be rounded to 18.  

We can accomplish Banker's rounding by these algorithms, assuming x is a positive number (x>0):

If abs(frac(x)) = 0.5 

Then round(x ÷ 2, 0) × 2

Else round(x, 0) 

IfEnd

If mod(x,1) = 0.5

Then round(x ÷ 2, 0) × 2

Else round(x, 0) 

IfEnd

The fx-3650P does not have a modulus or absolute value function.   We can accomplish absolute value by using √(x^2).

Program Code:  (46 steps)

(spaces are included for clarity)

? → A : Fix 0 : Rnd : Ans → B :

√ ( ( A - B ) ² ) ≠ 0.5 ⇒ Goto 1 :

A ÷ 2 : Rnd : 2 Ans → B :

Lbl 1 : Norm 1: B

Examples:

A = 36.3,  result = 36

A = 36.5,  result = 36

A = 37.5,  result = 38

A = 40.5,  result = 40

A = 41.2,  result = 41

Birthday Probably Function

What are odds that A people/objects do not a share a characteristic in C categories?   

Famously stated:  what are odds that N people do not share a birthday in a 365-day year?  

The probability is calculated as:

p = Π(1 - m ÷ C, m = 1, N - 1) = nPr(C, N) ÷ C^N

Program Code:  (19 steps)

(spaces are included for clarity)

? → A : ? → C :

C [nPr] A ÷ ( C ^ A ) → B

nPr appears as a bold P.

Example:

Probability that 24 people do not share a birthday:

A = 24, C = 365,  result = 0.461655742

Probability that 40 students who do not share a college class, if the college offers 300 classes:

A = 40, C = 300, result = 0.065725193

Voltage Drop of a Copper Wire

The program calculates the voltage drop of a copper wire (conductivity of 12.9).  The wire is assumed to be insulated at 75°C. 

Formula:

1 Phase: (domestic and office appliances)

VD = 2 × 12.9 × B × D ÷ C

3 Phase: (large electronic equipment)

VD = √3 × 12.9 × B × D ÷ C = 1-Phase-VD × √3 ÷ 2

B = current (amps)

C = circular mils* (see below)

D = length of the wire (feet)

C:  

Enter the wire cross area in circular mils.  However, the code allows for three common wire types:

C = 10  (AWG 10):  10,380

C = 12  (AWG 12):  6,530

C = 14  (AWG 14):  4,110

The voltage drop for both 1 phase (stored in X), followed by 3 phase circuits (stored in Y) are displayed.  

Program Code:  (72 steps)

(spaces are included for clarity)

? → B :

? → C :

C = 10 ⇒ 10380 → C :

C = 12 ⇒ 6530 → C :

C = 14 ⇒ 4110 → C :

? → D :

2 × 12.9 × B × D ÷ C → X ◢

X × √3 ÷ 2 → Y

Examples:

Input:

B = Current = 300 A

C = 10  for a #10 AWG wire

D = Length = 24 ft

1 phase voltage drop:  17.89595376

3 phase voltage drop:  15.49835058

Input:

B = Current = 320 A

C = 14  for a #14 AWG wire

D = Length = 30 ft

1 phase voltage drop:  60.26277372

3 phase voltage drop:  52.18909295

Eddie

All original content copyright, © 2011-2023.  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. 

Casio fx-3650P and fx-CG50: Partial Fraction Decomposition

Casio fx-3650P and fx-CG50:   Partial Fraction Decomposition

Casio fx-3650P (II) Program: Partial Fraction Decomposition

The following program calculates the coefficients decomposition, X and Y, as follows:

(A ∙ t + B) ÷ ((t + C) ∙ (t + D)) = X ÷ (t + C) + Y ÷ (t + D)

Note:  C ≠ D

where:

X = (B - A ∙ C) ÷ (D - C)

Y = A - X

Program:  (35 Steps)

? → A : ? → B : ? → C : ? → D : 

( B - A C ) ÷ ( D - C → X ◢ A - X → Y

Example:  

(2t - 3) ÷ ((t - 1)(t + 4))  = -0.2÷(t-1) + 2.2÷(t + 4)

A = 2, B = -3, C = -1, D = 4

Result:  -0.2, 2.2

The above algorithm should be good for the fx-7000G, fx-50FII, fx-4000P, fx-5800P, and other programming and graphing calculators (modifications may be necessary).

