Follow instructions for LABS -as outlined in the syllabus (about neatness, organization and the like)
We spoke in class how circle may be defined by either its center and its radius, a point and its center (the distance between them implies a radius) or alternatively by a system of three points that mark out the circle's edge. Three points may be used to find first the center and then the equation of the circle whose edge they are on by using a combination of the perpendicular bisectors of the chords and the distance formula. The following instructions will guide you through a process that will lead you to the circle I took your points from. As you go through this process you will have to print off certain results you get using the equation grapher program on green globs. There are a couple things you need to know.
GREEN GLOBS is installed on all the computers in the computer lab. When you double click on it where it is found in the upper left hand corner of the desk top, it will open the program which actually houses a number of other programs in the one package. The one you will need of for this assignment is the equation grapher. Open up that program by clicking programs and then clicking equation grapher. You might want to read first how to write equations before actually using it for your lab. You'll find "How to write equations" in the Equation Grapher menu along with the various windows sizes available for graphing equations on. You'll use (-10,-8) to (10,8)
To use it for your lab, you will type in and graph various equations that you have figured out by hand in the steps below. You will do this to verify that you are working through them properly. if you are not it will hopefully become apparent to you quickly.
There is a little problem with the new version of green globs in that it does not have a print screen command under file options and so you will have to perform the following actions to show me your results.
To print the results:
1) open a word documen and change the page orientation to portrait
2) type in your name and the date along with the title geometry lab
3) go to the green globs screen that you are trying to print and once its on your screen and ready
4) hit the Print Screen/SysRq key that is in the top row of the keyboard. This key takes a screen shot of your work which you can then paste [CTRL-V] into your open word document.
5)Go back to your word document and paste it in sizing it appropriately to fill the space. You can also mess with the zoom stuff before taking the screenshot but it shouldn't be necessary. If you keep pasting to the same document you can save it all as one file.
Okay, Now the lab. A lot of this you can do ahead without using the Green GLobs equation grapher tool. In fact you could do the whole thing and then go graph it, but if you made a mistake that mistake would not be revealed until you the end and that's never any fun.
THe Directions
1. In class you were given or choose three points (__, __) , (__, __), and (__, __). In the order that you chose them call them points A, B and C (as this allows me to simplify my directions) and on a graph paper you will include with your results and calculations mark those points and connect them to make the triangle ABC.
2. Using the midpoint formula, find the midpoint of each side of the triangle ( side AB, side BC, and side AC) showing the necessary calculations and adding each midpoint to your graph.
3. Find the slope and equation of the line containing each side of the triangle showing all those calculations.
3b. Use the green globs equation grapher to check your results graphed together make the correct triangle. Print out your result, write in the scale if not shown and labeling the points.
4. Using the previous two results write the equation of the perpendicularbisector for each side of the triangle. That is to say find the equation of the line through the midpoint that is perpendicular to each side of the triangle.
4b. Graph these along with your answers from 3b with the green globs grapher to demonstrate that they do cut each side in half at a right angle. (also if done correctly they should all meet in a single point). You should do this before you proceed further.
5. The point of intersection between the perpendicular bisectors of the triangle is called the circumcenter. Find it by using substitution or elimination method to identify the coordinates of the point of intersection for two of your perp. bisectors.
5b. Check your answer by plugging it into the remaining equation. If you have performed all parts correctly thus far, The resulting coordinate from the previous step should work in your remaining perp. bisector's equation. (you may also do an optional check using your graphing calculator by using 2nd trace (CALC) #5 intersection with two of the equations).
6. Almost done, we've found the center of the circle. Use the distance formula with the center and one of the points you started with to find the radius.
7. Write the equation of the circle using the radius you found and the circumcenter as the center. Check that each point substituted into the equation as a (x, y) validates your result.
Now Perform the following two graphical checks. I'd have you do both at once but I believe Green Globs only supports 6 equations at a time in the Equation graphing program.
7b. Using the Green Globs equation grapher, input all the equations for the sides again from question 3 then input your equation for the circle. If performed correctly. Your circle should cross through each corner of the triangle. Print this off and include it in your results.
7c. Again using the equation grapher, input the three equations you found for the perpendicular bisectors and graph them along with the equation of the circle you found. if you did this correctly the center of the circle should be the intersection of the equations.
8. On a new piece of graph paper, graph the triangle, the midpoints and center, connect the midpoints to and through the center in both directions for the perpendicular bisectors and when you com to class I'll loan you a compass to complete the circle you whose equation you found.
Turn in the whole packet to me at the time of the final.
