A hospital H receives a report about a serious road accident at C. An ambulance reaches the scene by traveling 5 km north, 15 km east, then 3km north. A helicopter travels directly from H to C. Their paths intersect at X. Find the distance from the hospital to X

  10 5/8 km

Step-by-step explanation:

Name the point 8 km north of the hospital point N. Then triangle NHC is similar to triangle AHX, where A is the point 5 km north of the hospital.

This means that ...

  HX/HC = HA/HN = 5/8

  HX = (5/8)HC

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The distance HC can be found using the Pythagorean theorem. It tells you ...

  HC^2 = HN^2 +NC^2 = 8^2 +15^2 = 289

  HC = √289 = 17

so ...

  HX = (5/8)(17) = 10 5/8

The distance from the hospital to X is 10 5/8 km.

The arithmetic sequence given has a first term (a1) equal to 3 and common difference (d) equal to 4. The nth term of an arithmetic sequence is calculated through the equation,
                               an = a1 + (n - 1) x d
Substituting the known values,
                               a30 = 3 + (30 - 1) x 4 = 119
Thus, the 30th term of the sequence is 119.