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Chapter 14: Q19. (page 767)

Find the amplitude if it exists and period of the function y=15sin胃 and then graph the function.

Short Answer

Expert verified

The amplitude of y=15sin胃is 15.

The period of y=15sin胃 is 2蟺.

Step by step solution

01

Step 1. Write down the given information.

The given function is y=15sin胃.

02

Step 2. Concept used.

A function of the form y=asinbxandy=acosbx has amplitude of a and period 360掳bor2蟺b.

03

Step 3. Evaluating amplitude and period of the given function.

With the help of concept stated above, the amplitude and period of the function is evaluated as:

The amplitude of y=15sin胃is 15=15.

The period of y=15sin胃 is 2蟺1=2蟺.

04

Step 4. Sketch the graph for the function.

The graph for the function y=15sin胃 is shown below.

05

Step 5. Conclusion.

The amplitude of y=15sin胃is 15.

The period of y=15sin胃 is 2蟺.

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BOATING

For Exercises 39-41, use the following information.

A marker buoy off the coast of Gulfport, Mississippi, bobs up and down with the

waves. The distance between the highest and lowest point is 4 feet. The buoy moves

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For Exercises 39-41, use the following information.

A marker buoy off the coast of Gulfport, Mississippi, bobs up and down with thewaves. The distance between the highest and lowest point is 4 feet. The buoy movesfrom its highest point to its lowest point and back to its highest point every 10 seconds.

What is the height of the buoy after 12 seconds?
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