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Arisa [49]
3 years ago
7

An airplane is flying on a bearing of 265° at 420 mph. a wind is blowing with a bearing of 210° at 30 mph. find the actual speed

and direction of the plane.
Mathematics
1 answer:
photoshop1234 [79]3 years ago
8 0
In both cases, y and x components are solved and added. The resulting hypotenuse is then computed and its direction calculated.

Airplane:
Ф = 270 - 265 = 5°
Hypotenuse, h = 420 mph
y component = 420 Sin Ф = 420 Sin 5 = 36.61 mph
x component = 420 Cos Ф = 420 Cos 5 = 418.40 mph

Wind
Ф = 270 -210 = 60°
Hypotenuse, h = 30 mph
y component = 30 Sin 60 = 25.98 mph
x component = 30 Cos 60 = 15 mph

Total y = 36.61+25.98 = 62.59 mph
Total x = 418.40+15 = 433.40 mph

Resulting speed of airplane = Sqrt (y^2+x^2) = Sqrt (62.59^2+433.40^2) = 437.9 mph
Direction = 270 -[tan^-1 (y/x)] = 270 -[tan^-1(62.59/433.40)] = 261.78°
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3 0
3 years ago
The manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour. (a-1) At α = .05 i
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Answer:

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

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Step-by-step explanation:

<u><em>Explanation</em></u>:-

Given sample size 'n' =16

Given the manufacturer of an airport baggage scanning machine claims it can handle an average of 560 bags per hour.

mean of the Population 'μ' = 560

Mean of the sample Χ⁻ = 538

sample standard deviation' S' = 50

<em><u>Null hypothesis</u></em><em>:H₀:μ > 560</em>

<em><u>Alternative Hypothesis</u></em><em>:H₁ : :μ < 560 (left tailed test)</em>

<em>Test statistic</em>

   t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }

  t = \frac{538-560 }{\frac{50}{\sqrt{16} } } = -1.76

|t| = |-1.76| = 1.76

<em>Degrees of freedom </em>

<em>γ = n-1 =16-1 =15</em>

t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } =t_{0.025} =2.131

<em><u>Conclusion</u></em>:-

The calculated value t = 1.76 < 2.131 at 0.05 level of significance

Null hypothesis is accepted

The manufacturer’s claim is greater than 560 bags per hour

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