Alan

The force times the perpendicular distance from the force to the pivot point (i.e. the point about which the moment is being taken)

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A litre is 1000 cm³ 

Volume = pi*r²*h  where r is radius and h is height, so

pi*r²*18 = 2500  (we have to turn the litres into cm³)

Divide both sides by 18pi

r² = 2500/(18pi)

Take the square root of both sides

r = 50/√(18pi)

$${\mathtt{r}} = {\frac{{\mathtt{50}}}{{\sqrt{{\mathtt{18}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{6.649\: \!038\: \!006\: \!690\: \!545\: \!1}}$$

So the radius is approximately 6.65cm

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"I think I can see that a shell  has the volume of    dA= 2pi L dR       Is that right?"

Be careful not to confuse your r (a radial distance) with your R (electrical resistance).

The surface area of the shell is  2pi*r* L (the volume would be 2pi*r*L*dr) - see below.

ρ is an intrinsic property of the material (unlike resistance, which depends of the size of the material).

The relationship between ρ and R is  ρ = RA÷l where A is cross-sectional area and l is length in the direction of electrical current flow. In this problem l is not L, it is r.  Or, rather, for the shell it is dr.  The relevant cross sectional area of the shell (bearing in mind that current is flowing radially) is 2pi*r*L (this is stated incorrectly in the problem, though the correct value is used in the integral - perhaps this was the cause of xvxvxv's confusion), so the small increase in resistance across the shell is dR = ρl/A

or dR = ρdr/(2pi*r*L).

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Depends on the equation, but if it's something like y = some function of x, then set y = 0, and find the values of x that make the function zero.  Can't be more specific unless you supply the equation.

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-5x + y = 3

Add 5x to both sides

-5x + y + 5x = 3 + 5x

so y = 3 + 5x  as the 5x's on the left-hand side cancel each other out.

3x - 8y = 24

Add 8y to both sides 

3x - 8y + 8y = 24 + 8y

so 3x = 24 + 8y

Subtract 24 from both sides

3x - 24 = 24 + 8y - 24

so 3x - 24 = 8y

Divide all terms by 8

3x/8 - 24/8 = 8y/8

so 3x/8 - 3 = y     (or y = 3x/8 - 3)

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Rearrange them to get them in the following forms:

y = 5x + 3

and

y = (3/8)x - 3

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Use the sine rule:  sin(A)/a = sin(B)/b etc.

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The maximum of your function will occur at one of the black points.  I'll leave you to work out which one.

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Odd - I can't get it to work myself now!!

Oh! Yes I can - I just forgot to paste it into the search box.  

So what I get from "Open image in new tab", going to that tab, then copying the URL that is at the top, is the following:

Well, if you right-click over the question mark icon and then choose Copy image URL you can paste the result (a URL) into the search box and it seems to find some questions.

You can also choose Open image in new tab and then copy the URL at the top.

Not sure if this is what you are after!

Is the question mark icon only available to moderators?

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