**Filling the Memory of a Casio fx-4000P**

How many programs does it take to fill the 550 step memory? Here are six programs that pretty much does the job. I purposely aimed for descriptive prompts and messages.

Spaces are added for readability.

Here's are the six programs:

**Prg 1: Approximating the cumulative distribution function of the Normal Curve - to 3 decimal places**

Mode +: COMP, Number of Steps: 82

"Z≥0" : ?→Z : Fix 3 : 1 - ((1+.196854 Z +.115194 Z² + .000344 Z^3 + .019527 Z^4)^ -4) ÷ 2 : Rnd : Norm : "AREA=" ◢ Ans → A

Source: Abramowitz and Stegun, __Handbook of Mathematical Functions__. 1972.

Examples:

Z = 1.6

Results: AREA = 0.945

Z = 1

Results: AREA = 0.841

For best results, enter a positive Z.

**Prg 2: Binomial Distribution PDF with Mean and Variance **

Mode +: COMP, Number of Steps: 86

"P(WIN)" : ?→P : "TRIALS" : ?→T : "WINS" : ?→N : "PDF=" ◢ T nCr N × P x^y N × (1-p) x^y (T-N) ◢ "MU=" ◢ T P ◢ "VAR=" ◢ Ans (1 - P)

Note: The combination function, nCr, is shown on the screen as a lone solid C. I have the nCr for clarification.

P(WIN): probability of a successful event

TRIALS: number of events

WINS: number of successful events

PDF: probability of we get the number of successful events

MU: expected value, mean - depending on P(WIN) and TRIALS

VAR: variance - depending on P(WIN) and TRIALS

Example:

P(WIN) = 0.7, TRIALS = 25, WINS = 10

Results: PDF = 1.324897424 x 10^-3, MU= 17.5, VAR= 5.25

**Prg 3: Angles of a triangle given 3 side lengths in Degrees - Solve a SSS (side-side-side) Triangle**

Mode +: COMP, Number of Steps: 86

Deg : "A" : ?→A : "B" : ?→B : "C" : ?→C : "<A=" ◢ cos^-1 ((A² + B² - C²) ÷ (-2 B C)) → D ◢ "<B=" ◢ sin^-1(B sin D ÷ A) → E ◢ "<C=" ◢ 180-D-E→F

Angle <A (stored in D) is opposite of side with length A

Angle <B (stored in E) is opposite of side with length B

Angle <C (stored in F) is opposite of side with length C

Degrees mode is set in the program.

Example:

Triangle with lengths A = 24, B = 60, C = 44

Results: <A = 20.04997572, <B = 58.99241697, <C = 100.9576073

**Prg 4: Free Fall with Air Resistance (from Ke!san)**

Assume coefficient is standard at k = 0.24 kg/m

(angle is not needed, hyperbolic trig does not depend on angle unit)

Site: https://keisan.casio.com/exec/system/1231475371

(last retrieved: February 27, 2023)

Mode +: COMP, Number of Steps: 88

.24 → K : 9.80665 → G : "MASS" : ?→M : "DIST" : ?→D : √(M ÷ G ÷ K) → X : "TIME=" ◢

X cosh^-1 (e(D K ÷ M)) → T ◢ "VEL=" ◢ X G tanh(T ÷ X) → V

SI units are assumed.

Example:

MASS = 68 kg, DIST (free fall distance) = 1874 m

Results: TIME = 39.27745305 s, VEL (velocity at free fall) = 52.71191359 m/s

**Prg 5: Sums of 1 to n for k, k^2, k^3, and K^4**

Mode +: COMP, Number of Steps: 83

"1 TO..." : ?→N : "K =" ◢ N (N+1) ÷ 2 → S ◢ "K²=" ◢ S (2 N + 1) ÷ 3 → T ◢

"K◢3=" ◢ S² → U ◢ "K◢4=" ◢ T (3 N² + 3 N - 1) ÷ 5 → V

The power character, x^y can not be used in a string or an error occurs. The stop character, ◢, can be used.

K: Σ (K from K = 1 to K = N)

K²: Σ (K^2 from K = 1 to K = N)

K◢3: Σ (K^3 from K = 1 to K = N)

K◢4: Σ (K^4 from K = 1 to K = N)

Example:

N = 9

Results:

K: 45

K²: 285

K◢3: 2025

K◢4: 15333

**Prg 6: Simple Ohm's Law Wheel/Volts, Current, Resistance: "PIE" chart**

Mode +: COMP, Number of Steps: 121

Lbl 0 : "ENT 0 TO SLV" ◢ "I" ◢ ?→I : "V" ◢ ?→ V : "R" ◢ ?→R : I=0 ⇒ Goto 1 : V=0 ⇒ Goto 2: R=0 ⇒ Goto 3: Goto 0: Lbl 1: "I=" ◢ V ÷ R → I ◢ Goto 4: Lbl 2: "V=" ◢ I R → V ◢ Goto 4: Lbl 3: "R=" ◢ V ÷ I → R ◢ Lbl 4: "END"

I: current (amps, A)

V: voltage (volts, V)

R: resistance (ohms, Ω)

The inputs will be in this order. Enter a zero for the variable you want to solve for.

Examples:

Solve for I: I = 0, V = 12, R = 3

Result: I = 4

Solve for V: I = 20, V = 0, R = 30

Result: V = 600

Solve for R: I = 17, V = 120, R = 0

Result: R ≈ 7.05

Total Number of Programs: 6

Total Steps Used: 121 (I only have 4 left)

Eddie

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