Given:
second term = 18
fifth term = 144
The nth term of a geometric sequence is:
Hence, we have:
Divide the expression for the fifth term by the expression for the second term:
Substituting the value of r into any of the expression:
Hence, the explicit rule for the sequence is:
The value of the angle subtended by the distance of the buoy from the
port is given by sine and cosine rule.
Reasons:
Location from which the ship sails = Port
The speed of the ship = 10 mph
Direction of the ship = N35°W
Location of the warning buoy = 5 miles north of the port
Required: The bearing of the warning buoy from the ship after 7.5 hours.
Solution:
The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
Where;
a = The distance between the ship and the buoy
b = The distance between the ship and the port = 75 miles
c = The distance between the buoy and the port = 5 miles
Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°
Which gives;
a = √(75² + 5² - 2 × 75 × 5 × cos(35°))
By sine rule, we have;
Therefore;
Which gives;
Similarly, we can get;
The angle subtended by the distance of the buoy from the port, <em>C</em> is therefore;
C ≈ 180° - 142.68° - 35° ≈ 2.32°
By alternate interior angles, we have;
The bearing of the warning buoy as seen from the ship is therefore;
Bearing of buoy ≈ 270° + 35° + 2.32° ≈ <u>307.35°</u>
Learn more about bearing in mathematics here: