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## #1 Re: Help Me ! » Find the unit tangent vector T(t) » 2012-11-18 18:38:57

i am having one idea i.e first obtain locus of above coordinate system

x^2/3  +y^2/3=16 now obtain dy/dx for this curve that comes out to be -tan(t)

now obtain equation of tangent to this curve

but what i understand that you want to apply concept of gradient in above problem but that always gives equation of normal

## #2 Re: Help Me ! » Polynomials » 2012-10-16 20:57:09

d is correct answer of this question
we know that irrational root occur in conjugate pair
we assume g(x)=(x-y)f(x)
(x-y)(x^2+ax+b)
x^3+ax^2+bx-yx^2-axy-by=x^3+px+q
x^3+(a-y)x^2+(b-ay)x-by=x^3+px+q
a=y
b-ay=p
-by=q
from here no relation will match

## #3 Re: Help Me ! » minimum value » 2012-06-16 23:32:14

please mention that a,b are positive or not

assume a,b>0
is  tending to zero at theta=pi/2-(tan^-1b/a)

## #4 Re: Help Me ! » Small doubt in function » 2012-04-24 20:20:07

it is a function because a line parallel to y axis cuts at only at one point hence it will having unique image.it represent relation also because all functions are relation also

## #5 Re: Help Me ! » Maximumvalue » 2012-04-17 20:25:38

obtain partial differential of above function w.r.t x&y equals it to be zero from here obtain value of x,y then obtain f" if it is less than zero then maxima will exist at that coordinate.

## #6 Re: Help Me ! » minimum distance » 2012-01-18 22:08:06

if any faimly of line f(x)+tF(x)=0 is given then minimum distance friom origin is (constant term)/[coef. of(x^2)+coef. of(y^2)]

since ans of above ques. =t^2 +2t +4

## #7 Re: Help Me ! » Dynamics » 2011-03-21 21:36:25

Fnet=(6i+2j)
anet={Fnet/2}=(3i+j)........Ans
Vx=V(initial)+ax*t
4+3*3=13
Vy=0+3*1=3
Vnet=Vxi+Vyj
(13i+3j).........Ans
X=X0+v(initial)*t+1/2*ax*t^2
=2+4*3+1/2*3*9
=27.5
Y=Y0+0+1/2*1*9
=-1+4.5
=3.5
="hence requried position vector=(27.5i+3.5j)".........Ans

## #8 Re: Help Me ! » When will bomb explode? » 2011-03-16 17:49:16

when material inside bomb burn then burning material creats fume inside it then by this process a situation occur when pressure inside is greater than atmosphetric pressure so it explode in many small part now small parts are aso exploded this process occur on the microscopic label

## #9 Re: Help Me ! » Sum, difference and product functions » 2011-03-16 17:37:06

i think that all plots are correct but in second plot at x=0 the slope will must be{ -infinite}

## #10 Re: Help Me ! » Line integral of a complex function » 2011-02-24 22:23:32

1.....when you obtain integration in close path then it may or may not be o
......it will be 0 if field will be coservative
.......coservative means du/dy=+or-dv/dx but it will be applicable if u is function of x only and v is function of y only
.......if it will function of x &y both then integration over close path will be o if curl of that field vector will be o

## #11 Re: Dark Discussions at Cafe Infinity » How can momentum over 4D solve restenergy of higherdimensional matter? » 2011-01-31 19:02:13

hello friend E=mc^2 fails if any material particle travell more faster than {c} "& such particle will having immaginary mass &hence not possible to exist"

MATHEMATICALY
m=m0/squrt(1-v^2/c^2)
IF......v>c  then 1-v^2/c^2<0
hence m is immaginary

