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Mathematics: Post your doubts here!

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sitooon

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midha.ch
See if you can help!
There is no one on xtremepapers to clear our doubts except you!:(
Part ii & iii of both if you can
upload_2014-4-6_0-46-8.png

upload_2014-4-6_0-46-56.png
 
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sagar65265

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Thought blocker said:
View attachment 38411
Click to expand...

Since the box is a prism, the cross-sectional area is constant from bottom to top, so the total volume is simple to calculate as:

Volume = Area of Cross Section * Height
= (0.5 * r^2 * θ) * h
= 0.5hr^2

Since we are given this to be 300 cm^3, we can equate the two to get:

300 = 0.5hr^2
600 = hr^2
h = 600/r^2

So there's our first equation, that relates the two unknowns in this question.

Secondly, we need to calculate the area. The surface area of the top and bottom surfaces are each equal to 0.5 * r^2 * θ, so their TOTAL area is the sum of these, is equal to r^2.

The square surfaces on the side each have area r * h = rh. Therefore, their TOTAL area = 2rh.

The rightmost surface, the curved surface, can be stretched flat into a rectangle that has width rθ and has height h. So, the surface area of this is rh.

Summing all these, we get:

Surface area = r^2 + 2rh + rh = r^2 + 3rh
Substituting h = 600/r^2 in the above equation, we get:

Surface area = r^2 + 3 * r * 600/r^2 = r^2 + 1800/r = Answer.

Hope this helped!
Good Luck for all your exams!
 
Thought blocker

Thought blocker

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sagar65265 said:
Since the box is a prism, the cross-sectional area is constant from bottom to top, so the total volume is simple to calculate as:

Volume = Area of Cross Section * Height
= (0.5 * r^2 * θ) * h
= 0.5hr^2

Since we are given this to be 300 cm^3, we can equate the two to get:

300 = 0.5hr^2
600 = hr^2
h = 600/r^2

So there's our first equation, that relates the two unknowns in this question.

Secondly, we need to calculate the area. The surface area of the top and bottom surfaces are each equal to 0.5 * r^2 * θ, so their TOTAL area is the sum of these, is equal to r^2.

The square surfaces on the side each have area r * h = rh. Therefore, their TOTAL area = 2rh.

The rightmost surface, the curved surface, can be stretched flat into a rectangle that has width rθ and has height h. So, the surface area of this is rh.

Summing all these, we get:

Surface area = r^2 + 2rh + rh = r^2 + 3rh
Substituting h = 600/r^2 in the above equation, we get:

Surface area = r^2 + 3 * r * 600/r^2 = r^2 + 1800/r = Answer.

Hope this helped!
Good Luck for all your exams!
Click to expand...
ty ;)
hope u will allow to borrow me your brain for exams ;)
 
mak kings

mak kings

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assalam alikum guys.... cud sm1 plssssss help me in ques 5a. plss. i cant even have a glimpse of wat to doo its very confusing :S OCTOBER NOVEMBER 2013 ,PAPER 6 VARIANT 3 ..pls any one
and also if sm1 cud explain 6 iii and iv from the same year!! :
 
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sagar65265

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Faaiz Haque said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_41.pdf

Q4 ii?
Click to expand...

When particle P changes the direction of it's motion, it's velocity turns from negative to positive or positive to negative (since the motion is only along a straight line, it can only travel in two ways).

However, before that changeover happens, the velocity of the particle has to equal zero - if it is initially positive, it slows down, reaches zero, then starts moving in the negative direction. Similar logic applies if it's original velocity was negative.

Therefore, we have to find the time when the velocity is Zero.

Since v = 0.75t^2 − 0.0625t^3, setting v = zero = 0 gives us

0.75t^2 = 0.0625t^3

Cancelling out the t^2, we get

0.75/0.0625 = t = 12 seconds.

The other roots of this equation are repeated roots = zero. In other words, the velocity of the particle is zero only at t = 0 and t =12 seconds.

Since v = ds/dt , we can write

v dt = ds

(0.75t^2 - 0.0625t^3) dt = ds

Carrying out the integral with the limits on the left side being

Lower Limit = 0 Seconds
Upper Limit = 12 Seconds

and the limits on the right side being

Lower Limit = 0 Meters
Upper Limit = S Meters (where S is our final answer), we get

[0.25t^3 - 0.015625t^4] ==> o.25 * 1728 - 0.015625 * 20736 = 108 Meters = Answer

Hope this Helped!
Good Luck for all your exams!
 
midha.ch

midha.ch

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sitooon said:
midha.ch
See if you can help!
There is no one on xtremepapers to clear our doubts except you!:(
Part ii & iii of both if you can
View attachment 38394

View attachment 38395
Click to expand...
For the third part of your first question, I think it's bit too lengthy for an answer worth 4marks. Every question has thousand different ways to be answered and now that I have shown you one of them, you can think of an alternative and a much more shorter one. If you do get a shorter procedure, then please inform me too! :):)

for the 2nd picture, if you compare with the first one, it's almost same stuffs asked in a twisted way (Credit goes to the "twisted and infinitely torturous brains" of CIE :mad:)
change a few statements and turn upside-down few of the steps and you'll get the answer for 2nd question

P.S. I'm not sure if my answers match with CIE ms or not! :p
 

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sitooon

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midha.ch said:
I'm weak in complex numbers especially these loci stuffs so ahmed abdulla if you can solve that complex number question, please tag me so that I'm informed :):)
Click to expand...
Thanks :) .
as for vector questions , lambda is 3/8 not -1/2 and the second question doesnt fit also the mrk scheme answer >> i think you did some calculation mistake :whistle:
its from on2011& on2010 , va'31
btw, dont EVER use correction fluid in the exam .
 
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