C285 Task 1 Tyler P
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Western Governors University *
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C285
Subject
Mathematics
Date
Apr 3, 2024
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docx
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5
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Tyler Phanhthavilay December 6, 2023
C285 Task 1 Student ID: 010979783
A1. Student ID: 010979783
N= 53194.7292576 rounded to N= 53194.7, when d = 10. After 10 days there will be approximately 53,194.7 bacteria. A2a. Image Provided
A2b. N= Maximum number of Bacteria N= 364668.078 Max
Tyler Phanhthavilay December 6, 2023
C285 Task 1 Student ID: 010979783
A3a. Gives the exact answer of X and provides a graph for the maximum number of bacteria using Wolfram Alpha’s calculator. A3b. Maximum bacteria. A4. Using an exact solution for a mathematical or a real-world situation gives you the highest level of precision and accuracy. This allows for reliable results, which makes it essential to have low percentage error, theoretical predictions, validating models, and engineering applications. It is highly important to use an exact solution when precision is of high importance to give us a deeper understanding of systems and processes. A4a. Using an approximate solution in real-world situations and mathematical scenarios is that it
allows for efficiency and practicality. Some exact solutions may be a lot of writing and time consuming to obtain, using approximations allow for quicker answers and allow for rapid assessments and analyzations. This makes projects more practical and efficient when accuracy is not as important.
Tyler Phanhthavilay December 6, 2023
C285 Task 1 Student ID: 010979783
A5. Using graphing calculators and math-specific technologies allow for several advantages within the classroom. First it allows for students to see mathematical concepts visually through graphs, data tables and seeing relationships of math concepts in real time efficiently. Seeing math visually allows students to grasp abstract concepts easier and make it more tangible for them to understand the principles of math. Secondly, these technologies promote efficiency and accuracy with computations that are quite complex and time consuming. It allows for students to use complex calculations and critical thinking without having to worry about the time constraint of solving each step with pen and paper. It gives students an advantage because it allows them to utilize technology to be efficient and prepare them to utilize technology in the future to give them dynamic visuals and quickly analyze mathematical data. B1. To analyze two geometric properties of a triangle, I used the Desmos Geometry software to see the properties. I first made 3 points and connected the lengths to form a triangle, this allowed me to explore the different shapes of a triangle creating acute, obtuse, and right-angled triangles. I then looked at the 3 points graphed to see how it effected the shape of the triangle. Secondly, I utilized the Desmos software to look at the angles in terms of degrees by connecting all 3 corners to create a triangle, then I clicked on 3 points in different orders to get all three angle degrees. I then was also able to get the lengths of the sides to show the relation from angles
to sides of a triangle. B2.
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Tyler Phanhthavilay December 6, 2023
C285 Task 1 Student ID: 010979783
C1. I chose the theorem 1, Triangle sum theorem about triangles state, “The total of the three interior angles in any triangle is 180 degrees” (Triangle Theorem). I noticed that as I moved the dynamics of the triangle using Desmos Geometry is that the sum of all interior angles each time would equal 180 degrees. No matter which direction you move it in, no matter how far or how small you moved it, the interior angles would always equate to 180. C2. These pictures show that the theorem is true because when adding the interior angles, they equaled 180 degrees every time. The sides may be different, the area, and the perimeter but the
Tyler Phanhthavilay December 6, 2023
C285 Task 1 Student ID: 010979783
sum of angles will always be 180 as it was stated through the theorem. To make these dynamic movements, I would simply just drag one point to another place, and it would create a triangle. D. Desmos Geometry and GeoGebra Both applications are popular for dynamic geometry and can both be used effectively in education. Some strengths and limitations are portrayed: Learning Curve: Desmos has a friendly user interface as the design is simple and provides videos and examples of
how to use their functions. It is easy for beginners to pick it up and to start using it. Although, it is easy to use but it may be limited for those who have no idea or foundation of geometry software. As for GeoGebra, the strengths are that it had a lot of tools and functions that users could use for mathematical concepts such as geometry. They had a lot of advanced and complex things you could do on there which would provide very valuable for harder math concepts. The limitations are that it would be very difficult to start using this software from scratch as it was a little confusing to start for myself. Features: The strengths for demos are the simplicity and how easy it is so use; it allows for easy visualization through graphs. Although it is limited in advanced features that is showcased in GeoGebra which limits the level of how far you can go with Desmos. GeoGebra showcases its strengths as you can use tools for geometry, 3D graphing, calculus and more. Although, it is very
overwhelming even for someone like me who has done a fair share of math. E. Sources Triangle Theorem
. (n.d.). Unacademy. https://unacademy.com/content/jee/study-material/mathematics/triangle-theorem/