MATHEMATICS HIGH SCHOOL

A rotating light on top of a lighthouse sends outrays of light in opposite directions. As the beacon
rotates, the ray at an angle 8 makes a spot of light
that moves along the shore. The lighthouse is
located 500 m from the shoreline and makes
one complete rotation every 2 min.
Determine the equation that expresses the
distance, d, in metres, as a function
of time, t, in minutes.

Answers

Answer 1

Answer:

Answer:

$\sf d = 500 \cdot (\theta(t))$

Step-by-step explanation:

The equation can be derived using the following trigonometric identity:

That is:

$\sf tan(\theta) =( opposite )/( adjacent)$

In this case, the opposite side is the distance from the lighthouse to the shoreline and the adjacent side is the distance from the lighthouse to the spot of light on the shoreline (500m)

The angle is equal to the angle of the light beam.

It is changeable according to the time. so,

$\sf \theta \textsf{ will be } \theta t$

Substituting these values into the trigonometric identity gives us the following equation:

$\sf tan(\theta t) = (d)/(500)$

Solving for d gives us the following equation:

$\sf d = 500 \cdot (\theta(t))$

Therefore, the equation to express the distance, d, in metres, as a function of time, t, in minutes is:

$\sf d = 500 \cdot (\theta(t))$

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Answers

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Answers

Answer:

(0, -2) and (1, 1) both work in this system of equations.

Step-by-step explanation:

Happy to help! The best way to find if it is a solution is to look for those points on the graph. When we graph the point, it needs to fall in an area where both lines or shaded or on a solid line.

Look carefully and see if you can find points like these!

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Therefore, (0, -2) and (1, 1) both work in this system of equations.

Good luck!

Answer:

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Step-by-step explanation:

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