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ijlal
 5 years ago
http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20%20Mathematics/9709_s10_qp_13.pdf
help me in Question no.9 pls
reply quick thank you :)
ijlal
 5 years ago
http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20%20Mathematics/9709_s10_qp_13.pdf help me in Question no.9 pls reply quick thank you :)

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TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2First we need the points A and B, know how to find that?

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2right, so our integration will be from 1 to 4 what is the outer radius of each disk we will use in our method? what is the radius of the inner disk?

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0i dont know how a cylinder is formed in this curve

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2we are making rings out of each section of areadw:1327072712405:dwthe outer radius of each ring will be\[r_0=5\]the inner radius will be\[r_i=x+\frac{4}{x}\]the area of each disk wile therefor be\[\pi r_0^2\pi r_i^2\to\pi(r_0^2r_i^2)\]

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2dw:1327073020023:dwhere is a crosssection of each ringdw:1327073083149:dwtherefor adding up these rings we will integrate the areas of the rings from x=1 to x=4\[\pi\int_{1}^{4}r_0^2+r_i^2dx=\pi\int_{1}^{4}5^2(x+\frac{4}{x})^2dx\]make sense?

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2*slight typo above, should be minus in the first integral (because we are subtracting the area of the inner disk from that of the outer)\[\pi\int_{1}^{4}r_0^2r_i^2dx=\pi\int_{1}^{4}5^2(x+\frac{4}{x})^2dx\]

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0Yes the Volume of the ring is i guess 57pie

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2I guess, I haven't checked. I'll leave the integration for you to do. But your final answer is a volume of a shape, each section is a ring. (Just pointing out the discrepancy in calling the whole thing a ring)

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0the answer of the question is 18pie i dont know how the cylinders height is 4units can you tell me that i will be done with my question done

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2which cylinder has a height of 4 units?

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0there is only one cylinder formed

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2\[\pi\int_{1}^{4}r_0^2+r_i^2dx=\pi\int_{1}^{4}5^2(x+\frac{4}{x})^2dx=\pi\int_{1}^{4}25x^28\frac{16}{x^2}dx\]\[=\pi(17x\frac{x^3}{3}+\frac{16}{x})_{1}^{4}\]\[=\pi[(68\frac{16}{3}+4)(17\frac{1}{3}+16)]\]whatever that simplifies to... The whole shape will have a length of 3 units (from x=1 to x=4) if that is what you mean....

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2I got\[\pi\int_{1}^{4}r_0^2r_i^2dx=\pi\int_{1}^{4}5^2(x+\frac{4}{x})^2dx=\pi\int_{1}^{4}25x^28\frac{16}{x^2}dx\]\[=\pi(17x\frac{x^3}{3}+\frac{16}{x})_{1}^{4}\]\[=\pi[(68\frac{16}{3}+4)(17\frac{1}{3}+16)]=32\pi\]and you say that you know the answer to be 18pi ?

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0yes the answer is 18 pi it is given in the mark scheme of this question

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0and this solution simplifies to 34pi not 32pi

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2Oh, I just made some silly arithmetic mistake apparently (this is why I left the integral for you to do) As you can see by wolfram it is set up right\[\pi\int_{1}^{4}r_0^2r_i^2dx=\pi\int_{1}^{4}5^2(x+\frac{4}{x})^2dx\] http://www.wolframalpha.com/input/?i=int%20from%201%20to%204%20(25(x%2B4%2Fx)%5E2)dx&t=crmtb01 so you figure out where I messed up...

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0the solution of this integral gives 90pi

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2no, look at the link I posted. Wolfram does no lie: http://www.wolframalpha.com/input/?i=pi*int+from+1+to+4+%285%5E2%28x%2B4%2Fx%29%5E2%29dx there it is explicitly, clearly the answer to the integral I wrote is 18pi

ijlal
 5 years ago
Best ResponseYou've already chosen the best response.0oh sorry i neglected the minus sign by mistake :P thank you :)

TuringTest
 5 years ago
Best ResponseYou've already chosen the best response.2very welcome :) I apparently made a similar mistake trying to do it by eye, so it happens.
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