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  • 1 answers

Sia ? 6 years, 1 month ago

 


{tex}v = \frac{1}{3}\pi {r^2}h{/tex} {tex}\left[ {{r^2} = \sqrt {{R^2} - {x^2}} } \right]{/tex}
{tex}V = \frac{1}{2}\pi .\left( {{R^2} - {x^2}} \right).\left( {R + x} \right){/tex}
{tex}\frac{{dy}}{{dx}} = \frac{1}{3}\pi \left[ {\left( {{R^2} - {x^2}} \right)\left( 1 \right) + \left( {R + x} \right)( - 2x)} \right]{/tex}
{tex} = \frac{1}{3}\pi \left[ {\left( {R + x} \right)\left( {R - x} \right) - 2x\left( {R + x} \right)} \right]{/tex}
{tex} = \frac{1}{3}\pi \left( {R + x} \right)\left[ {R - x - 2x} \right]{/tex}
{tex} = \frac{1}{3}\pi \left( {R + x} \right)(R - 3x){/tex}....(1)
Put {tex}\frac{{dv}}{{dr}} = 0{/tex}
R = - x (neglecting)
R = 3x
{tex}\frac{R}{3} = x{/tex}
On again differentiating equation (1)
{tex}\frac{{{d^2}v}}{{d{x^2}}} = \frac{1}{3}\pi \left[ {(R + x)( - 3) + (R - 3x)(1)} \right]{/tex}
={tex}{\left. {\frac{{{d^2}v}}{{d{x^2}}}} \right]_{x = \frac{R}{3}}} = \frac{1}{3}\pi \left[ {\left( {R + \frac{R}{3}} \right)( - 3) + \left( {R - 3.\frac{R}{3}} \right)} \right]{/tex}
{tex}\frac{1}{3}\pi \left[ {\frac{{4R}}{3} \times - 3 + 0} \right]{/tex}
{tex} = \frac{{ - 1}}{3}\pi 4R{/tex}
{tex}\frac{{{d^2}v}}{{d{x^2}}} < 0{/tex} Hence maximum
Now {tex}v = \frac{1}{3}\pi \left[ {\left( {{R^2} - {x^2}} \right)\left( {R + x} \right)} \right]{/tex}{tex}\left[ {x = \frac{R}{3}} \right]{/tex}
{tex}v = \frac{1}{3}\pi \left[ {\left( {{R^2} - {{\left( {\frac{R}{3}} \right)}^2}} \right)\left( {R + \left( {\frac{R}{3}} \right)} \right)} \right]{/tex}
{tex} = \frac{1}{3}\pi \left[ {\frac{{8{R^2}}}{9} \times \frac{{4R}}{3}} \right]{/tex}
{tex}v = \frac{8}{{27}}\left( {\frac{4}{3}} \right)\pi {R^3}{/tex}
{tex}v = \frac{8}{{27}}{/tex} Volume of sphere
Volume of cone {tex} = \frac{8}{{27}}{/tex} of volume of sphere.

 

 

  • 5 answers
each & every ques. r imp.

Khuskaran Sidhu 6 years, 1 month ago

Maxima &minima

Khuskaran Sidhu 6 years, 1 month ago

Limit as a sum

Khuskaran Sidhu 6 years, 1 month ago

Property of determinant

Khuskaran Sidhu 6 years, 1 month ago

Row operation
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  • 2 answers

Raj Mehra?️ 6 years, 1 month ago

1-9 chp

Naresh Joshi 6 years, 1 month ago

Ask to ur school teacher
  • 1 answers

Khuskaran Sidhu 6 years, 1 month ago

Tan x + 1/tan x =1 Tan^2 x+1=tanx Sec^2 x= tan x ...???
  • 2 answers
revise basic cocepts..

Bhumika Mishra 6 years, 1 month ago

Learn ur chapters by makin notes yhat will help in quick revision
  • 3 answers

Ravi Joshi 6 years, 1 month ago

Integrate 1/x+x ki power 5

Shreya Dixit 6 years, 1 month ago

1/2logx +C

Satyam Sharma 6 years, 1 month ago

Plz tell the question rightly
  • 1 answers

Khuskaran Sidhu 6 years, 1 month ago

keep l.h.l.=r.h.l. For example,x->1+ Then, put x=1+h & when x->1 - Put x= 1-h
  • 1 answers

Satyam Sharma 6 years, 1 month ago

Tale 1+x2 in denominator of y and tan-1x then u got the linear equation. After that solve it
  • 1 answers

Supriya Kumari 6 years, 1 month ago

Yes
  • 0 answers
  • 6 answers

Řøhăň Řąjpůť ✌️✊ 6 years, 1 month ago

I think the simple formula is to do consistent study. nothing else. ? do 18 hours study daily. with short break.

