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Mathematics: Post your doubts here!

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Can anyone please solve winter 2012 Question 7 part ii of this winter 2012 paper 33 question. The value of k=10 .Can someone please explain how do we get it?math p3 winter 2012.JPG
 
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Can anyone please solve winter 2012 Question 7 part ii of this winter 2012 paper 33 question. The value of k=10 .Can someone please explain how do we get it?View attachment 23763
ok so
all u do is
pie/4 times 40
so
i'm gonna refer to the shaded are as a triangle which it roughly is :p
area of the first triangle is A
the triangle right next to it (under the x-axis)
area of those two would be 2A and area of 3 triangles would be 3A and so on............
and then the x-coordinates will be pie/4 + pie/4+...................
now that we want 40A
we do pie/4 times 40 which is equal to 10 pie so k=10
i hope you get it :)
 
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Okay so now we have to find angle between a line and plane.
To do this we need two things we need is the b1 of the line which we can obtain by subtracting one point on the line from another on the line
(-5,3,6) – (5,8,1) = (-10,-5,5) this is b1
Second thing is n1 which are the coefficients of x y and z in the equation of plane
I.e. = (2, -1,4)
Now know that when a line and a plane is involved then we use sin*
If both cases if there are angles to be found in two lines or two planes we use cos*
Here we use sin
Frst take modulus of b1= root of ((-10) ^2 +(-5)^2+ 5^2)
(100+25+25 )
=root 150
Then of n1= root of( (2^2)(-1^2)(4^2)
=root 21
Now put in formula
B1.n1 = mod of b1* mod of b2 * sin a
(-10,-5,5) . (2, -1,4) = root 150* root 21 sin a
-20 +5 +20 = root 150* root 21 sin a
-5/ root 150* root 21 = sin a
A= sin inverse of -5/ root 150* root 21
A= 5.1 ignore the negative sign as you need acute angle and other wise ul get obtuse. J
Dun frgt me in ur prayers J and if u dint get it ask me again J
 
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CHALLENGING QUESTION !!!

i think this question is GOING to come this year and i am 100 % sure !!
so any help ???

A ball is dropped froma height of 2m above a hard floor.
After each bounce , a ball rises to 3/4 of its previous height.

(a) how far has it travelled in total when strikes the ball for the nth term?
(b) show that the ball never travels more than 14 m in total .

i tried my best but never got it !

(a) ans is 14 - 16 * 0.75 ^n metre
ahmed abdulla syed1995 A star

This of pure 1, no Mechanics nor Physics knowledge needed.

as you did,
2(1-0.75^n)/1-0.75

but we also have to multiply with 2, since when a bounces it goes up and down so it travel the distance twice not once, except for the first where it only go down, then bounces..therefore

{[2(1-0.75^n)/1-0.75] x 2} -2
[8-8(0.75^n)] x 2 -2
16 - 16(0.75^n) - 2
14 - 16(o.75^n)


(b) sum of infinity
(2/1-0.75) x 2 -2
8 x 2 -2
16 -2
14.
 
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ahmed abdulla syed1995 A star

This of pure 1, no Mechanics nor Physics knowledge needed.

as you did,
2(1-0.75^n)/1-0.75

but we also have to multiply with 2, since when a bounces it goes up and down so it travel the distance twice not once, except for the first where it only go down, then bounces..therefore

{[2(1-0.75^n)/1-0.75] x 2} -2
[8-8(0.75^n)] x 2 -2
16 - 16(0.75^n) - 2
14 - 16(o.75^n)


(b) sum of infinity
(2/1-0.75) x 2 -2
8 x 2 -2
16 -2
14.
if this kind of question apeared only math wiz or a mechanics student wil be able to solve it correctly. (n)
 
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if this kind of question apeared only math wiz or a mechanics student wil be able to solve it correctly. (n)
Well, whenever I solve, I draw a sketch of what the question tells, this help me while solving! In Mechanics nearly every question requires drawing for me.
So, if you get stuck try sketching, myt help!
 
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wow sooo much p3 :p .. sab sir say guzar raha hai :D
a better dialogue p3 p3 every where xD. anyway in s1 heres a good one there are 9 pies to be divided between 3 people so that each person gets a odd no of pies. in how many no of ways can they be divided. i know the answerso i am posting it so u guys can solve it and others can get help. :)(y)
 
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