You have a (disk-shaped) grindstone with a mass of 100 kg and a radius of 0.32 m. initially, it is turning at 150 rpm. you press a steel axe head against the grindstone with a radial force of 40 n to sharpen it. calculate the torque acting on it.

T = 12.8 N*m

Explanation:

For calculate the torque we only have to follow the next equation:

T = FRd

where R is the radius of the disk , F the force to sharpen the steel axe and d is the lever arm

In this case the lever arm is equal to 1 because the force is  exercised radially the d, So:

T = FRd

T = 40N(0.32 m)( 1 )

T = 12.8 N*m  

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.