The linear density of a string decreases by 1/4 when it is stretched. what happens to the speed of a wave on the string?

The speed doubles.

Explanation:

The speed of a wave in a string is:

v = √(T / ρ)

where T is the tension and ρ is the linear density (mass per length).

If T is held constant, and ρ decreases by 1/4, then:

v = √(T / (ρ/4))

v = √(4T / ρ)

v = 2√(T / ρ)

The speed doubles.

powerful computers now, not then

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.