(12C Platinum) Parabola - arc length

[StephenG1CMZ]

(06-29-2019 10:22 AM)Gamo Wrote:  The Arc Length of a Parabola calculator compute the arc length (S)

of a parabola based on the distance height (H) and

the width (L) of the parabola at that point perpendicular to the axis.

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The formula for determining the length of an arc of a Parabola.



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Instruction: FIX 4

1. H [R/S] display Height
2. L [R/S] display Answer of the Arc Length of a Parabola

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Example: H is 20 feet and L is 90 feet, what is the length of S?

20 [R/S] display 20.000
90 [R/S] display 100.7376

Answer: 100.7376 feet

To check answer for difference problem or check if this program give
correct answer.

URL: https://www.vcalc.com/wiki/vCalc/Parabola+-+arc+length

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Program: ALG mode

Code:


[÷] [R/S] [STO] 0 [=] [STO] 1

[X^2] [+] 16 [1/x] [=] [√x] [+] [(] [(] 1 [÷] [(] 16 [x] [RCL] 1 [)] [)] [x]

[(] [(] [RCL] 1 [+] [(] [RCL] 1 [X^2] [+] 16 [1/x] [)] [√x] [)] [LN] [+]

4 [LN] [)] [)] [)] [x] 2 [x] [RCL] 0 [=]  // 51 program steps //

Gamo

The formula given in your image can be optimised, unless LN is a natural log.
It includes two instances of LN: LN4 and LN().
Where N = H/L
Thus LN 4 can be optimised to LH/L = H, and similarly for LN() if that is an implied multiply and not a natural logarithm.