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C2 Differentiation. watch

1. Its in this chapter, but this part doesn't require differentiation yet.

This is the question:

Its question 5 part a

This is what I've done:

But the correct answer is y = 1 - (x/2) - (pi*x/4)

I've clearly missed something important, can anyone help me see where I went wrong?
2. (Original post by mynameisntbobk)
I've clearly missed something important, can anyone help me see where I went wrong?
For part a) you're interested in the length of the wire. Total length is given as 2.
3. (Original post by ghostwalker)
For part a) you're interested in the length of the wire. Total length is given as 2.
Oh yeah. I just realised that. I used (1/2)(pi)(x) as the length of the curve, and it worked

Thank you.
4. (Original post by ghostwalker)
For part a) you're interested in the length of the wire. Total length is given as 2.
Do you think you could help me with part c. I was thinking about differentiating the expanded equation, but the pi is off putting, so I'm not sure what I'd do.
5. (Original post by mynameisntbobk)
Do you think you could help me with part c. I was thinking about differentiating the expanded equation, but the pi is off putting, so I'm not sure what I'd do.
Yes, I'd do it that way. Expand the brackets and differentiate.

Don't forget pi is just a constant, and as far as calculus is concerned it's no different to any other non-zero constant like, 2, or 7, etc.

See what you can do.
6. (Original post by ghostwalker)
Yes, I'd do it that way. Expand the brackets and differentiate.

Don't forget pi is just a constant, and as far as calculus is concerned it's no different to any other non-zero constant like, 2, or 7, etc.

See what you can do.
I got for my value of x after equalling my dR/dx to be ((4/pi) + 1)

And my max volume to be ((160/pi^2) + 4 + (4/pi))

I know my final answer is wrong though
7. (Original post by mynameisntbobk)
I got for my value of x after equalling my dR/dx to be ((4/pi) + 1)

And my max volume to be ((160/pi^2) + 4 + (4/pi))

I know my final answer is wrong though
Your value for x is also incorrect.

I suspect you differentiated correctly, but made a slip when you rearranged it.

Post working for that part, as we can check what's going on.
8. (Original post by ghostwalker)
Your value for x is also incorrect.

I suspect you differentiated correctly, but made a slip when you rearranged it.

Post working for that part, as we can check what's going on.
The sheet I worked on is quite messy, so I'll just type it for you.

R = ((-pi * x^2) / 8 ) + x (-x^2/2)

dR/dx = ((-pi * x)/4) + 1 - x

((-pi * x) / 4) + x (-x^2/2) = 0

(-pi * x) + 4 - 4x = 0

(-pi * x) - 4x = -4

x(-pi -4) = -4

x = -4/(-pi -4)

x = (4/pi) + 1
9. (Original post by mynameisntbobk)
x = -4/(-pi -4)

x = (4/pi) + 1
Yep. It's the very last line.

You can't simplify the denominator.

You seem to have done a/(b+c)= a/b +a/c which is a definite no, no.

x= 4/(4+pi) is really all you can do.
10. (Original post by ghostwalker)
Yep. It's the very last line.

You can't simplify the denominator.

You seem to have done a/(b+c)= a/b +a/c which is a definite no, no.

x= 4/(4+pi) is really all you can do.
Oh right. Thank you so much I didn't actually realise I made that mistake, so if I were to put that value of x into the equation for R, that would be fine right?

And sorry to be a burden, but I don't understand part a of question 6
11. (Original post by mynameisntbobk)
Oh right. Thank you so much I didn't actually realise I made that mistake, so if I were to put that value of x into the equation for R, that would be fine right?
Yep.

And sorry to be a burden, but I don't understand part a of question 6
AP^2 is the distance between A and P squared. So, you'd use Pythagoras on the two sets of co-ordinates.

AP^2 = (difference in x coordinates)^2 +....
12. Wait a sec i might be acting stupid
but
R = ((-pi * x^2) / 8 ) + x (-x^2/2)

dR/dx = ((-pi * x)/4) + 1 - x

Surely unless its x + (-x^2/2)
it should not be 1- x
rather-x^3/2 --> 3/2 x^2
13. (Original post by ghostwalker)
Yep.

AP^2 is the distance between A and P squared. So, you'd use Pythagoras on the two sets of co-ordinates.

AP^2 = (difference in x coordinates)^2 +....
Would I do (8-t)^2 + (-6-t)^2 + (5-2t)^2 ?

I'm sorry, I think the use of 3 points has confused me, I'm usually good with these kinds of questions
14. So makin

dR/dx = ((-pi * x)/4 -3/2x^2
15. Any one axplain what i dont get or was it just a typo
17. (Original post by Anony1234)
Wait a sec i might be acting stupid
but
R = ((-pi * x^2) / 8 ) + x (-x^2/2)

dR/dx = ((-pi * x)/4) + 1 - x

Surely unless its x + (-x^2/2)
it should not be 1- x
rather-x^3/2 --> 3/2 x^2
Sorry, yeah, I posted that quite ambiguously, it is like you said x + (-x^2/2) or x - (x^2/2)

(Original post by science-oliver)
Its fine thanks though.
18. (Original post by mynameisntbobk)
Sorry, yeah, I posted that quite ambiguously, it is like you said x + (-x^2/2) or x - (x^2/2)

Its fine thanks though.
19. How you doing on 6 If. You need help just use pythagors
ab2 = (8-t) sq +( -6-t )sq+5-2t)sq
= 64 -16t +tsq + 36 +12 t tsq + 4tsq -20t +25
6t^2 -24t+125 there
sorry for presentation sq = squared
20. (Original post by Anony1234)
How you doing on 6 If. You need help just use pythagors
ab2 = (8-t) sq +( -6-t )sq+5-2t)sq
= 64 -16t +tsq + 36 +12 t tsq + 4tsq -20t +25
6t^2 -24t+125 there
sorry for presentation sq = squared
Yeah thanks, I've done it already, but thanks for the help

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