Why is the efficiency of a machine always less than 100 percent

Explanation :

The efficiency of a machine is always less than 100 %. This is because some of the energy gets lost in the form of heat energy, sound energy and frictional energy.

Mathematically it is defined as :

Where,

is the efficiency

is output work

is input work

Hence, this is the required explanation.

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.