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Exercise 1:
There are some very famous circles on this
planet. Stonehenge is an astronomical monument comprised of three nested circles. Go to The Forgotten Wonders
of the World and use the given diameter to find the equation of the circle that
creates the main ring of giant blocks of stone. Assume the center of the monument is at
the origin. Then, using the aerial photo, approximate the equation of the circle that
forms the "ditch" surrounding Stonehenge. (You might want to use a ruler on the
photo to get a good approximation.)
(answer)According to scientists, what was the purpose of
Stonehenge? |
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Exercise 2:
If you think the circles at Stonehenge are out
of this world, check out the Crop
Circles OF 1999. (Remember Julia Sets from your fractal exercises in Chapter 2?) Assuming these
crop circles were made by some extremely creative humans, how do you think they did it?
Let's say you had some rope and a small board of wood (perhaps 1 foot long), how could
you:
| 1) |
Form the big spiral? |
| 2) |
Form all the circles? |
Get together with a
group of your classmates and discuss the possibilities.
To read more about the size of this
formation, go to 1996 Crop
Formations Biggest, Most Complex Ever Seen. How big was it? |
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Exercise 3:
Go to The XY Chart - History and answer the
following:
| 1) |
Who created the Cartesian
coordinate system? |
| 2) |
In what century was it created? |
| 3) |
Why was it created? |
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Exercise 4:
Go to the Equations Grapher
and do the following steps (keep track of your work by graphing each step by hand to turn
in):
| 1) |
Graph the line y = 5x+3. To graph this function, hit the NEW FUNCTION
button, type 5*x+3 in the white box and hit ENTER on your keyboard. |
| 2) |
Play with the ZOOM-IN and ZOOM-OUT
buttons so see what effect they have on the viewing window.
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| 3) |
Delete this line by clicking on
its equation button (on the left) and, then, selecting DELETE. |
| 4) |
Now, by experimenting with this
grapher, find the equations of the parabolas with the following characteristics:
a) No x-intercepts and opens up
b) Exactly one x-intercept and opens down
c) No x-intercepts and opens down(Note: To graph another function, hit the DONE button, then select
NEW FUNCTION and proceed as before.) |
| 5) |
Is it possible to graph a parabola
that is a function AND does not have a y-intercept?
(answer) |
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Exercise 5:
Solve the three quadratic equations you found
in exercise 4 for x (using chapter 2 methods). What connection do you see between your
graphs and your solutions?
(answer) |
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