There's no way to begin until we know the value of ' i ' .
If ' i ' doesn't represent √-1 , then we can stop here
and discard the question as unanswerable.
If ' i ' is the famous √-1 , then here's how i⁵⁰ can be simplified:
Notice the following:
-- The 1st power of i is √-1 .
-- The 2nd power of i is (√-1)² = -1
-- The 3rd power of i is -√-1
-- The 4th power of i is (-√-1)·(√-1) = -(-1) = 1 .
-- Every 4 powers of ' i ' brings you back to ' 1 '.
So from the exponent of 50, you can knock out
the largest possible multiple of 4 , and evaluate
what's left.
50 = 48 + 2
i⁵⁰ = i² = -1 .
The arrangement of the Eastern and Western lighthouses and the position of the boat are as shown in the attached diagram.
Using sine rule,
28/Sin 37 = 40/Sin B => Sin B = (40 Sin 37)/28 = 0.8597 => B = Sin ^-1(0.8597) = 59.287°
Therefore,
Angle E = 180 - (37+59.287) = 83.713°
Using the sine rule again;
BW/Sin E = 28/Sin 37 => BW = (28 Sin 83.713)/Sin 37 = 46.246 ≈ 46.27 miles.
The boat is 46.27 miles from the western lighthouse. The correct answer is A.
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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Answer:
Step-by-step explanation:
<em>See attached diagram (not to scale). </em>
<em>All given details reflected.</em>
a) <u>Find the measure of XZ using the law of cosines:</u>
- y = √(5² + 3² - 2*5*3*cos 135°) = 7 km (rounded)
b) <u>Now using the law of sines find the measure of angle X:</u>
- 7 / sin 135° = 5 / sin X
- sin X = 5 sin 135° / 7
- m∠X = arcsin (5 sin 135° / 7 ) = 28° (rounded)
<u>The bearing of Z from X is:</u>