Casio fx-CG50 Program:  PARTFRAC

The code listed will also be good for the fx-9750G/fx-9860G series.

The program PARTFRAC, 720 bytes, will execute partial fraction decomposition of any of the three types:

(1)    (A ∙ x + B)÷((x + C) ∙ (x + D)) = R÷(x + C) + S÷(x + D)

Inputs:  A, B, C, D

Outputs:  R, S

[[ R ] [ S ]] = [ [ D, C ] [ 1, 1 ] ]^(-1) ∙ [ [ B ] [ A ] ]

(2)  (A ∙ x^2 + B ∙ x + C)÷((x + D)^2 ∙ (x + E)) = R÷(x + D)^2 + S÷(X + D) + T÷(x + E)

Inputs:  A, B, C, D, E

Outputs:  R, S, T

[[ R ][ S ][ T ]] = [[ E, D ∙ E, D^2 ][ 1, D + E, 2 ∙ D ][ 0, 1, 1 ]]^-1) ∙ [[ C ][ B ][ A ]] 

(3)  (A ∙ x^2 + B ∙ x + C)÷((x+D)∙(x+E)∙(x+F)) = R÷(x+D) + S÷(x+E) + T÷(x+F)

Inputs:  A, B, C, D, E, F

Outputs:  R, S, T

[[ R ][ S ][ T ]] = 

[[ E ∙F, D ∙ F, D ∙ E ][ E+F, D+F, D+E ][ 1, 1, 1 ]]^-1) ∙ [[ C ][ B ][ A ]] 

Program Listing:

'ProgramMode:RUN

"2021-11-05 EWS"

"PARTIAL FRACTION"

"N(X)/D(X)"◢

Lbl 0

Menu "DENOMINATOR?","(X+C)(X+D)",1,"(X+D)_^<2>_(X+E)",2,"(X+D)(X+E)(X+F)",3,"EXIT",E

Lbl 1

"(AX+B)/((X+C)(X+D))"◢

"A"?->A

"B"?->B

"C"?->C

"D"?->D

[[D,C][1,1]]^<-1>*[[B][A]]->Mat A

Mat A[1,1]->R

Mat A[2,1]->S

"=R/(X+C)+S/(X+D)"◢

"R="

R◢

"S="

S◢

Goto 0

Lbl 2

"(AX_^<2>_+BX+C)/((X+D)_^<2>_(X+E))"◢

"A"?->A

"B"?->B

"C"?->C

"D"?->D

"E"?->E

[[E,D*E,D^<2>][1,D+E,2*D][0,1,1]]^<-1>*[[C][B][A]]->Mat A

Mat A[1,1]->R

Mat A[2,1]->S

Mat A[3,1]->T

"=R/(X+D)_^<2>_+S/(X+D)+T/(X+E)"◢

"R="

R◢

"S="

S◢

"T="

T◢

Goto 0

Lbl 3

"(AX_^<2>_+BX+C)/((X+D)(X+E)(X+F))"◢

"A"?->A

"B"?->B

"C"?->C

"D"?->D

"E"?->E

"F"?->F

[[E*F,D*F,D*E][E+F,D+F,D+E][1,1,1]]^<-1>*[[C][B][A]]->Mat A

Mat A[1,1]->R

Mat A[2,1]->S

Mat A[3,1]->T

"=R/(X+D)+S/(X+E)+T/(X+F)"◢

"R="

R◢

"S="

S◢

"T="

T◢

Goto 0

Lbl E

"DONE."

Download (fx-CG 50):

https://drive.google.com/file/d/1hAIFrlX6xLMYPRiLz_dt7hpiP64CxmKC/view?usp=sharing

Examples To Try:

Type 1: 

(8 ∙ x + 3) ÷((x + 4) ∙ (x - 6))  = (29/10) ÷ (x + 4) + (51/10) ÷ (x - 6)

Type 2:

(x^2 + 4 ∙x + 5) ÷ ((x - 3)^2 ∙ (x + 1)) = 

(13/2) ÷ (x - 3)^2 + (7/8) ÷ (x - 3) + (1/8) ÷ (x + 1)

Type 3:

(2 ∙ x^2 + 3 ∙ x - 1) ÷ ((x - 1) ∙ (x + 2) ∙ (x + 4)) = 

(4/15) ÷ (x - 1) + (-1/6) ÷ (x + 2) + (19/10) ÷ (x + 4)

Eddie 

All original content copyright, © 2011-2022.  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. 

