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3 years ago

5

From the top of a 193 foot lighthouse the angle of depression to a ship in ocean is 14° how far is the ship from the base of the

lighthouse give your answer to the nearest foot

1 answer:

Trava [24]3 years ago

4 0

Answer:

774 feet.

Step-by-step explanation:

Let x represents how far the ship is from the base of the lighthouse.

We use the tangent ratio, which involves opposite over adjacent to find x.

$\tan(14 \degree) = \frac{opposite}{adjacent}$

$\tan(14 \degree) = \frac{193}{x}$

$x = \frac{193}{ \tan(14 \degree) }$

$x = 774.08$

To the nearest whole number, the distance is 774 ft.

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Option B:

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To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

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Rewrite in terms of 'y'. This gives,

$x(y-2)=y+2\\xy-2x=y+2\\xy-y=2x+2\\y=\frac{2x+2}{x-1}$

The given function $y=\frac{2x+2}{x-1}\ne y=\frac{x+2}{x-2}$

So, option B is incorrect.

Option C:

$f(x)=\frac{x+1}{x-1}\\y=\frac{x+1}{x-1}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+1}{y-1}$

Rewrite in terms of 'y'. This gives,

$x(y-1)=y+1\\xy-x=y+1\\xy-y=x+1\\y=\frac{x+1}{x-1}$

The given function $y=\frac{x+1}{x-1}\ equals\ y=\frac{x+1}{x-1}$

So, option C is correct.

Option D:

$f(x)=\frac{x+5}{x-5}\\y=\frac{x+5}{x-5}$

To find $f^{-1}(x)$ , replace 'x' with 'y' and 'y' with 'x'. This gives,

$x=\frac{y+5}{y-5}$

Rewrite in terms of 'y'. This gives,

$x(y-5)=y+5\\xy-5x=y+5\\xy-y=5x+5\\y=\frac{5x+5}{x-1}$

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So, option D is incorrect.

Therefore, only option C is correct.

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