A plane is given by an equation x+y+2z-1=0.The distance of the plane from the origin is p. What is p?
Distance of plane from a point (a,b,c)=|(a+b+2c-1)/(√(1^2+1^2+2^2))|.Therefore p=1/(√6).
discuss the convergence of series summation for n>=1 [3n!+4^(n+1)/(3n+1)!]
The series can be broken down into sum of two series [1/(3n+1)]+[4^(n+1)/(3n+1)!],The series will converge only if both series converge. But [1/(3n+1)] diverge as seen by integral test or limit comparision test where a(n)=1/n and b(n)=[1/(3n+1)]. Therefore, c=a(n)/b(n) and c>0,so series diverge as b(n) is harmonic series which diverges
Why do we not power dc current in our houses but ac?
ac current can be stepped up which can reduce the loss of power using formula h=i^2rt, as an increase in voltage reduces the current according to the law of conservation of energy which thereby reduces the heat loss.Also, DC current cannot be stepped up as there is no change in polarity of current which does not change magnetic flux and hence no electromagnetic induction, the principle on which the transformers work