Fun With the Casio fx-3650P (April 4 Edition)

Fun With the Casio fx-3650P (April 4 Edition)

Self-Contained Simple Interest Solver

This program sets up the solver for simple interest using the equation:

A = B * (1 + 0.01 * C * D)

where:

A = future value

B = present value

C = interest rate as a percentage (i.e. enter 10 for 10%)

D = number of periods

The program will ask for each of the four variables.  For the variable to be solved for, enter a 0.  So:

To solve for future value, enter 0 for A.

To solve for present value, enter 0 for B.

To solve for interest rate, enter 0 for C.

To solve for the number of periods, enter 0 for D.

This program has explicit solutions for each of the variables, hence this is a larger program.  

Note:  spaces are added for readability.  When the programs are entered, there are no spaces on the fx-3650P. 

Program: (125 steps)

 ? →A : ? →B : ? →C : ? →D :

A = 0 ⇒ Goto 1 :

B = 0 ⇒ Goto 2 :

C = 0 ⇒ Goto 3 :

D = 0 ⇒ Goto 4 : Goto 5 :

Lbl 1 : B ( 1 + .01 C D → A : Goto 5 :

Lbl 2 : A ÷ (1 + .01 C D →B : Goto 5 :

Lbl 3 : 100 ( A ÷ B - 1 ) ÷ D →C : Goto 5 :

Lbl 4 : 100 ( A ÷ B - 1 ) ÷ C → D : Lbl 5

Examples:

Solve for A.  

Inputs:  A = 0,  B = 5000.00, C = 5, D = 6.

Solution:  A = 6500.00

 

Solve for B.  

A = 8275.00, B = 0,  C = 5, D = 6.  

Solution: B = 6365.38

Solve for C.  

A = 4200.00, B = 7600.00, C = 0, D = 6.  

Solution: C = 13.49

Solve for D.

A = 7150.00, B = 4950.00, C = 10, D = 0

Solution: D = 4.44

Drawing From a Bag of Two Kinds of Items

This program determines the probability of drawing a certain permutation from a bag containing two different types of balls (Ball A or Ball B).  I first discussed this problem and using the TI-84 Plus and TI-80 calculators here:  http://edspi31415.blogspot.com/2020/04/ti-80-and-ti-84-plus-ce-drawing-bag-of.html

Instructions:

1. Enter the number of Ball A objects.  This number is stored in the variable A.

2. Enter the number of Ball B objects.  This number is stored in the variable B.

3. Enter the number of draws.  This number is stored in the variable M.

4. For each X prompt:  enter either 1 for drawing Ball A or 2 for drawing B.  This continues until the number of draws have been completed.  Please keep track because the program has no counter.  

5. The program calculates the probability and stores it in the variable Y.     

Program:  (81 bytes)

? →A : ? →B : ? →M :

A + B : ( Ans nPr M ) ⁻¹ →Y :

Lbl 0 : ? →X : X = 1 ⇒ Goto 1 :

Y B →Y : B - 1 →B : Goto 2 :

Lbl 1 : Y A →Y : A - 1 →A :

Lbl 2 : 1 M- : M ≠ 0 ⇒ Goto 0 : Y

Example:

A bag has 6 of Ball A and 5 of Ball B.  (A = 6, B = 5).  There are five draws. (M = 5)

Combo AABBA.  X =  1, X = 1, X = 2, X = 2, X = 1.   

Solution:  Y = 0.043290043

Combo BBAAB.  X = 2, X = 2, X = 1, X = 1, X = 2.

