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cannot solve simple equation - Peter C - 11-23-2023 03:22 AM
I just got an HP Prime and was trying out its CAS function. I came across a question on special relativity and wanted to try it out.
Please help me out!
Peter
RE: cannot solve simple equation - Peter C - 11-23-2023 01:44 PM
in case the pictures in the first post didn't work:[attachment=12929][attachment=12930]
RE: cannot solve simple equation - Albert Chan - 11-23-2023 04:04 PM
Error screen already gives all the information you need.
v = tan(t) , t=-1.57 .. 1.57
tan(1.57) ≈ 1256., v guess (unit m/s) too low to have measurable relativistic effect
Let x = v/c, where c = 3e8
> solve(4.1 = 2.6/sqrt(1-x*x), x) → {−0.773213048007, 0.773213048007}
Iterative solve: 4.1/2.6 about sqrt(2) → x about 0.75
> solve(4.1 = 2.6/sqrt(1-x*x), x=0.75) → 0.773213048007
Bisection solve:
> solve(4.1 = 2.6/sqrt(1-x*x), x=0.6 .. 0.9) → [0.773213048007]
RE: cannot solve simple equation - C.Ret - 11-23-2023 05:30 PM
(11-23-2023 03:22 AM)Peter C Wrote: I just got an HP Prime and was trying out its CAS function. I came across a question on special relativity and wanted to try it out.
Hi Peter !
Apparently, you didn't get your Hp Prime from Officer Montgomery "Scotty" Scott (retired chief engineer responsible for the propulsion of the starship Enterprise).
With your new calculator, you have to give from her all she's got, Peter!. You cannot change the laws of the CAS's physics!.
You made no mistake, only the HP Prime is sometime quite a true obscure and unpredictable Klingon:
[attachment=12933]
RE: cannot solve simple equation - Peter C - 11-23-2023 08:13 PM
(11-23-2023 05:30 PM)C.Ret Wrote:(11-23-2023 03:22 AM)Peter C Wrote: I just got an HP Prime and was trying out its CAS function. I came across a question on special relativity and wanted to try it out.
Hi Peter !
Apparently, you didn't get your Hp Prime from Officer Montgomery "Scotty" Scott (retired chief engineer responsible for the propulsion of the starship Enterprise).
With your new calculator, you have to give from her all she's got, Peter!. You cannot change the laws of the CAS's physics!.
You made no mistake, only the HP Prime is sometime quite a true obscure and unpredictable Klingon:
I tried yours and it worked! Does it mean that I cannot use decimals in CAS?
Appreciate the help!
RE: cannot solve simple equation - nickapos - 11-24-2023 07:20 PM
Does anyone know why this is happening?
Why it does not work with 4.1 and it does work with 41/10?
I would be curious to see the reason behind this.
RE: cannot solve simple equation - Albert Chan - 11-24-2023 08:34 PM
(11-24-2023 07:20 PM)nickapos Wrote: Why it does not work with 4.1 and it does work with 41/10?
With exact number, solve does it symbolically.
It is equivalent to solve with symbols, then substitute for answer.
Cas> solve(a = b/sqrt(1-(v/c)^2), v) (a=4.1, b=2.6, c=3e8)
{231963914.402, −231963914.402}
With float, solver use Newton's method, but guess (v=tan(t), t = ±1.57) is too low.
There is no measurable relativistic effect, the region examined is just a flatline.
Cas> f(v) := 4.1 - 2.6 / sqrt(1-(v/3e8)^2)
Cas> f(tan(−1.57)) → 1.49999999998
Cas> f(0) → 1.5
Cas> f(tan(+1.57)) → 1.49999999998
We have to provide a better guess for v
Cas> solve(f(v), v=2e8) → 231963914.402
RE: cannot solve simple equation - nickapos - 11-25-2023 12:30 AM
(11-24-2023 08:34 PM)Albert Chan Wrote:Thank you very much Albert that makes sense(11-24-2023 07:20 PM)nickapos Wrote: Why it does not work with 4.1 and it does work with 41/10?
With exact number, solve does it symbolically.
It is equivalent to solve with symbols, then substitute for answer.
Cas> solve(a = b/sqrt(1-(v/c)^2), v) (a=4.1, b=2.6, c=3e8)
{231963914.402, −231963914.402}
With float, solver use Newton's method, but guess (v=tan(t), t = ±1.57) is too low.
There is no measurable relativistic effect, the region examined is just a flatline.
Cas> f(v) := 4.1 - 2.6 / sqrt(1-(v/3e8)^2)
Cas> f(tan(−1.57)) → 1.49999999998
Cas> f(0) → 1.5
Cas> f(tan(+1.57)) → 1.49999999998
We have to provide a better guess for v
Cas> solve(f(v), v=2e8) → 231963914.402