During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 33.5 rad/s. Find the angular displacement of the tub during a spin of 90.7 s, expressed both in radians and in revolutions.

3038.45 in radians and

483.52 in revolutions

The angular velocity (ω) of a rotating body is the time (t) rate of change in the angular displacement (θ) of the body. i.e

ω = θ / t;          (i)

The following are given in the question;

ω = 33.5rad/s

t = 90.7s

Substitute these values into equation (i) as follows;

33.5 = θ / 90.7

Solve for θ;

θ = 33.5 x 90.7

θ = 3038.45 rad

Convert the value of the displacement from radians (rad) to revolutions (rev)

Remember that;

2π rads = 1 rev

=> 3038.45 rads = (3038.45 / 2π) rev

Take π = 3.142

=> 3038.45 rads = (3038.45 / (2 x 3.142)) rev

=> 3038.45 rads = 483.52 revs

Therefore the angular displacement of the tub during a spin of 90.7s is 3038.45 in radians and 483.52 in revolutions

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.