Fraction within a fraction-urgent help needed from maths pundits!

nonconformist

nonconformist

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Hi guys, I need an answer quite urgently please.

I seem to have forgotten what to do when faced with a fraction where the denominator is a fraction.

As this is a physics question where I'm deriving the formula of a certain unit, it is all abstract.
Could anyone quckly inform me? I've got a nagging feeling there's sme X-multiplying ivolved.

Cheers in advance!
 
Example: If you have 3/(3/5), the three's cancel out and leave a five, for example, you would first do (3/5) which equals 0.6, then take 3 divided by 0.6, which is 5.

Or, if you have 3/5/5, then it's 0.12, 3, divided by 5, divided by 5.
 
a) use a calculator;) :)

b) say 1/ 2/5 how many 2/5ths are there in one in other words devide 2/5 by 1/1. et voila.
 
instead of dividing by a fraction. Multiply by 1 / fraction. ie invert it and multiply
 
Whats the question?

edit: you'll get the bill later
 
Ok the above example is easy to do in your head because your essentially asking whats 5/2*1/1 answer 2.5

but it's the same for anything just figure how many times you can get 5/2 into one times the actual numerator so if it's 8 it's 8*2.5 =20

Dead easy when you know how.

EDIT: ah I see you got it now good, that's GCSE maths, fall asleep that day :)

Now that you've done that show that sin^2 cos^2 =1/8(1-cos(4x))

Hence find the indefinite integral

Sin^2 x Cos ^2 x dx.

:) Show all working and explain how each step is accomplished, feel free to use double angle formulaes where apropriate. I figured since your doing A'level physics you could help me with my homework. :D
 
col said:
Whats the question?

edit: you'll get the bill later
Click to expand...
The question was to derive an equation for Charge/Time in terms of resistivity, area, length and voltage.

As for the bill, being a Labour chap, I'm sure it's means tested? :D
 
Sidhe said:
Now that you've done that show that sin^2 cos^2 =1/8(1-cos(4x))

Hence find the indefinite integral

Sin^2 x Cos ^2 x dx.

:) Show all working and explain how each step is accomplished, feel free to use double angle formulaes where apropriate. I figured since your doing A'level physics you could help me with my homework. :D
Click to expand...

I could do your homework, but I won't. Help I can manage though. The formula you might want to look at is sin(2x)=2*sin(x)*cos(x)
 
Sidhe said:
Ok the above example is easy to do in your head because your essentially asking whats 5/2*1/1 answer 2.5

but it's the same for anything just figure how many times you can get 5/2 into one times the actual numerator so if it's 8 it's 8*2.5 =20

Dead easy when you know how.

EDIT: ah I see you got it now good, that's GCSE maths, fall asleep that day :)

Now that you've done that show that sin^2 cos^2 =1/8(1-cos(4x))

Hence find the indefinite integral

Sin^2 x Cos ^2 x dx.

:) Show all working and explain how each step is accomplished, feel free to use double angle formulaes where apropriate. I figured since your doing A'level physics you could help me with my homework. :D
Click to expand...
I found the power-reducing formulas sin^2 x = (1-cos 2x)/2 and cos^2 x = (1+cos 2x)/2 helpful for the first part of your problem. Once you get the answer they're looking for, integrating it should be simple.
 
That's great, thanks, I'll dig it out tomorrow, I think I came unglued when I saw the answer, and couldn't work out how one of the steps had occured, this is tricky one, but your help is much apreciated :)
 
Bootstoots suggestion works as well. I did it differently to him. And since I'm bored, I will do your homework, behind a spoiler.

Spoiler :
LHS = (sin*cos)^2
=(sin(2x)/2)^2 (using sin 2x = 2*sin*cos)
=sin^2(2x)/4
={[1-cos(4x)]/2]}/4 (using sin^2 x = (1-cos2x)/2)
=[1-cos(4x)]/8
=RHS

Integration is easy. 1/8(x-sin(4x)/4) +c
=1/32(4x-sin(4x))+c
 
X divided by Y is the same as X multiplied by the inversion of Y (1/Y)
 
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