Solution: Y = 0.032467532

Depth of a Well

This program calculates the depth of a well, which is determined by the time between a person drops a rock and the person hears the rock hit the bottom of the well.  The program uses SI units (meters, kilograms, seconds) with the following constants:

Earth’s Gravitational Acceleration:  g = 9.80665 m/s^2

g/2 = 4.903325 m/s^2

Speed of Sound, in dry air, 20°C temperature: s = 343.21 m/s

Equations:

X = (-B + √(B^2 + 4*A*B)) / 2

Y = g/2 * a^2

where:

B = s / (g/2) (see the above constants)

A = amount of time, in seconds, between the person drops the rock and hears the rock hit the bottom (input)

X = amount of time, in seconds, that it actually takes the rock from the time it was dropped until the rock hits the bottom of the well (output)

Y = depth of the well, in meters (output)

Program: (53 bytes)

? →A :  343.21 ÷ 4.903325 →B : 

( - B + √ ( B ² + 4 B A ) ) ÷ 2 →X ◢

4.903325 X ² →Y

Example:

Input:  A = 3.55 sec

Results:  

X = 3.386185535 sec

Y = 56.22276244 m 

Source:

Saul, Ken.  The Physics Collection:  Ten HP-41C Programs for First-Year Physics Class   Corvallis, OR.  1986

The Power of a Windmill

This program calculates the power generated by a windmill, given the diameter and velocity of the windmill’s fans.   SI units (meters, kilograms, seconds) are used.   The general equations used are:

Area of the swept by the windmill’s fans (in m^2):

A = ( π * diameter^2 ) / 4 

Power generated (in W (Watts), J/s, m^2 kg/s^3):

P = ½ * area * density * velocity^3 

Density of air = 1.225 kg/m^3

Variables:

C = velocity of the fans, m/s (input)

D = diameter of the fans, m (input)

A = power of the windmill, W (output)

Program: (28 steps)

? →D : ? →C :

.5 × π × D ² ÷ 4 × 1.225 × C ³ → A

Example:

Input:  D = diameter = 7.3152, C = velocity = 9.3878

Result: A = power = 21298.05133

Source:

Sharp Electronics Corporation.  Conquering The Sciences: Applications for the SHARP Scientific Calculators EL-506P, EL-510S, EL-515S  Japan. 1984

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.

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.

Casio fx-3650P: Chebyshev Polynomials, Roots of a Complex Number, Reversion Value, Mach Speed, Trapezoid Perimeter

Casio fx-3650P: Chebyshev Polynomials, Roots of a Complex Number, Reversion Value, Mach Speed, Trapezoid Perimeter

Chebyshev Polynomials of the First Kind

Values of the Chebyshev polynomials can calculated by the following:

T_n (x):

cos (n acos x) if |x| ≤ 1

cosh (n acosh x) if x ≥ 1

(-1)^n cosh (n acosh(-x)) if x ≤ 1

Inputs: x, y (n) order. The program assumes y is an integer.

Program (74 bytes):

? → X : ? → Y : X > 1 ⇒ Goto 1 :

-1 > X ⇒ Goto 2 : cos ( Y cos¹ X ) → A : Goto 3 :

Lbl 1 : cosh ( Y cosh¹ X ) → A : Goto 3

Lbl 2 : (-1)^Y * cosh ( Y cosh¹ X ) → A :

Lbl 3: A

Examples

T_Y(X)

X: -3, Y: 5, Result: -3363

X: 0.3, Y: 5, Result: 0.99888

X: 3, Y: 5, Result: 3363

Roots of a Complex Number

This program calculates the roots of a complex number (x + yi)^a, which is calculated as:

r^(1/n) * ( cos((θ + 2 π k)/n) + i*sin((θ + 2 π k)/n) )

where k = 0 to n-1

r =√(x^2 + y^2)

θ = angle(x + yi) = atan(y/x)

Program (66 bytes):

? → X : ? → Y : ? → A : 0 → M :

Rad : Pol(X,Y) : A x√ X → B :

Y → D : Lbl 1 : M ⊿ Rec(B, (D + 2 π M )/A) ⊿

Y ⊿ 1 M+ : M ≠ A ⇒ Goto 1 : M

The program stops when M = A.

Example:

(-2 + 4i)^(1/4)

X: -2, Y: 4, A: 4

(Fix 4 setting)

M: 0, X: 1.2701, Y: 0.7082

M: 1, X: -0.7082, Y: 1.2701

M: 2, X: -1.2701, Y: -0.7082

M: 3, X: 0.7082, Y: -1.2701

M: 4 (end)

Business: Reversion Value

Input:

A = n: number of payments

B = I%: periodic interest rate (in decimal)

C = monthly rent

D = asking price

Note: For monthly payments, divide the annual interest rate by 1200.

