Sunday, January 9, 2022

Fun With The HP 27S

Fun With The HP 27S


Notes:


*  The HP 27S is set to FIX 4


*  Since none of the formulas have trigonometric functions, they can also be programmed on the HP 17B and HP 17BII+


Partial Fraction Decomposition


(A ∙ x + B)÷((x + C) ∙ (x + D)) = R÷(x + C) + S÷(x + D)


Inputs:  A, B, C, D

Outputs:  R, S


Formula:


PARTFRAC2:(A+B+C+D)×0=IF(S(R):(B-C×A)÷(D-C)-R:(B-D×A)÷(C-D)-S)


Example:  (4 ∙ x + 3) ÷ ((x - 5) ∙ (x + 1))

A = 4, B = 3, C = -5, D = 1

Results:  R = 3.8333, S = 0.1667


Use that the 0×(var1+var2+...) to set an order of variables in the solver.  


2 x 2 Simultaneous Equations


A ∙ x + B ∙ y = C

D ∙ x + E ∙ y = F


The solutions are:


x = (C ∙ E - B ∙ F) ÷ (A ∙ E - B ∙ D)

y = (A ∙ F - C ∙ D) ÷ (A ∙ E - B ∙ D)


Formula:


SIM2X2:0×(A+B+C+D+E+F+L(M:A×E-B×D))=IF(S(X):(C×E-B×F)÷G(M)-X:(A×F-C×D)÷G(M)Y)


Example:  2x + 3y =5, -3x + 8y = -8

A = 2, B = 3, C = 5, D = -3, E = 5, F = -8

Results:  X = 2.5789, Y = -0.0526


Floor Function


floor(x):  the greatest integer less than or equal to x


floor(x):

If frac(x) = 0 Then return x

 Else If x≥0, then return intg(x) else return intg(x)-1


Formula:


FLOOR=IF(FP(X)=0:X:IF(X>=0:IP(X):IP(X)-1))


Examples:

X = 2.38, FLOOR = 2.0000

X = -9.21, FLOOR = -10.0000


Ceiling Function


ceil(x):  the least integer greater than or equal to x


ceil(x):

If frac(x) = 0 Then return x

  Else If x≥0, then intg(x)+1 else return intg(x)


Formula:


CEIL=IF(FP(X)=0:X:IF(X>=0:IP(X)+1:IP(X)))


Examples:

X = 2.38, CEIL = 3.0000

X = -9.21, CEIL = -9.0000


Rydberg Formula


The Rydberg formula measures the light's wavelength when an electron moves between energy quantum numbers (from higher to lower levels).  The Rydberg formula is to be used for simple atoms only, and is most used for hydrogen atoms.


1/λ = R ∙ Z^2 ∙ (1/n1^2 - 1/n2^2)


R = Rydberg's Constant ≈ 1.097373157 × 10^7 m^(-1)

Z = atomic number, 1 for hydrogen

n1, n2:  energy levels


Formula:


RYDBERG:INV(L)=1.09737316E7×SQ(Z)×(INV(SQ(N1))-INV(SQ(N2)))


N2 > N1


Example:

The energy of an hydrogen election from level 4 to level 2.  Z = 1

Z =1,  N1 = 2, N2 = 4

Result:  L = 4.8601E-7


Source:

Helmenstine, Todd. "What Is the Rydberg Formula and How Does It Work?" ThoughtCo, Aug. 28, 2020, https://www.thoughtco.com/what-is-the-rydberg-formula-604285   Retrieved November 4, 2021



Moment of Inertia - Circular Ring


D$OUT:  outside diameter

D$IN:  insider diameter.  For a circle, set D$IN = 0

I: moment of inertia


Formula:


I=PI×(D$OUT^4-D$IN^4)÷64


Examples:


Circular Ring:

D$OUT = 6.2, D$IN = 1.9;  I = 71.8935


Circle:

D$OUT = 6.2, D$IN = 0; i = 72.5332


Source:

"Properties Of Annual Sections" HP-19C/HP-29C Solutions: Civil Engineering  Hewlett-Packard.  1977



All original content copyright, © 2011-2022.  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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