Answer the questions in RED and follow the steps in BLUE.
1. Go to schmucker.wikispaces.com in a separate window. On the precalc page, click on the “Spring Simulation” link at the top.
2. Press the start button and what the spring’s motion and how it follows a trig graph. Which trig graph does this simulation represent?
3. Press the reset button. Now change the “Spring Constant” value. Only add small increments of 5 because it will only change within certain limits. Change it at least twice and press start each time to see the change. What impact does this value have on the graph? What do you think a spring constant is as you watch the graph and why does it impact the graph this way?
4. Press the reset button. Change the spring constant back to 20. Now change the “Mass” value. Only add small increments of 5 because it will only change within certain limits. Change it at least twice and press start each time to see the change. What impact does this value have on the graph? Why do you think mass changes the graph this way?
5. Neither of these values change the amplitude. What do you think would change the amplitude of the curve? (Hint: think about how you would get the spring started)
Follow the steps and answer the BLUE questions.
1. Go to the following site: http://mathplotter.lawrenceville.org/mathplotter/MSP/resources/NIntegrals/NumericalIntegration
2. Type in a function of your choice in the upper left hand corner. Change your x and y axis accordingly. Press “Graph.” Put the number of divisions as 4.
3. Change the Scroll down “Draw using” to Left Hand Sum, then hit graph. Change it to Right Hand Sum and hit graph, and then Midpoint Sum and graph. Again, what is the difference between the three sums?
4. Look below the graph at the values and analyze the Left Hand Sum, Right Hand Sum, Midpoint Sum, and Exact Value. Which value is closest to the exact value? Explain why that makes sense.
4. Leave the sum as the Midpoint option and then change the rectangles/number of divisions to 5, then 10, then 40, then 100. Make sure you press graph after each one to see the change. Look below the graph at the calculations. What happens to the Midpoint Value as the number of rectangles increase?
Part I:
In the Law of Sines section, you have been using the law to solve oblique triangles. Can the law of sines be used to solve right triangles? Use the example above and explain why or why not. If you can use the law of sines, which method would you use if you had a choice in solving a right triangle? Explain why.
Part II:
Look at the figure above. Find sinB in terms a, b, c and/or h (meaning the fraction). Find sinC in terms of a, b, c and/or h (meaning the fractions). State both of your equations.
Solve both equations for h. Based on these two equations, show and explain how the law of sines was derived.
Please answer the following questions below. Please remember to HIGHLIGHT and COPY your answers before you submit your answers. You may want to type the answers in word and then paste them into the blog. You will not lose them this way. Each answer must be at least 5 complete sentences.
a. Describe the end behavior of the graph from the activity and explain why the characteristic is or is not appropriate for the AIDS virus.
b. Discuss the inconsistencies, assumptions and problems with the simulation.
c. How do you think AIDS prevention programs and awareness change the graph? Do you think these programs change the graph in reality?
Use the equation above and answer all questions. Remember to use your blog name and be THOROUGH!
1. What must you do first to graph this function?
2. What are your next steps? Why are these steps important and why are these parts of the graph necessary to find?
3. Describe the process of graphing after completing step 2.
4. In general, what will your graph look like?
5. Once you finish the questions, go to Microsoft word, make the graph by inserting shapes and drop it into my stu_drop folder. Document name: ratlfunc.lastname
Look at the graph below and then answer the questions.
1. Describe what the velocity graph would look like and how you know.
2. Describe what the acceleration graph would look like and how you know.
*Remember what the word derivative means. Think about the definition.
*Use your blog name and remember to be thorough.
3. Lastly, in word actually create the velocity and acceleration graphs you described, and drop the document in the stu_drop folder. Name the document derivative.lastname.
If we were to fill a glass with water at a constant rate (for example, 1 cubic inch per minute), we could graph the height of the water in the glass as time goes by. Suppose we fill the three glasses below in such a manner. Match up each glass with the graph that best describes the height of the water in the glass over time.
Please describe your matching answers and analysis. Your analysis should be thorough and complete and in complete sentences.
Mathforum.com Problem of the Week
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