Showing posts with label Labs. Show all posts
Showing posts with label Labs. Show all posts
Tuesday, April 14, 2009
Tuesday, April 22, 2008
House Lab Parts 1 & 2
College Algebra;
House Lab Part I and directions for Part 2
Note: Part 2 is not required this year.
Lab 3 Part 1
"Buying the House"
DUE: Wednesday 4/22/09
Prep work: I’ve done it for you. Use the Excel sheet I’ve sent. You can print it out or type into it but you still have to show your work as specified in the following directions.
You're now ready to begin….
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1. Suppose you are looking to buy a house in a range of values from $50,000 to $350,000. Find such a house in a local you are interested in and print off the listing to include with your lab. If part two is assigned this is the house you will furnish.
Note: Part 2 is not required this year.
Lab 3 Part 1
"Buying the House"
DUE: Wednesday 4/22/09
Prep work: I’ve done it for you. Use the Excel sheet I’ve sent. You can print it out or type into it but you still have to show your work as specified in the following directions.
You're now ready to begin….
.
1. Suppose you are looking to buy a house in a range of values from $50,000 to $350,000. Find such a house in a local you are interested in and print off the listing to include with your lab. If part two is assigned this is the house you will furnish.
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2. Suppose you make an offer and they counter-offer and you both agree to a price that is 8% below what they are asking. What is the selling price of the house?
2. Suppose you make an offer and they counter-offer and you both agree to a price that is 8% below what they are asking. What is the selling price of the house?
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To get a good interest rate depends a lot on your credit score but also on the amount you put down on the house initially. Banks are looking for buyers to have at least a 20% stake in the house they intend to buy to make it harder to walk away from it, if times get rough financially.
To get a good interest rate depends a lot on your credit score but also on the amount you put down on the house initially. Banks are looking for buyers to have at least a 20% stake in the house they intend to buy to make it harder to walk away from it, if times get rough financially.
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3. Assume you will make a 20% down payment. Determine what your down payment will be and how much you will you have to borrow. You will also be responsible for about $6000 for closing costs, government stamps, title insurance and what-not. You can add this $6000 to your down payment, even though technically it is something else, but we’ll allow it because it, like the down-payment, is an out-of-pocket cost as well.
3. Assume you will make a 20% down payment. Determine what your down payment will be and how much you will you have to borrow. You will also be responsible for about $6000 for closing costs, government stamps, title insurance and what-not. You can add this $6000 to your down payment, even though technically it is something else, but we’ll allow it because it, like the down-payment, is an out-of-pocket cost as well.
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4. Research on-line to find the best mortgage you can available in Florida for each of the term lengths given in the table. Fill in the table with these rates and attach a print out of the webpage that you found the rate on, circle it and attach the print out (NO COPIES) to the rear of your lab. Use the link http://www.bankrate.com/brm/rate/mtgRsearch_loanamt.asp?params=0,FL,569&refi=0&product=1&points= . I used Winterhaven as my location but you don’t have to.
4. Research on-line to find the best mortgage you can available in Florida for each of the term lengths given in the table. Fill in the table with these rates and attach a print out of the webpage that you found the rate on, circle it and attach the print out (NO COPIES) to the rear of your lab. Use the link http://www.bankrate.com/brm/rate/mtgRsearch_loanamt.asp?params=0,FL,569&refi=0&product=1&points= . I used Winterhaven as my location but you don’t have to.
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NOTE: When you get there be careful to ignore the fields that are advertisements. They are “sneaky”. Anything that takes you away from Bankrate.com means you clicked an advertisement. Also when you search for available rates make sure you pick the lowest one with 0.000 discount and origination points. This is another way bankers make their rates look more competitive but hit you for it with extra fees up front.
NOTE: When you get there be careful to ignore the fields that are advertisements. They are “sneaky”. Anything that takes you away from Bankrate.com means you clicked an advertisement. Also when you search for available rates make sure you pick the lowest one with 0.000 discount and origination points. This is another way bankers make their rates look more competitive but hit you for it with extra fees up front.
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5. Calculate by hand the monthly payment based on the loan amount you determined for two of the term lengths given using the rates you found and the formula found on page 171. Show all your set-up and your step by work on a separate page and label the page “WORKSHEET”. Label the work for each as well so I know which problem you are doing. State clearly what the values are that you are using for each of the variables in the formula and show all the steps required for simplifying the formula. If you are a little off because of rounding that is to be expected but round as little as possible.