Program (55 bytes):

Fix 2 : ? → A : ? → B : ? → C : ? → D :

-C (1 + B) ( (1 + B)^A -1 ) ÷ B → X :

X + D (1 + B)^A → X : X

Example:

5 years of monthly payments, A = 60

Interest rate, B = 6/1200

Monthly Rate, C = 1895

Asking Price, D = 250000

Result: 204337.26

Source:

Roger F. Farish and Elbert B. Greynolds, Jr., Ph.D., CPA Calculator Analysis for Business and Finance Texas Instruments Incorporated 1978 ISBN 0-07-063757-1

Mach Speed

This program calculates the mach speed, a ratio of the speed of sound given:

A = the altitude of the object, such as a vehicle (in feet)

B = temperature (°F)

C = velocity of the vehicle (mph)

Equations used:

Mach Number = velocity of the vehicle / speed of sound

where Speed of Sound = 44100 / 1519 * √( 459.7 + B – 3.57 * A / 1000)

Program (52 bytes):

? → A : ? → B : ? → C :

44100 ÷ 1519 * √ ( 459.7 + B – 3.57 A ÷ 1000 ) → D :

C ÷ D → M

A lapse rate of -3.57° per 1000 ft altitude is assumed.

Example:

Input:

A: altitude = 2500 ft

B: temperature = 63 °F

C: velocity = 795 mph

Result:

mach speed: 1.208091501

Source:

“Mach Number and Airspeed vs Altitude” Granite Island Group (Technical Surveillance Counter Measures) http://www.tscm.com/mach-as.pdf Retrieved January 26, 2019

Perimeter of a Trapezoid

P + A + B + C * (1/sin X + 1/sin Y)

Program (38 bytes):

Deg : ? → A : ? → B : ? → C : ? → X : ? → Y :

A + B + C ( 1 ÷ sin X + 1 ÷ sin Y )

Example:

A = 227.6

B = 305.4

C = 10.5

X = 86°

Y = 5°

Result: 663.999629

Eddie

All original content copyright, © 2011-2019. 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.

Fun With the Casio fx-3650P: Program Collection 5/29/2018

Fun With the Casio fx-3650P

Previous Entries

5/11/2014:

http://edspi31415.blogspot.com/2014/05/casio-fx-3650p-programming.html

1. Circular Sectors
2. Stopping Sight Distance
3. Resistors in Parallel
4. Net Present Value
5. Rod Pendulum
6. Vectors: Dot and Cross Products

10/27/2015:

http://edspi31415.blogspot.com/2015/10/casio-fx-3650p-programming-sequel.html

1.  Combination with Replacement

2.  Great Circle (Distance in km) 

3.  Orbital Speed and Period 

4.  Eccentricity and Area of an Ellipse

5.  Super Factorial

6.  Escape Velocity 

7.  Finance: Payment of a Monthly Mortgage

8.  Wind Chill Factor

9.  Speed of Sound in Dry Air 

7/2/2017:

https://edspi31415.blogspot.com/2017/07/fun-with-casio-fx-3650p.html

1.  Modulus Function

2.  Normal CDF

3.  Sum:  Σ (AX + B)^C,  from X = 0 to X = Y

4.  Sun Altitude and Azimuth Based on the Vernal Equinox

5.  Trapezoid: Midsegment, Height, and Area

6.  Solar Irradiance

7.  General a list of X Random Integers from 0 to Y

Contents for this Blog Entry:

1. kth Derivative of f(x) = y^n

2. Sight Reduction Table

3. Distance Off at Second Bearing by Two Bearings and Run

4. Hydraulic Cylinder:  Force and Flow

5. Mass Held by Two Strings

6. Atwood Machine: Tension and Acceleration

kth Derivative of f(x) = x^n

This program calculates the kth derivative of x^n. Using the variables of the Casio fx-3650p, this program calculates:

‘d^A/dx^A X^B.  A is an integer, where B and X are real numbers.

Program (47 steps):

? → A : ? → B : → X : 1 → C : Lbl 1 : CB → C : B – 1 → B : A – 1 → A : A ≠ 0 ⇒ Goto 1 : CX ^ B

Input order:  A = order, B = power, X = x

Examples:

A = 3, B = 2.5, X = 3.  Result:  1.08253175473

A = 4, B = 6, X = 1.  Result:  360

Sight Reduction Table

The program calculates altitude and azimuth of a given celestial body.

