** Sharp EL-5100 Programs**

We can use the formula programming engine of the classic Sharp EL-5100 (1979) to store multiple formulas and invoke some simple programs.

**Quadratic Formula**

ax^2 + bx + c = 0

x = (-b ± √(b^2 - 4ac)) / (2a)

Formulas (AER Mode):

1; f(A,B,C)=(B²-4AC) STO D ◣

2; (-B+√D)÷(2A STO E, (-B-√D)÷(2A STO F

Instructions (COMP Mode):

1. Press [ 1; ], enter A, B, and C. D is shown as ANS 1. If D ≥ 0, then the polynomial have real roots. Continue to the next step. If D < 0, then the polynomial has complex roots, stop.

2. Press [ 2; ], the two roots are displayed.

Examples:

Example 1: A = 1, B = -1, C = -3.75; Results: 2.5, -1.5

Example 2: A = 2, B = 26, C = 84; Results: -6, -7

**Power of a Complex Number (Principal)**

(a + bi)^c = d + ei

The →POL stores θ in I and displays r, which r is not automatically stored.

Formulas (AER Mode):

1; f(A,B,C)=A →POL B STO I, I^C×COS(JC) STO D, I^C×SIN(JC) STO E

^ represents Y^X.

Instructions (COMP Mode):

1. Set the calculator to Radians mode. Press [ 1; ].

2. You get three results: I (r), real part, imaginary part. Press [ COMP ] to see each result (ignore the first result)

Examples:

Example 1: (4 + 4i)^3 = -128 + 128i; r = 5.56854249

Example 2: (5 - 6i)^0.5 = 2.5308348108 - 1.18537961766i; r = 7.810249676

**Confidence Interval**

Here, we can use one formula to store values for use in the next formula.

confidence interval = A ± J * B / √C

where:

A = mean

B = variance

C = n

J = z* (see table below)

z* values:

F: 99% confidence level, value = 2.576

G: 98% confidence level, value = 2.326

H: 95% confidence level, value = 1.96

I: 90% confidence level, value = 1.645

Formulas (AER Mode):

1; 2.576 STO F 2.326 STO G 1.96 STO H 1.645 STO I ◣

2; f(A,B,C,J)=A-JB÷√C STO D, A+JB÷√C STO E

Instructions (COMP Mode):

1. Initialize by pressing [ 1; ]. When the display says ANS1 = 0, the initialization is complete.

2. Press [ 2; ], enter mean for A, press [ COMP ], enter variance for B, press [ COMP ], enter n for C, press [ COMP ], choose F, G, H, or I for J (confidence level), press [ COMP ].

Examples:

Example 1:

99% level with mean = 34.56, variance = 19.79, n = 53. For 99%, enter F for J.

Result: 22.557490316, 41.562509684

Example 2:

90% level with mean = 100, variance = 12, n = 42. For 90%, enter I for J.

Result: 96.9540518717, 103.045948128

**Sum of a Function**

On the EL-5100, we will have to manually keep track of the loop.

∑ f(I) from I=A to B (increment 1), result is stored in M.

Formula Template (AER Mode):

1; f(I)= STO I, 0 →M ◣

2; [enter function here] M+, 1+I STO I

Instructions (COMP Mode):

1. Press [ 1; ]. At the f(I)= prompt, store the lower limit. Press [ COMP ]

**twice**to complete the initialization.2. Press [ 2; ]. The first result is f(I). Press [ COMP ] to increase I by 1. Repeat the pattern by pressing [ COMP ]. Do this until ANS2 > B (you need to keep track manually)

3. Press [ RM ] to get the final result.

Example:

∑( (I-2)×(I+6) ) for I=1 to 5

Setup (AER Mode):

1; f(I)= STO I, 0 →M ◣

2; (I-2)×(I+6) M+, 1+I STO I

[1; ] [COMP] [COMP]

[2; ] [COMP] [COMP] ANS2 = 2

[2; ] [COMP] [COMP] ANS2 = 3

[2; ] [COMP] [COMP] ANS2 = 4

[2; ] [COMP] [COMP] ANS2 = 5

[2; ] [COMP] [COMP] ANS2 = 6

[ RM ]

Result: 55

Fun to explore different ways to solve problems, and play with retro calculators.

Eddie

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