5. Calculate by hand the monthly payment based on the loan amount you determined for two of the term lengths given using the rates you found and the formula found on page 171. Show all your set-up and your step by work on a separate page and label the page “WORKSHEET”. Label the work for each as well so I know which problem you are doing. State clearly what the values are that you are using for each of the variables in the formula and show all the steps required for simplifying the formula. If you are a little off because of rounding that is to be expected but round as little as possible.
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6. Verify the monthly payments you calculated are accurate by comparing them to the estimated payments found in the loan data sheet you printed off from the internet (it is the 8th column)
6. Verify the monthly payments you calculated are accurate by comparing them to the estimated payments found in the loan data sheet you printed off from the internet (it is the 8th column)
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7. After doing two of the monthly payment calculations by hand, you can fill in the monthly payments for the remaining two term lengths using the estimates provided by the internet site.
7. After doing two of the monthly payment calculations by hand, you can fill in the monthly payments for the remaining two term lengths using the estimates provided by the internet site.
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8. Finally, fill in all remaining empty cells in the table, showing and labeling all the work for the last 3 columns on the WORKSHEET. Use additional pages as needed. Be neat and well organized. .
9. ESSAY Question for part ONE:
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Based on your research, describe in a two-three paragraph comparative essay, both the pros and cons to short and long term mortgages. Be sure to compare them citing some of the values found in your table and what they mean particularally the last column. Also state what demographic you believe each term length would appeal to and why. If you aren’t familiar with the term demographic try http://en.wikipedia.org/wiki/Demographic and look at demographic profiles or if that doesn’t work come by my office.
8. Finally, fill in all remaining empty cells in the table, showing and labeling all the work for the last 3 columns on the WORKSHEET. Use additional pages as needed. Be neat and well organized. .
9. ESSAY Question for part ONE:
.
Based on your research, describe in a two-three paragraph comparative essay, both the pros and cons to short and long term mortgages. Be sure to compare them citing some of the values found in your table and what they mean particularally the last column. Also state what demographic you believe each term length would appeal to and why. If you aren’t familiar with the term demographic try http://en.wikipedia.org/wiki/Demographic and look at demographic profiles or if that doesn’t work come by my office.
.
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Part II Pg 195-197/Lab exercise 5
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"Furnishing The House"
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DUE: Not assigned this term
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For this part of the lab furnish you house following the instructions for lab exercise 5. Attach the Web pages with pictures and prices for the furniture you pick. No copies of web pages accepted. Advertisements from Newspaper circulars like Sears are also acceptable. Just cut them out making sure to include both the price and picture and attach them. Answer all the questions given in the book with the addition of the following:
.
Short response QUESTION for part two:
.
The original offer was a typical 20% down, 0%financing, same-as-cash ploy many businesses employ to sucker their customers. While for the first 24months the offer is truly same as cash, we see that if the complete balance was not paid off in the given 2 year cycle the deferred finance charges get billed to the account at a very high interest rate. Given that fact and the work you did for questions three and four discuss why a credit card purchase might be a better choice for a financing option (given a reasonably low APR). A short, one paragraph answer is sufficient for answering this question
Part II Pg 195-197/Lab exercise 5
.
"Furnishing The House"
.
DUE: Not assigned this term
.
For this part of the lab furnish you house following the instructions for lab exercise 5. Attach the Web pages with pictures and prices for the furniture you pick. No copies of web pages accepted. Advertisements from Newspaper circulars like Sears are also acceptable. Just cut them out making sure to include both the price and picture and attach them. Answer all the questions given in the book with the addition of the following:
.
Short response QUESTION for part two:
.
The original offer was a typical 20% down, 0%financing, same-as-cash ploy many businesses employ to sucker their customers. While for the first 24months the offer is truly same as cash, we see that if the complete balance was not paid off in the given 2 year cycle the deferred finance charges get billed to the account at a very high interest rate. Given that fact and the work you did for questions three and four discuss why a credit card purchase might be a better choice for a financing option (given a reasonably low APR). A short, one paragraph answer is sufficient for answering this question
Wednesday, February 07, 2007
Applied Astronomy Lab
Big Points.
Directions.
Neatly Number and Label all your work. Good Drawings complete sentences. You may work together but each of you is responsible for your own understanding, explanations and the original report you hand in. List your partners after your name. Do not quote them but indicate their contributions. If you need help with the charts or the pictures come see me.
On December 4th, 2005 an astronomer observed that two of the three planets circling Snoopy in the Dogstar galaxy aligned behind their sun in his line of sight. Determined to capture this image but unprepared at the time, he began observing the planets’ movements through the course of month until he was able to determine the speed of each planet. Armed with this information he calculated that the first planet, Brutus, makes one complete orbit about its sun every two years. The second planet, Hooch, takes three years to complete its orbit, while the last planet, Sadie, takes ten years, to complete its cycle. Since all the planets’ orbit were relatively circular he decided it would be best to convert this data in to a rotational speed (that is a speed given in degrees about the sun per year) to make finding the next time of alignment more easily.
