Let T be the set of all triangles in a plane with R is a relation in T given by R=`{(T_(1),T_(2)): T_(2)` is congruent to `T_(2)` and `T_(1), T_(2) in T)`. Show that R is an equivalence relation.

Find the slope of the tangent to x = t^2 and y = 2t at t = 1.

Show that the relation R, defined in the set of A all triangles as R = {(T_(1), T_(2)):T_(1) , is similar to T_(2) }, is equivalence relation. Consider three right angle triangles T_(1) , with sides 3, 4, 5, T_(2) , with sides 5, 12, 13 and T_(3) with sides 6, 8, 10, which triangle among T_(1), T_(2) , and T_(3) are related?

Write the Arrhenius equation for the rate constants K_(1) and K_(2) at temperature T_(1) and T_(2) in terms of activation energy E_a .

Which order of reaction obeys the relation t_(1//2)=1//ka :

For a reaction of II order kinetics, t_(1//_2) is:

Find the equation of tangent to the curve x=sin 3t,y=cos 2t at t =pi/4

If cosx=sqrt(1/(1+t^2)),sin y=(2t)/(1+t^2) then show that (dy)/(dx) is independent of t.