A ship from Port travels fot 60km on the bearing of 129°.It continues to travel and changes direction for another 50km on a bearing of 080°

The ship is approximately 100 km to the Port.

Step-by-step explanation:

The sketch to the question gives a triangle with two sides and an included angle. Let the distance from the Port to the stopping point of the ship be represented by c. It can be determined by the application of cosine rule. Cosine rule states that:

= + -2ab Cos C

a = 50 km

b = 60 km

C = 51 + 80 =

So that;

= + -2(50 x 60) Cos

   = 2500 + 3600 -6000 x -0.6561

   =  6100 + 3936.6

= 10036.6

c =

  = 100.183

c = 100.18 km

Thus, the ship is approximately 100 km to the Port.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."