Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the se
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The value of the angle subtended by the distance of the buoy from the
port is given by sine and cosine rule.
- The bearing of the buoy from the is approximately <u>307.35°</u>
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:
Answer:
The probability of getting two of the same color is 61/121 or about 50.41%.
Step-by-step explanation:
The bag is filled with five blue marbles and six red marbles.
And we want to find the probability of getting two of the same color.
If we're getting two of the same color, this means that we are either getting Red - Red or Blue - Blue.
In other words, we can find the independent probability of each case and add the probabilities together*.
The probability of getting a red marble first is:
Since the marble is replaced, the probability of getting another red is:
The probability of getting a blue marble first is:
And the probability of getting another blue is:
So, the probability of getting two of the same color is:
*Note:
We can only add the probabilities together because the event is mutually exclusive. That is, a red marble is a red marble and a blue marble is a blue marble: a marble cannot be both red and blue simultaneously.