**Fun With the Casio fx-3650P**

Previous Entries

5/11/2014:

1. Circular Sectors

2. Stopping Sight Distance

3. Resistors in Parallel

4. Net Present Value

5. Rod Pendulum

6. Vectors: Dot and Cross Products

2. Stopping Sight Distance

3. Resistors in Parallel

4. Net Present Value

5. Rod Pendulum

6. Vectors: Dot and Cross Products

10/27/2015:

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:

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

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content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
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