Math history and tech task 1
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School
Western Governors University *
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Course
C285
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
Pages
6
Uploaded by GeneralElephantMaster926
A.
Use technology to analyze the modeling function in the problem in the Assumptions section by doing the following:
1.
Using a calculator, determine the number of bacteria when d = 10.
18693.3668122270742
2.
Use a graphing utility to do the following:
Note: The TI family of graphing calculators or the Desmos online graphing utility may be used. (See the “Desmos Graphing Utility” web link.)
a.
Provide a single image of the graph that displays both the curved nature and the maximum value of the function.
Note: In order to show the entire graph on the screen, you will need to adjust the y-axis to account for the large y values generated by the equation. If using
Desmos, do not use the zoom feature.
Note: This assessment requires you to submit pictures, graphics, and/or diagrams. Each file must be an attachment no larger than 30 MB in size. Diagrams must be original.
b.
Using the image in part A2a, identify an approximate decimal value for the maximum number of bacteria.
The maximum number of bacteria is approximately 100000. 3.
Use a computer algebra system to do the following:
a.
Provide an image of the output from the computer algebra system that shows
the exact value (not a rounded or truncated decimal) for the maximum
number of bacteria.
Note: The Wolfram Alpha online algebra utility may be used. (See the “Wolfram Alpha Algebra Utility” web link.)
b.
Using the image in part A3a, identify the exact value for the maximum number of bacteria.
1
611
(
33135707
+
6
√
27937983386795
)
4.
Explain the benefit of using an exact solution for a real-world or mathematical scenario.
The benefit of using an exact solution for a real-world problem is that it gives you a real, exact answer. This helps with specificity and accuracy. For example, if you are doing any kind of research, you will most likely want to know the exact results so that you can make more informed decisions as opposed to only knowing an estimate. a.
Explain the value of using an approximate solution for a real-world or mathematical scenario.
The benefit of using an approximate solution is that you can see the big picture, especially if you just want a simple answer. For example, if you are doing research and you are presenting your findings to a group of people that are not as informed, they won’t really care about the specific, exact answer. They just want the general idea. 5. Explain
two
advantages of using graphing calculators or other math-specific technologies in the classroom.
When using graphing calculators as apposed to other math-specific technologies,
students can visualize what the graph means. This is not necessarily true with other math-specific technologies because students can’t see the graph.
The other advantage of using graphing calculators as apposed to other math-
specific technologies is that the students can get an answer quickly. A graphing calculator will give students answers that other math-specific technologies won’t because graphing calculators have more specific answers.
B.
Use your choice of dynamic geometry software to draw a geometric shape, and then do the following:
Note: Desmos Geometry or GeoGebra may be used. (See the “Desmos Geometry” and “GeoGebra” web links.)
1.
Explain how you used the software to analyze two geometric properties of the shape (e.g., side lengths, angle measures, sums of angles, facts about diagonals,
bisectors).
To measure the angle BAC, I clicked the Angle option from the measure section, then clicked points B, A, and C in that order.
To measure side AC in the triangle ABC, I clicked the Distance or Length option from the measure section, then clicked side AC.
2.
Provide a visual image (e.g., screenshot, graphic) of the shape produced by the dynamic geometry software that includes the two geometric properties from part
B1.
C.
Use the dynamic (movement) features of the geometry software to explore a theorem relevant to the shape used in part B, and then do the following:
Theorem: The interior angles of the triangle will always equal 180 degrees
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1.
Explain how you used the dynamic (movement) features of the software to explore your chosen theorem.
Because of the dynamic features of GeoGebra, I was able to move points around to prove that the interior angles of any triangle would equal 180 degrees
2.
Provide a progression of images (e.g., screenshots) that demonstrates how you used the dynamic (movement) features of the software to show the chosen theorem is true.
You can see that the dynamic features of GeoGebra were used to prove my chosen theorem. I was able to move each point and the measurements of the angles always equaled 180 degrees.
D.
Compare the dynamic geometry software you used in part B to a similar software, including the strengths and limitations (e.g., learning curve, cost, access, features) of both.
I used the software GeoGebra for part B. A similar software is Desmos. Desmos is easier to learn how to use and when using it for formulas is easy to understand the tools and the results of the formula. It is also better when you are using it as a scientific calculator. The limitations are that when you want to use it for geometry, you must know the formula or coordinates of the shape you are trying to make. One of the benefits of GeoGebra is that it has features that allow you to simply click on the shape you want and then click on the part of the graph you want it. There are also options to automatically measure angles, sides, and lines. While GeoGebra is better for geometry, it is not as good for more advanced formulas and equations.
Desmos. (2011).
Desmos Graphing Calculator
. Desmos Graphing Calculator; Desmos. https://www.desmos.com/calculator
Geogebra. (2023).
Calculator Suite - GeoGebra
. Www.geogebra.org. https://www.geogebra.org/calculator
- Wolfram|Alpha
. (n.d.). Www.wolframalpha.com. Retrieved June 7, 2023, from https://www.wolframalpha.com/input
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