Solve for the resultant displacement of the two vectors: A = 2.3 km at 45 degrees B = 4.8 km at 90 degrees

The resultant of the vector is 6.63 km

Explanation:

Given;

vector A = 2.3 km 45°

vector B = 4.8 km 90°

The vectors in the x - direction is given by;

Aₓ = 2.3 km Cos 45° = 1.6263 km

Bₓ = 4.8 km Cos 90° = 0

The sum of the vectors in x -direction is given by;

∑X =  1.6263 km + 0 = 1.6263 km

The vectors in the y - direction is given by;

Ay = 2.3 km Sin 45 = 1.6263 km

By = 4.8 km Sin 90° = 4.8 km

The sum of the vectors in y -direction is given by;

∑Y =  1.6263 km + 4.8 km = 6.4263 km

The resultant vector is given by;

R = √(X² + Y²)

R = √[(1.6263)² + (6.4263)²]

R = 6.63 km

Therefore, the resultant of the vector is 6.63 km

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.