Question

ques

Answer 1

Oh really???

Answer 2

A polygon is continuously being converted to a circle by adding sides to it at a rate of \[\frac{dn}{dt}\]If the rate of increase in sides is proportional to \[1+n^2\]
If we start with a triangle and time taken for a hexagon is 1.25seconds.
Then,
(i)Write the general solution of the differential equation of the problem.
(ii)Find the constant of proportionality.
(iii)What will be the value of n for a circle?
(iv)How long(approx.) will it take to convert it to a circle?

Answer 3

dn/dt= k(1+n^2)
dn/(1+n^2) = kdt
integrate
tan^-1( n) = k(t) use the limits so that another constant wont appear n from 3 to 6 and t from 0 to 1.25 sec
first and second part solved
no. of sides in circles can be considered as infinite so upper limit infinite tan^-1 infinite = pi/2 , lower limit 3 and time from 0 to t
evaluate t
third and fourth part solved

Answer 4

Nice!