Help me and a colleague with 2 equations please?

[Mathmasteriw]

Hi there!
Have been doing some maths with a colleague and is wondering if these sums are correct?
(I apologise if I have posted this in the wrong maths thread category )
Thanks for your time

 

[Cubist]

In your first image there's a mistake:- the square root symbol should be preserved when doing dimensional analysis.

In the second image your sum of the arithmetic series is correct.

 

[Dr.Peterson]

Hi there!
Have been doing some maths with a colleague and is wondering if these sums are correct?
(I apologise if I have posted this in the wrong maths thread category )
Thanks for your time

It would help if you gave a few words of explanation for the first page. What does the first line have to do with the rest?

But, assuming the second line comes correctly from elsewhere, the only error I see here is that in the next line you move T^-2 from the bottom to the top unchanged.

There is a simpler way to do the sum in the second page, instead of your formula: the sum of an arithmetic series is the average of the first and last terms, times the number of terms: (2+40)/2 * 20 = 21*20 = 420.

 

[Mathmasteriw]

Thank you very much for your reply!
will look again on the dimensional analysis.
Thanks.

In your first image there's a mistake:- the square root symbol should be preserved when doing dimensional analysis.

In the second image your sum of the arithmetic series is correct.

 

[Mathmasteriw]

It would help if you gave a few words of explanation for the first page. What does the first line have to do with the rest?

But, assuming the second line comes correctly from elsewhere, the only error I see here is that in the next line you move T^-2 from the bottom to the top unchanged.

There is a simpler way to do the sum in the second page, instead of your formula: the sum of an arithmetic series is the average of the first and last terms, times the number of terms: (2+40)/2 * 20 = 21*20 = 420.

Thank you very much for your reply! Much appreciated! In regards to the first image, the second line is correct from elsewhere. I am unsure what to do with the T^-2 ? Does it not stay the same as it has no powers on the top to add or subtract?
Thanks for your help and the formula you quoted to the arithmetic series is very useful! Awsome!
Appreciate your time!

 

[Deleted member 4993]

Thank you very much for your reply! Much appreciated! In regards to the first image, the second line is correct from elsewhere. I am unsure what to do with the T-2 ? Does it not stay the same as it has no powers on the top to add or subtract?
Thanks for your help and the formula you quoted to the arithmetic series is very useful! Awsome! Appreciate your time!

Use following fact (rule of "power"):

\(\displaystyle \frac{1}{x^{n}} \ \ = \ x^{-n}\)

 

[Steven G]

Dividing by T^-2 is not the same as multiplying by T^-2. If it were then division and multiplication would be the same!

 

[Dr.Peterson]

Thank you very much for your reply! Much appreciated! In regards to the first image, the second line is correct from elsewhere. I am unsure what to do with the T^-2 ? Does it not stay the same as it has no powers on the top to add or subtract?
Thanks for your help and the formula you quoted to the arithmetic series is very useful! Awsome!
Appreciate your time!

When you move a power from bottom to top or from top to bottom, you change the sign of the exponent. So T^-2 on the bottom becomes T² when you move it to the top. Or you could think of it as subtracting -2 from a 0 exponent on top (because there is no T there).

And when there is no fraction bar, you're "on top" -- I've described it as, "the first floor of the house is at ground level; the basement is below".

 

[Mathmasteriw]

When you move a power from bottom to top or from top to bottom, you change the sign of the exponent. So T^-2 on the bottom becomes T² when you move it to the top. Or you could think of it as subtracting -2 from a 0 exponent on top (because there is no T there).

And when there is no fraction bar, you're "on top" -- I've described it as, "the first floor of the house is at ground level; the basement is below".

Great stuff thanks a lot for the help! That's an awesome way to explain it! I really appreciate everyone's input and help!
I'll post a photo of the amended work!

 

[Mathmasteriw]

Dose this look correct?

 

[Steven G]

If t is proportional to M^2*T^2 then how do you conclude that t = M^2*T^2? What happened to the sqrt sign?

Can you explain what it means if A is proportional to B? How about A is proportional to sqrt(B)?

 

[Dr.Peterson]

In regards to the first image, the second line is correct from elsewhere.

My guess is that the second line really is supposed to come not "from elsewhere", but from the first line with the substitution [MATH]F = MLT^{-2}[/MATH]; if that is true, then as has been pointed out several times, you dropped the square root.

Dose this look correct?

You accidentally changed the [MATH]\propto[/MATH] to "="; and if we restore the dropped square root, we end up with [MATH]t\propto \sqrt{M^2T^2}\propto MT[/MATH]

 

[Mathmasteriw]

My guess is that the second line really is supposed to come not "from elsewhere", but from the first line with the substitution [MATH]F = MLT^{-2}[/MATH]; if that is true, then as has been pointed out several times, you dropped the square root.


You accidentally changed the [MATH]\propto[/MATH] to "="; and if we restore the dropped square root, we end up with [MATH]t\propto \sqrt{M^2T^2}\propto MT[/MATH]

Awsome stuff and yes I forgot the square root! Thanks for the help and clear explanation!!