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Pooja gupta 9 years ago

find the envelope of the one-parameter system of planes
3a^2x-3ay+z=a^3

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kalava hemalatha 9 years ago

how to prepare for amcat

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Pooja gupta 9 years ago

Obtain the Riccati equation associated with the equation
y' +w^2 y =0

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Pooja gupta 9 years ago

solve diffrential equation
q=-xp+p^2

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Pooja gupta 9 years ago

If the rate of change of y with respect to x is 5 and x is changing at 3 units per second, then y is changing faster than x.
true or false??

Reply Like? Yes (1) | No

Rishu 9 years ago

true

dy/dx=5
dx/dt=3

dx=3dt
dy/(3dt)=5
dy/dt=15

so x changes 3 times in one second and y changes 15 times in one second

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Pooja gupta 9 years ago

If y = f ( x )=( lx + m )/( nx - l ) then show
that f ( y )= x ??

Reply Like? Yes (1) | No

neha gupta 9 years ago

f(x) = (lx + m)/(nx-l)
y = f(x)
so
f(y) = f(f(x))
= f((lx + m)/(nx-l))
=( l(lx + m)/(nx-l) + m) / (n(lx + m)/(nx-l))x-l)
=( l(lx+m) + m(nx-l)) / (n(lx + m) - l(nx-l))
= (l^2 x +ml +mnx - ml) / (nlx + mn - nlx + l^2)
= (l^2 x +mnx) / (mn + l^2)
= x (l^2 +mn) / (mn + l^2)
= x
thus f(y) = x

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