Chapter 2 Project

Chapter 5 Construction Exploration Project

1) Angle A stays the same in both triangles and sin (pi - C) = sin C so sin C stays the same in both triangles
2) A unique triangle is determined when BC = AB. BC and AB are the sides of the triangle and when we constructed a perpendicular from ray AC to ray AB, we made a 90° angle, which made it a right triangle. If we have BC, angle B and AB, we have a SAS case which determines only one unique triangle and the unique triangle is a isosceles right triangle.
3) IF angle A is obtuse then:
When BC > AB, 1 triangle can be formed
When BC = AB, no triangles can be formed
When BC < AB, no triangles can be formed IF angle A is acute then: When AC > BC > H, 2 triangles can be formed
When BC > AC > H, 1 triangle can be formed
When BC = H, 1 right t

Ch. 4 Project

Ch 1 Project - Modeling with Functions and Regression Equations

1. The first thing i did was draw the shapes and their diagonals. The triangle is excluded because it doesn't have any diagonals.
2. Next, I made a scatter plot of the data. The values of n (number of sides) went in the L1 column and the values of d (number of diagonals) went in the L2 column.
3. Next, I used the calculator to find the linear regression, power regression, quadratic regression, cubic, and quartic regression. The closer the absolute value or r or R^2 is closer to 1, then the closer it is fitting the data.
4.After all that, i found that the quadratic regression perfectly fitted the data. The equation is 0.5x^2 - 1.5x. R^2 is a positive 1, so it tells me that the correlation is positive and that the curve fits the data perfectly.
5.Finally, i used my equation 0.5x^2 - 1.5x. to find the number of diagonals in a 150-gon. I plugged in 150 for x and got 11,025. Therefore, the number of diagonals in a 150-gon is 11,025

Ch. P - Applying Linear Equation in Two variables

My project revolves around the speed of light. First, i had to search up information I needed to help solve my problems numerically such as distance and time that light traveled. Next, I had to convert kilometers into miles (1 km = 0.614 m) to make all the terms match up because the textbook gave me miles per second while the information i searched up gave me kilometers per second. Then, I used the linear equation d = r x t (distance = rate x time) to make calculations with r = 186,000 miles per second. Finally, i substituted the distances into the equations to find the time it takes light to reach an astronomical body from the origin or the place where i started from and substituted the time it takes to reach an astronomical body to find the distance between the two bodies. All calculations was solved with a calculator because the numbers were big to work with.

Ch. P - Graphing Functtions

1. I started by graphing the original (parent) function of y = ³√x (cubic root of X), which is the graph (black) intersecting the origin.
2. Next, I translated the function y = ³√x, 9 units up along the y-axis to create a vertical translation of y = ³√x+9. The translation is shown in red intersecting at (0,9).
3. Then I created a horizontal translation, by moving the function 9 units to the right along the x-axis to create y = ³√(x-9). The translation is shown in blue intersecting at (9,0).
4. Then I combined both vertical and horizontal translation, I transformed the original function into y = ³√(x-9)+9, where the graph moved 9 units to the right of the x-axis then 9 units up the y-axis. The translation is shown in green marker in the first quadrant and intersecting at (9,9).
5. Then I did a reflection where I reflected the original function across the x-axis to create y = -³√x which is shown in purple intersecting at the origin.
6. Finally, I graphed a transformation by combining the vertical translation, horizontal translation and the reflection over the x-axis. I moved the original function reflected across the x-axis, translated 9 units to the right and 9 units down to make y= -³√(x-9)-9. The transformation is shown in black marker in the fourth quadrant intersecting at (9,-9).

About Davis Infintity

Education: Lincoln Elementary, Edna Brewer Middle School, and currently a Sophmore at Oakland High School

Work/Volunteer: Never worked before, but volunteered picking up trash for a program/neighbors before.

What I want to be: I'm still choosing between an engineer or video game designer.

Interests: Some of my interests are dancing, listening to music, hanging out with friends, and sleeping.