## #12 Re: Dark Discussions at Cafe Infinity » Only a small black hole could obtain the density and heat of Big Bang! » 2011-01-31 18:59:06

you are wrong you see my answer i answerd in this forum

## #13 Re: Dark Discussions at Cafe Infinity » If a black hole was as hot and dense as Big bang, would it explode? » 2011-01-31 18:53:16

a black hole will create or form if
1.......a star will die
2......star will be 4to20 times more massive than sun
FRIST CONDITION WILL BE NECESSARY
so how it can be explode
obiously a blackhole is hot"because any body is black means it absoarbs the tempreature by "steafn's law"....."
there will be no doubt it is dence also FIELD=GM/R^2
if R.....> 0 then Field is tending to infinite "this R is known as critical radius"
because R is much small after destroying the planet so it is dence also as comparison of its larger mass

example sun is also a black hole

## #14 Re: Dark Discussions at Cafe Infinity » How can momentum over 4D solve restenergy of higherdimensional matter? » 2011-01-31 18:17:22

hello friend E=mc^2 fails if any material particle travell more faster than {c} "& such particle will having immaginary mass &hence not possible to exist"

MATHEMATICALY
m=m0/squrt(1-v^2/c^2)
IF......v>c  then 1-v^2/c^2<0
hence m is immaginary

## #15 Re: Help Me ! » algebra » 2011-01-30 17:03:58

p(x)=x^2-squrt2 *x+1=0 is minimal polynomial

## #16 Re: Help Me ! » Which Values make the triangle obtuse? » 2011-01-30 16:47:05

frist let k is biggest side of triangle
then for formation of triangle {sum of two smallest side will always greater than biggest side}
(13+9)>k
k<22.................(1)

let in above triangle ABC  the k is side infront of angle A

then for obtuse angle cosA<0
hence cosA=(9^2 +13^2-K^2)/2*9*13
2nd lowest statement emplies...........9^2 +13^2<k^2

on solving above inequality the accepted valu of k is greater than 15.81
hence integer values are 16 17 18 19 20 21 (total 6 integer value)

"NOW CHANGING CONDITION"

i.e 13 is biggest side
13^2>k^2+9^2
-9.38< k<9.38
but k+9>13
k>4
hence total integer valu 5 6 7 8 9
hence total no of integer value will be 11

## #17 Re: Help Me ! » Confuzzling equations » 2011-01-22 01:10:26

A bulit is fired with velocity (v=2t). It strikes the tree having resistence 5 newton. Find velocity  vs distance travell plot &total distance travell by bullet before stop as well as acceleration vs time plotl

## #18 Re: Help Me ! » Inequality » 2010-12-18 00:15:02

max\$min(3x+2y+5z)
Let  ->
A=Xi+Yj+Zk
B=3i+2j+5k
A.B=mod(A)mod(B) cos (t) "max if cos(t)=1,min if cos(t)=-1"
3x+2y+5z=squrt(x^2+y^2+z^2)*squrt(38) cos(t)
put valu of x^2+y^2+z^2=45 \$get ans

## #19 Re: Help Me ! » Inequality » 2010-12-18 00:02:35

sorry friend  in 1/(3-5cosx) you are wrong

CORRECT ANS
the denominator 3-5cosx=0 ->cosx=3/5 which is in the region [-1 1]
hence correct range is(-∞ -1/2]U [1/8 ∞)
hence you can see wht is max\$min

## #20 Re: Help Me ! » Inequality » 2010-12-09 18:25:29

what is maximum \$minimum valu of 1/(3-5cosx)

## #21 Re: Help Me ! » Inequality » 2010-12-09 18:22:45

if x,y,z  are sides of a triangle R is radius of circumcircle A is area of triangle
then prove that
log(A)+log(4)+log(R)>=3(log(x)*log(y)*log(z))^1/3

## #22 Re: Help Me ! » Inequality » 2010-12-09 18:12:36

hello friend.........
find max,min (3x+2y+5z)
if[x^2+y^2+z^2]=45

## #23 Re: Help Me ! » Inequality » 2010-12-08 19:52:05

what is natural log of squt(-1)