1. If we break each planets orbit into 360 degrees, find the rotational speed of each planet in the units degrees of travel per year (about Snoopy) and also degrees of travel per month (you will need one or both to answer the following questions).
On December 4th, 2005, he observed that it was only the innermost and outer most planets that were aligned while Hooch was 1/6 of her orbit out in front of them.
2. Based on this information, what was the angular distance between Hooch and the other two planets on that day. Draw a picture to represent this, presenting and labeling the the planets in their proper order circling the star and entitle it "The Dogstar galaxy" December 3rd, 2005
If we use the aligned angular position of Brutus and Sadie on the day of their alignment as the reference point (the place from which we will do all measuring) it should be clear that since they are both at the reference their positions are both zero.
3. What would Hooch’s angular position be?
4. Since you have the speed of each planet you should be able to develop a chart indicating each planets’ angular distance from the reference position each month over the next year. Keep in mind that Hooch begins out in front and do so now.
5. Having done that develop another chart indicating the position each planet over the next five years skipping by a half year intervals.
6a and 6b. Use each chart to develop a linear equation for each planet that gives the planet’s location (L) as function of the time that has passed since Dec 4th, 2005. For time in your monthly equation use m (for months. For time in your yearly equation use y (for years).
7. Now you should have two equations representing each planets’ movement. Evaluate each equation to find the location of each planet, once for m= 18 and again for y =1.5. Compare your results and explain what you observe. (if you use m = 12y something cool happens too!)
8. Use your equation to find how many degrees of separation will keep Sadie from Hooch on my 30th birthday. February 4th 2007Inorder for two planets to align they must be at the same angular location L at exactly the same time. As such a system of equations can be used to solve for when and where this special occurrence of alignment will happen.
9. Use your monthly equations to create a system that can be solved to find when Hooch and Brutus will next align.Going back to the charts, we should keeping in mind that 360 degree is an equivalent position to 720 or 1080 or even 0, and 45 is the same as 405. In so doing we find that we can reduce any values for location greater than 360 by subtracting that number repeatedly until the results are within the range of 0 to 360 (0 and 360 being the same). When you make this adjustment in all your charts you will find a number of places where two of the planets are in alignment.
10. Make this adjustment then find and circle the places where at least two of the planets are in alignment.Your chart should now indicate that 2.5 years from now Brutus will again aligned with Sadie. While this is of no help to the astronomer (as the planets are perpendicular to his line of sight) it can show us something valuable when solving systems of equations like this.
11. If you test y=2.5 in both Brutus’s and Sadie’s equations you get different results that are actually the same. What are the results and Why are they actually the same?
What question 11 reveals to us is that when dealing with a cyclic system like this we can add or subtract 360 to the constant row for free to get a new, but no less valid equation and which will give a new, but no less valid result. Try these last three problems with this idea in mind.
12. Take your original equations for Brutus and Sadies location and set them up as a system to solve. Solve them. What is the result and why would it be of no help to the astronomer?
13. Take your original equations for Brutus and Sadie again and change one of the zeros in one of the equations to any multiple of 360 and try again (that is to say: since 0 = 360 in terms of angular location, add 360 to one of your equations at no cost). What are your new results and what do they mean.
14. Repeat question 13 with a different multiple of 360 (if you should get a negative be reminded that means months or years ago rather than months or years in the future but it is still okay). List your new results and explain what they mean to the astronomer?Hopefully at this point you are prepared to answer the seemingly trivial question which follows.
15. How long must the astronomer wait until the two planets he originally observed will be aligned in his line of sight (that is at either 180 or 0 with the reference) so that he can take his picture with both planets and Snoopy too.
Bonus:Having done all this work above what follows is for a five point bonus on your final exam:
Find, Explain, Show the work or the tables you used and prove to me by testing in your original equations your answer is correct for the following question.
How long must the astronomer wait to get a picture of all three doggie planets and their sun in alignment in his line of sight?
Hope you’ve had fun learning. Have a nice break. Mr. Rosever
Directions.
Neatly Number and Label all your work. Good Drawings complete sentences. You may work together but each of you is responsible for your own understanding, explanations and the original report you hand in. List your partners after your name. Do not quote them but indicate their contributions. If you need help with the charts or the pictures come see me.
