Algebra

[Old_Geezer]

You know those times when you know you are missing something obvious but can't work out what, or find the answer anywhere, and would prefer to post anonymously so, if someone can tell you, you don't feel embarrassed ? This is one of those times :-( (Must be my age.)

@ 7.06 minutes in...

https://youtu.be/bjVfL8uNkUk

If you have a fraction, in this case meters divided by seconds. And of course both numerator and denominator are to the power of 1. How come, after cubing it the numerator is squared but the denominator is cubed ? Shouldn't they be the same, preferably cubed ?

Taking the rest of the larger equation on trust, it seems it has to be correct or the whole thing doesn't work. But this power difference is foxing me.

(Maybe I can get Ed to delete this after I've read the simple solution to save me further embarrassment.)

Cheers.

[fiction-factory]

I doubt this bit of maths on the clip is wrong. We need to know the step beforehand. What makes you think that they started with (m/s) and then cubed it?

[Old_Geezer]

Because speed is length over time. And the overall equation needs it cubed.

[fiction-factory]

Where does it say we need to cube (distance/time)? Do I need to watch the earlier bits? Maybe it was acceleration not speed - m/s² ?

[nescio]

OG, those lengths, times, etc. are the dimensions of the physical constants in the equation, which eventually cancel to give a length

[THECORBYLOON]

The equation involves the speed of light (C) cubed. The dimensions of C are L/T so C cubed should be L^3/T^3 but it shows as L^2/T^3.

[nescio]

OG,
apologies - I have just looked at the cancelling and yes, you are right; for some inexplicable reason, c^3 is given dimensions of L^2.T^-3. When the various terms are cancelled, it correctly gives L^3 in the denominator.

[Gizmonster]

I think there's an error as it doesn't add up:

I simplified it to:

LP = √((L^5)/(L^2))
LP = √(L^3) and not L^2

I'd guess that the error is in the video and that because speed = distance / time, then C^3 should be L^3/T^3 and not L^2/T^3 ... which would now add up as the final answer would now be:
LP = √((L^5)/(L^3)

[jim360]

It's a straight-up typo. Don't be embarrassed for noticing it. Not many people watching the video did, so if anything be pleased.

[Old_Geezer]

Gee, updated the android tablet. Took about half an hour ! Well, back now :-)

Ah thanks. I've not forgotten primary school sums then.

I tried to work put the large equation but must've got something wrong. Now we've discussed it I see the length squared mystically turns into the length cubed in the following resultant equation.

Cheers for all the help. It was 'doing my brain in'. These things tend to, and I can't progress well until I've understood.

[fiction-factory]

Glad it's sorted. I'll watch whole clip when i get back

[ToraToraTora]

Al-Gebra? Aren't they a terrorist outfit? Apparently they have weapons of Maths Instruction.