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Complete Question
A boat sails 4km on a bearing of 038 degree and then 5km on a bearing of 067 degree.(a)how far is the boat from its starting point.(b) calculate the bearing of the boat from its starting point
Answer:
a)8.717km
b) 54.146°
Step-by-step explanation:
(a)how far is the boat from its starting point.
We solve this question using resultant vectors
= (Rcos θ, Rsinθ + Rcos θ, Rsinθ)
Where
Rcos θ = x
Rsinθ = y
= (4cos38,4sin38) + (5cos67,5sin67)
= (3.152, 2.4626) + (1.9536, 4.6025)
= (5.1056, 7.065)
x = 5.1056
y = 7.065
Distance = √x² + y²
= √(5.1056²+ 7.065²)
= √75.98137636
= √8.7167296826
Approximately = 8.717 km
Therefore, the boat is 8.717km its starting point.
(b)calculate the bearing of the boat from its starting point.
The bearing of the boat is calculated using
tan θ = y/x
tan θ = 7.065/5.1056
θ = arc tan (7.065/5.1056)
= 54.145828196°
θ ≈ 54.146°
8/5 is rational. It is expressed as a ratio of two integers.
√4 = 2 = 2/1 . This is rational because it expressed as ratio of two integers.
√64 = 8. This is rational because it expressed as ratio of two integers.
√10 = 3.16227..... The decimal part does not end and it is irrational because it can not be expressed as ratio of two integers.
Therefore √10 is irrational.
Problem 1
<h3>Answer: choice B) They are supplementary angles</h3>
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Explanation:
The two angles combine to form a straight angle (which is 180 degrees). Another term for these angles is "linear pair" since they form a straight line.
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Problem 2
<h3>Answer: choice B) x = 7</h3>
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Explanation:
The diagonal is never used in this problem. For any rhombus, the four exterior sides are always the same length.
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Problem 3
<h3>Answer: Choice D) 62 degrees</h3>
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Explanation:
We use the angle addition postulate. This allows us to combine angles BAC and CAD to form angle BAD.
(angle BAC)+(angle CAD) = angle BAD
30 + x = 92
x = 92-30
x = 62
angle CAD = 62
Answer:
The rate of change: 1/5
Initial value: (0,-1)
Step-by-step explanation:
The rate of change is easily 5/25, we just have to simplify it to 1/5.
To get the intial value, just subtract (2,9) by the rate of change twice.
