let a,b,c,x,y and z be complex numbers
such that :
a=((b+c)/(x−2)), b=((c+a)/(y−2)), c=((a+b)/(z−2))
if xy+yz+zx=1000 and x+y+z=2016,
find the value of xyz
A lotus plant in a pool of water is (1/2)
cubit above water level. When
propelled by air, the lotus sinks in the
pool 2 cubits away from its position.
Find the depth of water in the pool.
A monkey climbs up a slippery pole for
3 seconds and subsequently slips for 3
seconds. Its velocity at time t is given
by v (t) = 2t(3 − t) ; 0 < t < 3 and
v (t) = − (t − 3)(6 − t) for 3 < t < 6 s
in m/s. It repeats this cycle till it
reaches the height of 20 m. At what
time is its average velocity maximum?
A bird is tossing (flying to and fro)
between two cars moving towards
each other on a straight road. One car
has a speed of 18 km/h while the other
has the speed of 27 km/h. The bird
starts moving from first car towards
the other and is moving with the speed
of 36 km/h and when the two cars were
separated by 36 km. What is the total
displacement of the bird?
A line segment moves in the plane
with its end points on the coordinate
axes so that the sum of the length
of its intersect on the coordinate
axes is a constant C .
Find the locus of the mid points of
this segment .
Ans. is 8(∣x∣^3 +∣y∣^3 )=C .
Λ means power . pls. solve it.
A string is stretched and fastened to two points l apart. Motion is started
by displacing the string into the form y = (lx − x^2 ) from which it is release
at time t = 0. Find the displacement of any point on the spring at a distance
x from one end at time t.
The triangle ABC has CA = CB. P is a
point on the circumcircle between A
and B (and on the opposite side of the
line AB to C). D is the foot of the
perpendicular from C to PB. Show that
PA + PB = 2∙PD.