## Sunday, April 4, 2021

### 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.

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