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matrenka [14]
2 years ago
9

1. A line passes through the point (2, k) and (4k, 5) and has a slope of 1/2 . Find the value of k.

Mathematics
1 answer:
Doss [256]2 years ago
5 0

(\stackrel{x_1}{2}~,~\stackrel{y_1}{k})\qquad (\stackrel{x_2}{4k}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{k}}}{\underset{run} {\underset{x_2}{4k}-\underset{x_1}{2}}}~~= ~~\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}} \\\\\\ 10-2k=4k-2\implies 10=6x-2\implies 12=6k\implies \cfrac{12}{6}=k\implies 2=k

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Answer: 42.21 km

Step-by-step explanation:

We can solve this using trigonometry, since we have the following data:

\theta=32.5\° is the the angle of elevation

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x is the hypotenuse of the right triangle formed between the radar station and the airplane

Now, the trigonometric function that will be used is <u>cosine</u>:

cos\theta=\frac{d}{x} because d is the adjacent side of the right triangle

cos(32.5\°)=\frac{35.6 km}{x}

Finding x:

x=\frac{35.6 km}{cos(32.5\°)}

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