Question

the equation below models the average velocity, v, needed for an object to travel from earth to a distant star in t number of hours. given that the distance to the star is approximately 4.1343 × 10¹³ kilometers, approximately how many hours would it take a spacecraft launched from earth to reach the star at an average velocity of 100,000 km/hr? v = 4.1343×10¹³ / t a 41,343 b 31,343,000 c 41,343,000

Explanation:

Step1: Solve for \( t \)

Given \( V=\frac{4.1343\times10^{13}}{t} \), and \( V = 100000\). Then \( t=\frac{4.1343\times10^{13}}{100000}\).

Step2: Simplify the expression

Since \( 100000=10^{5}\), then \( t=\frac{4.1343\times10^{13}}{10^{5}}\).
Using the rule of exponents \( \frac{a^{m}}{a^{n}}=a^{m - n}\), we have \( t = 4.1343\times10^{13-5}=4.1343\times10^{8}\).
\(4.1343\times10^{8}=413430000\).

Answer:

C. \(41,343,000\)