Priya Dharshini ? 6 years, 1 month ago

Do smart work and hard work.. both are necessary. Dont lose hope.. do so much practice. Cover ur concepts in detail than going behind questions. Questions are important. But without concepts u cant do anything. It may be maths or physics... dont mug up ans.. try to undetstand it... i know it is not possible sometimes but try. Do conceptual questions more. Do 10 topics but make it strong.. than doing 100 topic just like that from top. .. all the best.. i cant give guarantee for 100% u can score in science group but ya.. u can surely score 98%

Rohit Patel 6 years, 1 month ago

All is well

Cooper Livi'N 6 years, 1 month ago

And also, no one can give his 100 percent even detol kill only 99.9 percent germs

Cooper Livi'N 6 years, 1 month ago

Smart work is too better than hard work

Cooper Livi'N 6 years, 1 month ago

First, try to start,if you want to do something you have to start first..then try to confuse your mind and say we have only a single thing to do which is study then your mind follow it too..try to avoid social media last but not least write it in your mind if you can't do 5 to 6 hours self study per day in 24 hours then where these all hours gone?you have to study for yourself..I have not much time so it is enough that's it
  • 0 answers
  • 5 answers

Manu Kumar 6 years, 1 month ago

dont take tention because whenever we think more , so we hopless.

Tanu Tanu 6 years, 1 month ago

Same here even i have also mathematics paper tomorrow

Priya Dharshini ? 6 years, 1 month ago

Run behind concepts of sums not behind the no. Of sums u need to solve..

Priya Dharshini ? 6 years, 1 month ago

Ohh.. even i having my mid term exam . Today was phy. See do those chapter which are easy for u.. in 7 atleat 4 u must be knowing . Make it strong. Do whole ncert. If time peemits learn formula of remainig 3 chapters and try to attempt it. Dont leave it blank.. do anythinh with that question... try to solve with some basic concepts..

Mehul Rawal 6 years, 1 month ago

Start doing integration, differentiation,app of derivative and determinants
  • 0 answers
  • 2 answers

Kaustubh Pathak 6 years, 1 month ago

(x+2z)p+(4zx-y)q=2x-y px+2pz+4xqz-yq-2x+y=0 (p+4qz-2)x+(1-q)y+2pz=0

Deepak Chaudhary 6 years, 1 month ago

(x+2z)p+(4zx-y)q=2x-y Xp+2zp+4zxq-yq=2x-y
  • 4 answers

Kaustubh Pathak 6 years, 1 month ago

a+b+c

Khushi Jain 6 years, 1 month ago

Dont mind but this is a ques of cls 4-5!

Yogita Ingle 6 years, 1 month ago

3a+(-a+b)+(-a+c)
= 3a - a + b - a + c
= 3a - a - a +b +c
= a + b + c

Ravi Joshi 6 years, 1 month ago

a+b+c
  • 2 answers

Mehul Rawal 6 years, 1 month ago

For ex f(x)=3x+4 and g(x)=3x+2 then gof(x)=g(f(x)). Gof=g(3x+4) Gof=3(3x+4)+2

Mehul Rawal 6 years, 1 month ago

Gof = g(f(x))
  • 2 answers
10

Kaustubh Pathak 6 years, 1 month ago

clarify
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A ? 6 years, 1 month ago

Ncert and exampler...

Pragati Saini 6 years, 1 month ago

Ncert textbook and ncert examplar ... Read line by line from them
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  • 4 answers

Ravi Joshi 6 years, 1 month ago

False ,because det of singular matrix is 0, hence inverse doesn't exist

Sahdeo Koche 6 years, 1 month ago

False

Abhinav Gaur 6 years, 1 month ago

I think it's true.

Isha Raj 6 years, 1 month ago

false
  • 2 answers

Isha Raj 6 years, 1 month ago

log |secx| + C

Apurv Srivastava 6 years, 1 month ago

- log (cosx) + C
  • 1 answers

Harsha Vella 6 years ago

Tanx by cosecx

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