How to calculate a magnitude ​

1.) Determine the components of the vector. Every vector can be numerically represented in the Cartesian coordinate system with a horizontal (x-axis) and vertical (y-axis) component. It is written as an order pair

v = < x, y>

2.) Draw a vector triangle. When you draw the horizontal and vertical components, you end up with a right triangle. The magnitude of the vector is equal to the hypotenuse of the triangle so you can use the Pythagorean theorem to calculate it.

3.) Rearrange the Pythagorean theorem to calculate the magnitude. The Pythagorean theorem is

A2 + B2 = C2.

“A” and “B” are the horizontal and vertical components of the triangle while “C” is the hypotenuse. Since the vector is the hypotenuse you want to solve for “C”.

4.) Solve for the magnitude. Using the equation above, you can plug in the numbers of the ordered pair of the vector to solve for the magnitude.

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.