Inputs:

A: Local Hour Angle (LHA)

B: The observer’s latitude on Earth, north is positive, south is negative (L)

D: Declination of the celestial’s body, north is positive, south is negative (δ)

The latitude is often entered in degrees/minutes/seconds format. 

Do this using the [ ° ‘ “ ] key.   The calculator is set in Degrees program.

Formulas:

Altitude: 

H = asin (sin δ sin L + cos δ cos L cos LHA)

Zenith:

Z = acos ((sin δ – sin L sin H) ÷ (cos H cos L))

If sin LHA < 0 then Z = 360° - Z

Output variables:

C = altitude

X = zenith

Program (67 steps):

Deg : ? → A : ? → B : ? → D : sin^-1 ( sin D sin B + cos D cos B cos A ) → C ◢ cos^-1 ( ( sin D – sin B sin C ) ÷ ( cos C cos B ) ) → X: sin A > 0 ⇒ 360 – X → X : X

Source:  “NAV 1-19A Sight Reduction Table”    HP 65 Navigation Pac.  Hewlett Packard, 1974.

Distance Off at Second Bearing by Two Bearings and Run

This program calculates the distance off between to bearings. 

Input variables:

A:  first bearing

B:  second bearing

C:  run (typically in miles, distance will be in the same length unit)

Distance formula:

D = C * sin A° / sin |A° - B°|

Since the Casio fx-3650P does not have an absolute value function, the workaround    √(x^2) is used instead. 

Program (31 steps):

Deg : ? → A : ? → B : ? → C : C sin A ÷ sin ( √ (A – B) ^ 2 ) → D

Example:

A = 15°, B = 8 °, C = 1.5 miles

Result:  3.185613024 miles

(updated 7/1/2018; the result is now correct)

Source:  Henry H. Shufeldt and Kenneth E. Newcomer.  The Calculator Afloat: A Mariner’s Guide to the Electronic Calculator Naval Institute Press:  Annapolis, MD.  1980

Hydraulic Cylinders: Force and Flow

The program calculates the force and flow.

Input variables:

D:  large radius

C:  small radius, radius of the cut

X:  pressure

Y:  speed of the cylinder

Formulas:

Area: A = π (D^2 – C^2) / 4

Force: F = pressure * area = X * A

Flow:  q = velocity * area = Y * A

Program (36 steps):

? → D : ? → C : π ( D^2 – C^2 ) ÷ 4 → A : ? → X : AX ◢ ? → Y : AY

Example:

Input:

D = 8 in, C = 4 in  (8 in cylinder with a 4 in cutout), X = 68 psi, Y = 3.6 in/sec

Results:

Force:  2563.539605 lb,  Flow:  3.6 in^3/sec

Mass Held by Two Strings

The program calculates the tension of the two strings shown in the diagram above.  The tension of both strings are found by solving the following system of two equations:

cos A° * X – sin B° Y = 0

sin A° * X – cos B° * Y = M * g

Where g is Earth’s gravitation constant, or g = 9.80665 m/s^2 ≈ 32.174 ft/s^2

SI units are used in this program.

Program (45 steps):

Deg : ? → A : ? → B : ? → M : 9.80665 M ÷ ( tan A sin B – cos B ) → Y : Y sin B ÷ cos A → X ◢ Y

Example:

Input:

A = 43°, B = 89°, M = 16 kg

Results:

X = 234.4572201 N, Y = 171.4972763 N

Atwood Machine:  Tension and Acceleration

The program calculates the tension in the string of the Atwood Machine and the acceleration of the system.  If the acceleration is negative, the pulley is turning clockwise, otherwise it is turning counterclockwise.  The following system of equations is solved, where X is the tension of the strings and Y is the acceleration of the system.

X + A * Y = g * A

-X + B * Y = -g * B

Where g is Earth’s gravitation constant, or g = 9.80665 m/s^2 ≈ 32.174 ft/s^2

SI units are used in this program.

Program (45 steps):

? → A : ? → B : 9.80665 (A – B) ÷ ( A + B ) → Y : A (9.80665 – Y) → X ◢ Y

Examples:

Input:

A = 11.2 kg, B = 10.3 kg

Results:

X = 105.2367576 N, Y = 0.41051093 m/s^2

Eddie

All original content copyright, © 2011-2018.  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.  Please contact the author if you have questions.