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Amiraneli [1.4K]
3 years ago
12

A ship travels 62 km on a bearing of 12 degrees, and then travels on a bearing of 102 degrees for 111 km. Find the distance from

the starting point to the end of the trip, to the nearest kilometer. Show your work.

Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0
A bearing is an angle measured from the North.

The diagram should be something like that given above. (Note that the angles may not be measured accurately).

The diagram is drawn as follows:
1. The ship travels on a bearing of 12 degrees from the North line first so measure 12 degrees from the North line.
2. Then from that point, after it travels 62 km, the ship goes on a bearing of 102 degrees so draw another imaginary north line, and measure 102 degrees from it.

The diagram now takes shape of a triangle. Use the cosine rule to find the missing side (marked x km). Here is how I do the cosine rule:

First find the missing angle at the top of the triangle: 180 - 102 = 78 degrees. (Angles on a straight line add up to 180 degrees)

So, remember this formula:

Suppose the missing side is: c^2.

c^2 = a^2 + b^2 - (2ab cosC)

If you look at the diagram above, the angle C and the sides a, b, and c have been marked.

Use the formula given above and find the side c (that's the question you have been asked).

c^2 = 62^2 + 111^2 - (2(62)(111) cos 78)

c^2 = ANS (a very long number - better if you don't round off a number in the middle of an equation)

c = square root of ANS (following the rules of Algebra)

c = 115.34 km or simply 115 km

So the distance between the starting point to the end of the trip is 115 km.

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2 years ago
The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x)= 2/x^3 for x
natulia [17]

Answer:

a) 0.96

b) 0.016

c) 0.018

d) 0.982

e) x = 2

Step-by-step explanation:

We are given with the Probability density function f(x)= 2/x^3 where x > 1.

<em>Firstly we will calculate the general probability that of P(a < X < b) </em>

       P(a < X < b) =  \int_{a}^{b} \frac{2}{x^{3}} dx = 2\int_{a}^{b} x^{-3} dx

                            = 2[ \frac{x^{-3+1} }{-3+1}]^{b}_a   dx    { Because \int_{a}^{b} x^{n} dx = [ \frac{x^{n+1} }{n+1}]^{b}_a }

                            = 2[ \frac{x^{-2} }{-2}]^{b}_a = \frac{2}{-2} [ x^{-2} ]^{b}_a

                            = -1 [ b^{-2} - a^{-2}  ] = \frac{1}{a^{2} } - \frac{1}{b^{2} }

a) Now P(X < 5) = P(1 < X < 5)  {because x > 1 }

     Comparing with general probability we get,

     P(1 < X < 5) = \frac{1}{1^{2} } - \frac{1}{5^{2} } = 1 - \frac{1}{25} = 0.96 .

b) P(X > 8) = P(8 < X < ∞) = 1/8^{2} - 1/∞ = 1/64 - 0 = 0.016

c) P(6 < X < 10) = \frac{1}{6^{2} } - \frac{1}{10^{2} } = \frac{1}{36} - \frac{1}{100 } = 0.018 .

d) P(x < 6 or X > 10) = P(1 < X < 6) + P(10 < X < ∞)

                                = (\frac{1}{1^{2} } - \frac{1}{6^{2} }) + (1/10^{2} - 1/∞) = 1 - 1/36 + 1/100 + 0 = 0.982

e) We have to find x such that P(X < x) = 0.75 ;

               ⇒  P(1 < X < x) = 0.75

               ⇒  \frac{1}{1^{2} } - \frac{1}{x^{2} } = 0.75

               ⇒  \frac{1} {x^{2} } = 1 - 0.75 = 0.25

               ⇒  x^{2} = \frac{1}{0.25}   ⇒ x^{2} = 4 ⇒ x = 2  

Therefore, value of x such that P(X < x) = 0.75 is 2.

8 0
2 years ago
Solve the following problems. Choose the letter of the correct answer. (Show your complete solutions.)
motikmotik

:1

i didnt understand the question because of my English sorry

:2

we all know that the total of degrees is 180 so 70+70=140

180-140=40

so the answer is 40

3:

we have a figure with 4 angle so the total of degrees is 360 so the answer is 126

4:

the answer most be 50 becuse we have a Special degree witch always equal 90 if we have recatngle so

x+40=90

X=50 the answer and if you want to try again choose the second one

2x-10=90

2x=100

X=50 same answe you see

5:

in this quastion i searched and find alot of answers any way

its should be 7 or 3 but the correct answer in my opinion its 7

its shows in the picture i sent hopefully its helpful to you i will try to translate the first quastion and sent it to you

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If it costs $0.15 per square inch for the cardboard label, then what is the cost for plan B?
IceJOKER [234]

Answer:

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Step-by-step explanation:

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What is the value of x​
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Answer:

68

Step-by-step explanation:

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