Froskoy

Consider the phrases:

(1) Online dating is becoming increasingly popular.

(2) It is becoming increasingly popular for people to date online.

What tense is each of these written in and when is it better to use one of these two equivalent statements rather than the other?

It is common to say "less noise" - "fewer noise" sounds incorrect. But in a different context "fewer benefits" is correct whereas "less benefits" is not. It appears that "fewer" is used when dealing with plurals and "less" is used for a singular. Is this so and what is the exact name given to this device in the English language?

I guess this is called float charging?

I don't care about how fast the battery charges - I just want to leave 13.8V connected constantly across it, for an indefinite period of time.

What does "the probability of y having a value in the range (y,y+dy) is P(y)dy" mean? Is P(y) the cumulative distribution function?

And what is the best way of working it out, other than just listing all the possibilities?

Thanks!

Given a probability space (Ω,F,P), show that if E1,E2,...∈ F then ∩_{i=1}^∞ Ei ∈ F.

Thank you!

A truck travels from X to Y.

When the truck is going uphill, it goes at 56 mph, when it's going downhill, it goes at 72 mph, and when the ground is flat it goes at 63 mph. Given that it takes the truck 4 hours to get from X to Y and 5 hours to get from Y to X, what is the distance between X and Y?

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I really don't know where to start with this - can someone please help?

With very many thanks,

Froskoy.

Thanks.

Thank you!

I'm trying to work out the following problem:

I flip two coins. I tell you that the first one is a head. What is the probability that the second is also head?

Hi,

I'm etching a very simple pattern onto a PCB with some ferric chloride I had lying around.

My question is: if I cover with permanent marker the areas that I don't want the copper to be removed, and then spread some ferric chloride over the board, will the ferric chloride take the copper off the areas without pen on, but leave the areas protected by the pen untouched? I could then take the pen of with some isopropanol or similar.

Will this work or do I need a better way of protecting the areas I do not want to remove the copper from?

Many thanks,

Froskoy.

Hi,

I'm building a pair of helmholtz coils to do a variety of magnetism-related experiments. I've borrowed an old Avo Douglas coil winder and plan to do a couple of thousand turns on two sections of 50mm or 60mm diameter pipe. Some nylon threaded rod will pass through the middle of each coil, to make the distance between them tweakable, to ensure that the distance between them is exactly equal to the radius of each coil.

I have two questions:

1) Does the physical width of each coil have an effect? That is the width of each layer of the coil. Should this be minimised (e.g. just have five adjacent wires per layer) or does this not have any effect?

2) Is the distance r between the coils the distance between the centrepoint of each coil, or the distance between the closest points on each coil?

Any other comments to do with the practical aspects of making a pair of helmholtz coils and difficulties that may be encountered would be very much appreciated.

With very many thanks,

Froskoy.

The definite integral ∫(1-x^2)^n dx x=[0,1] is denoted by I(n)

Show that I(n)=(2n/(2n+1)).I(n-1)

Thanks very much!

Hi. I'm really stuck:

Solve the equation z^4=64(cosπ + i sin π) giving your answers in polar form.

Many thanks.

Many thanks!

Show that the set of real numbers excluding -1 forms a group under the operation * defined by a*b = a +b + ab

Thanks so much!

Hi,

How do you find the Cartesian equation for r=2sinθ (0<=θ<π)?

Many, many thanks,

Froskoy.

Prove that

n∫cosh^n(x) dx = cosh^(n-1) x * sinhx + (n-1)∫cosh^(n-2) x dx

Many thanks.

where I(n) initially = 0∫1 (lnx)^n dx

Thanks.