**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

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