Question

15 multiple choice 2 points at noon on a certain day, train a is 19 miles east and 16 miles north of the depot. at the same time, train b is 11 miles west and 13 miles south of the depot. find the distance between trains. (round your answer to the nearest tenth of a mile) 42.0 mi 42.3 mi 41.7 mi 42.6 mi

Explanation:

Step1: Determine the coordinates

Let the depot be at the origin \((0,0)\).
For Train A: \(x_1 = 19\), \(y_1=16\) (since it's east and north).
For Train B: \(x_2=- 11\) (west), \(y_2 = - 13\) (south).

Step2: Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values:
\(x_2 - x_1=-11 - 19=-30\)
\(y_2 - y_1=-13 - 16=-29\)
\(d=\sqrt{(-30)^2+(-29)^2}=\sqrt{900 + 841}=\sqrt{1741}\)

Step3: Calculate the square - root

\(\sqrt{1741}\approx41.7\)

Answer:

41.7 mi