NASA is sending a probe to Alpha Centauri and then to Sirius. A problem with the probe is noticed while it is at Alpha Centauri, so it must go back to Erth before going to Sirius. Alpha Centauri is 4.3 light-years away from Earth and Sirius is 8.6 light-years away. The probe is traveling at 18.03 km/s, there are 1.58125 x 10-5 light-years in one astronomical unit. How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?

Time = 9.0252 *10^12 s

Step-by-step explanation:

Given:

- The distance from Earth to Alpha Centauri = 4.3 light years

- The distance from Earth to Sirius = 8.6 light years

- Speed of the probe is V = 18.03 km/s

- 1 AU = 1.58125 x 10-5 light-years

Find:

How long will the probe have been traveling from when it first leaves Earth to when it arrives at Sirius?

Solution:

- We will track probe for each destination it reaches one by one:

                       Earth > Alpha Centauri d_1 = 4.3 light years

                       Alpha Centauri > Earth d_2 =4.3 light years

                       Earth > Sirius                  d_3 = 8.6 light years  

                       Total distance                       D    = 17.2 light years.

- Now we know the total distance traveled by the probe is D. We will convert the distance into km SI units:

                          1 AU    > 1.58125 x 10-5 light-years

                          x AU   > 17.2 light years.

- Using direct proportions

                           x = 17.2 / (1.58125 x 10-5) = 1087747.036 AU

Also,

                          1 AU  > 149597870700 m

                           1087747.036 AU  >    D m

- Using direct proportions

                            D =   1087747.036*149597870700  = 1.62725*10^17 m

- Now use the speed - distance - time formula to compute the total time taken:

                            Time = Distance traveled (D) / V

                            Time = 1.62725*10^17 / 18.03*10^3    

              Time = 9.0252 *10^12 s

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step-by-step explanation:

the following points can be visualized easily from the graph

x= cost per bracelet

number of bracelets * x + shipping charge = total cost

so

9x+9=72