Astreet light is mounted at the top of a 15-ft-tall pole. a man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. how fast is the tip of his shadow moving when he is 30 ft from the pole?

2.67 ft/s

Explanation:

1) The diagram with the triangle that represents the situation is in the image attached.

2) Similarity properties

(x + y) / 15 = y/6

⇒ 6(x+y) = 15y

⇒ 6x + 6y = 15y

⇒ 6x = 15y - 6y

⇒ 6x = 9y

⇒ y = 6x / 9

⇒ y = 2x / 3

3) Velocity is the derivative respecto to time. Then, find the derivative respect to time, t, on both sides

dy/dt = (2/3)dx/dt

4) The statement tells v = dx/dt = 4 ft/s

⇒ dy/dt = (2/3) 4 ft/s = (8/3)m/s ≈ 2.67 ft/s

Notice that this speed is constant, it does not depends upon the distance of 30 ft.

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.