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irga5000 [103]
3 years ago
8

Solve this equation, and show work. worth 40 points.

Mathematics
1 answer:
ioda3 years ago
7 0

Answer:

r=-3/5=-0.6

Step-by-step explanation:

We have the equation:

6^{-3r}=6^{2r+3}

Since their bases are the same, the exponents must be equivalent. So:

-3r=2r+3

Solve for r, subtract 2r from both sides:

-5r=3

Divide both sides by -5:

r=-3/5=-0.6

So, the value of r is -3/5.

And we're done!

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The boat's travel from when it was first noticed until it stopped is 554.89 ft.

<h3>What is trigonometry?</h3>

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly.

From the given information we can draw a right-angle triangle.

14°52' = 14 + 0.86 = 14.86 degree

45°10' = 45 + 0.16 = 45.16 degree

In the right-angle triangle ACD

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AC = 753.772 ft

In the right-angle triangle DBC:

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AB = AC - CB

AB =  753.772 ft - 198.886 ft

AB = 554.886 ≈ 554.89 ft

Thus, the boat's travel from when it was first noticed until it stopped is 554.89 ft.

Learn more about trigonometry here:

brainly.com/question/26719838

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