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Vilka [71]
3 years ago
11

Two tracking stations are on the equator 158 miles apart. A weather balloon is located on a bearing of N42°E from the western st

ation and on a bearing of N14°W from the eastern station. To the nearest tenth of a mile, how far is the balloon from the western station? *

Mathematics
2 answers:
Alinara [238K]3 years ago
7 0

Answer:

199.38

Step-by-step explanation:

To better understand the problem I leave an associated graph.

We must calculate the distance of AC, we know AB

AB = 158 miles.

Now we will apply the law of sine where:

AB / sin (° ACB) = AC / sin (° ABC)

We know the ° ABC = 14 °, the statement gives us the ° CAB = 90 ° - 38 ° = 52 °

Now assuming that within a triangle all the angles must add up to 180 °, then

° ACB = 180 ° - 52 ° - 14 ° = 114 °

Solving for AC:

AC = (AB * sin (° ABC)) / sin (° ACB)

AC = (158 * sin (14 °)) / sin (114 °)

AC = 199.38

Therefore the distance between the balloon from the western station is 199.38 miles

Alisiya [41]3 years ago
7 0

Answer:

184.9 miles

Step-by-step explanation:

The image attached will provide the necessary diagram and better explanations

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Write the slip-intercept form of the equation of the line described
kompoz [17]

Answer:

1) y=⅚x -2⅓

2) y=8/3x -5

Step-by-step explanation:

<u>Point-slope form:</u>

y=mx+c, where m is the gradient and c is the y-intercept.

Parallel lines have the same gradient.

Gradient of given line= \frac{5}{6}

Thus, m=⅚

Susbt. m=⅚ into the equation,

y= ⅚x +c

Since the line passes through the point (4, 1), (4, 1) must satisfy the equation. Thus, substitute (4, 1) into the equation to find c.

When x=4, y=1,

1= ⅚(4) +c

1 =  \frac{20}{6}  + c \\ c = 1 -  \frac{20}{6}  \\ c = 1 - 3 \frac{1}{3}  \\ c =  - 2 \frac{1}{3}

Thus the equation of the line is y =  \frac{5}{6} x - 2 \frac{1}{3}.

The gradients of perpendicular lines= -1.

Gradient of given line= -⅜

-⅜(gradient of line)= -1

gradient of line

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y =  \frac{8}{3} x + c

When x=3, y=3,

3 =  \frac{8}{3} (3) + c \\ 3 = 8 + c \\ c = 3 - 8 \\ c =  - 5

Thus the equation of the line is y =  \frac{8}{3} x - 5.

4 0
3 years ago
Help me pls I don’t under stand pls help
Elena-2011 [213]

your answer is D hope this helps and mark for brainlest

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2 years ago
1.
Alenkasestr [34]

All four choices are correct responses to the question.

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Answer:

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Step-by-step explanation:

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