On December 4th, 2005 an astronomer observed that two of the three planets circling Snoopy in the Dogstar galaxy aligned behind their sun in his line of sight. Determined to capture this image but unprepared at the time, he began observing the planets’ movements through the course of month until he was able to determine the speed of each planet. Armed with this information he calculated that the first planet, Brutus, makes one complete orbit about its sun every two years. The second planet, Hooch, takes three years to complete its orbit, while the last planet, Sadie, takes ten years, to complete its cycle. Since all the planets’ orbit were relatively circular he decided it would be best to convert this data in to a rotational speed (that is a speed given in degrees about the sun per year) to make finding the next time of alignment more easily.
1. If we break each planets orbit into 360 degrees, find the rotational speed of each planet in the units degrees of travel per year (about Snoopy) and also degrees of travel per month (you will need one or both to answer the following questions).
On December 4th, 2005, he observed that it was only the innermost and outer most planets that were aligned while Hooch was 1/6 of her orbit out in front of them.
2. Based on this information, what was the angular distance between Hooch and the other two planets on that day. Draw a picture to represent this, presenting and labeling the the planets in their proper order circling the star and entitle it "The Dogstar galaxy" December 3rd, 2005
If we use the aligned angular position of Brutus and Sadie on the day of their alignment as the reference point (the place from which we will do all measuring) it should be clear that since they are both at the reference their positions are both zero.
3. What would Hooch’s angular position be?
4. Since you have the speed of each planet you should be able to develop a chart indicating each planets’ angular distance from the reference position each month over the next year. Keep in mind that Hooch begins out in front and do so now.
5. Having done that develop another chart indicating the position each planet over the next five years skipping by a half year intervals.
6a and 6b. Use each chart to develop a linear equation for each planet that gives the planet’s location (L) as function of the time that has passed since Dec 4th, 2005. For time in your monthly equation use m (for months. For time in your yearly equation use y (for years).
7. Now you should have two equations representing each planets’ movement. Evaluate each equation to find the location of each planet, once for m= 18 and again for y =1.5. Compare your results and explain what you observe. (if you use m = 12y something cool happens too!)
8. Use your equation to find how many degrees of separation will keep Sadie from Hooch on my 30th birthday. February 4th 2007Inorder for two planets to align they must be at the same angular location L at exactly the same time. As such a system of equations can be used to solve for when and where this special occurrence of alignment will happen.
9. Use your monthly equations to create a system that can be solved to find when Hooch and Brutus will next align.Going back to the charts, we should keeping in mind that 360 degree is an equivalent position to 720 or 1080 or even 0, and 45 is the same as 405. In so doing we find that we can reduce any values for location greater than 360 by subtracting that number repeatedly until the results are within the range of 0 to 360 (0 and 360 being the same). When you make this adjustment in all your charts you will find a number of places where two of the planets are in alignment.
10. Make this adjustment then find and circle the places where at least two of the planets are in alignment.Your chart should now indicate that 2.5 years from now Brutus will again aligned with Sadie. While this is of no help to the astronomer (as the planets are perpendicular to his line of sight) it can show us something valuable when solving systems of equations like this.
11. If you test y=2.5 in both Brutus’s and Sadie’s equations you get different results that are actually the same. What are the results and Why are they actually the same?
What question 11 reveals to us is that when dealing with a cyclic system like this we can add or subtract 360 to the constant row for free to get a new, but no less valid equation and which will give a new, but no less valid result. Try these last three problems with this idea in mind.
12. Take your original equations for Brutus and Sadies location and set them up as a system to solve. Solve them. What is the result and why would it be of no help to the astronomer?
13. Take your original equations for Brutus and Sadie again and change one of the zeros in one of the equations to any multiple of 360 and try again (that is to say: since 0 = 360 in terms of angular location, add 360 to one of your equations at no cost). What are your new results and what do they mean.
14. Repeat question 13 with a different multiple of 360 (if you should get a negative be reminded that means months or years ago rather than months or years in the future but it is still okay). List your new results and explain what they mean to the astronomer?Hopefully at this point you are prepared to answer the seemingly trivial question which follows.
15. How long must the astronomer wait until the two planets he originally observed will be aligned in his line of sight (that is at either 180 or 0 with the reference) so that he can take his picture with both planets and Snoopy too.
Bonus:Having done all this work above what follows is for a five point bonus on your final exam:
Find, Explain, Show the work or the tables you used and prove to me by testing in your original equations your answer is correct for the following question.
How long must the astronomer wait to get a picture of all three doggie planets and their sun in alignment in his line of sight?
Hope you’ve had fun learning. Have a nice break. Mr. Rosever
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