Prove the relation `N(t)=N_0e^(-lamdat)`

Taking the price of an article as (p) , their number as (n) and the total price as (t) , in what all ways can we write the relations between (p), (n) and (t) ?

What is the effect of temperature on the reaction? N 2 ( g ) + 3 H 2 ( g ) ↔ 2 N H 3 ( g ) + H e a t

Prove by the mathematical induction that the rule of exponents (ab)^n=a^nb^n .

Prove that the function f(x)=x^n is continuous at x=n, where n is a positive integer.

Prove that ""^(n)C_(0)""^(n)C_(0)-^(n+1)C_(1) ""^(n)C_(1)+^(n+2)C_(2)""^(n)C_(2)....=(-1)^(n)

If alpha and beta are the roots of x^2 - 2x + 4 = 0 , Prove that alpha^n+beta^n = 2^(n+1) cos((npi)/3)

Prove that overset(n) underset(r=0)Sigma^(n)C_(r) sin rx cos (n-r)x=2^(n-1) sin (nx) .

If one root of the quadratic equation ax^(2)+bx+c= 0 is equal to the nth power of the order, then prove that (ac^(n))^((1)/(n+1)) + (a^(n)c)^((1)/(n+1))=-b