Question

for a vector v, $v_x = vcos\theta$ $v_y = vsin\theta$ $v_x^2+v_y^2 = v^2$ $\tan\theta = v_y/v_x$ question 3 (2 points) one year is 31 million, 540 thousand seconds measured to the closest ten thousand seconds. report this measurement in seconds in scientific notation with the correct uncertainty in the measurement. this question is worth two points: one point for writing the value correctly in scientific notation, and one point for identifying the correct number of zeroes in the answer.

Explanation:

Step1: Write the number in standard form

31 million, 540 thousand = 31540000

Step2: Determine the scientific - notation form

The scientific - notation is of the form \(a\times10^{n}\), where \(1\leq a<10\) and \(n\) is an integer. For 31540000, \(a = 3.154\) and \(n = 7\) since we move the decimal point 7 places to the left.

Step3: Consider the uncertainty

Measured to the closest ten - thousand, the uncertainty is \(\pm5000\). In scientific notation, \(5000=5\times 10^{3}\)

Answer:

\(3.154\times 10^{7}\pm5\times 10^{3}\)