Consider a mass m moving in a frictionless plane that slopes at an angle a with the horizontal. write down the lagrangian in terms of coordinates x, measured horizontally across the slope, and y, measured down the slope. (treat the system as two-dimensional, but include the gravitational potential energy.) find the two lagrange equations and show that they are what you should have expected.

chemical properties of thing

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.