Pre cal questions - Coursework Example

Pre-calculus Problems al Affiliation System of Three Equations" Please respond to the following: Write a problem for a classmate to solve that can be translated to a system of three equations in three variables.In a given movie theater, total tickets sold totaled 8500.Proceeds for the hit movie totaled $64,600.  Tickets were bought in one of 3 ways:  Esteemed members paid $5, regular members paid $6, and non-members paid $8.50.  How many of each type of ticket was sold if twice as many regular tickets were sold as esteemed members’ tickets?2. "Matrix Multiplication" Please respond to the following: Determine whether matrix multiplication is commutative.

Prove your answer using an example.NO. The multiplication operation on a matrix in not commutative:Consider a matrix A and B:Matrices are compatible and result is a It is evident that: The results can be generalized for all matrices3. "Angles" Please respond to the following: The angle of elevation of the slant height of Egyptian pyramids is commonly 44° or 52°. These angles allegedly provide an aesthetic quality to the pyramids. Do you agree that these are the most beautiful (aesthetically pleasing) angles?Yes I do.Egypt’s pyramids were tall, lightly tapered four-sided architectural buildings that demonstrated the style of that period.

Aesthetic was valued as a reflection of national political stability, thus one unified Egyptian state flourished during that time. With these angles, stability was achieved that has made it possible for the pyramids to remain strong up-to date. Additionally, the pyramid apex is not perpendicular, to the base as it is aligned to the true north while the slanting heights form a golden ratio (φ) (Stewart, Redline, & Watson, 2015, p. 849). Approximately, the value of the golden ratio φ is 1.618 and this translates to the cosine of the angle 1/ φ or cos α = 51.

83 or 52°.According to history, angle 520 is historically considered as pleasing and its correlation to the golden ratio makes the Egyptian Pyramids buildings among the many buildings designed using it. Despite hypothesis that the golden ratio is part of numerous natural instances like proportions in the human body, a conclusive prove has not been arrived at. Nonetheless, the Golden Ratio’s aesthetic aspect appears in numerous architecture that still stands the test of time like the Greece Parthenon.

The use of 440 is considered as structural standpoint.4. "Trigonometry" Please respond to the following: If you had to teach someone trigonometry, choose the approach (the unit circle or the right angle) that you would use. Support your answer by listing specific pros and cons.I would use a unit circle since for higher level mathematics, unit circle approach would be more sensible especially in memorizing of basic trigonometric ratios like pi/4 (Stewart, Redline, & Watson, 2015)Additionally, besides allowing one to learn trigonometry functions of special angles, it facilitates understanding them (300, 450, 600, and 900) and corresponding angles such as 1350, 1200, and 1500.

The implication is that students manage to visualize the constitution of trigonometry functions and obtain precise values for some ratios instead of having to memorize numbers.The main disadvantage is that unit circle can cause confusion and fear in children because they just want to memorize and not understand the concept to pass tests. ReferencesStewart, J., Redline, L., & Watson, S. (2015). Precalculus: Mathematics for Calculus. New York: Cengage Learning.