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Written Assignment Unit 2
College Algebra (MATH 1201 )
University of the People
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Written Assignment Unit 2 Questions For this written assignment, answer the following questions showing all of your work.
- Determine whether the lines given by the equations below are parallel, perpendicular, or neither. Also, find a rigorous algebraic solution for each problem.
a. b. c. [Suggestion: go to desmos/calculator, write the two equations and try to conclude the answer.] Answers a) 3y + 4x = 12, hence, slope = b / -2a => slope = -4/ -6y = 8x + 1, hence, slope = -8/6 => slope = -4/3. The slope are the same, hence it is parallel. Graph is as follows:
b) 3y + x = 12, has slope = -1/3, y = 8x + 1 has slope 8. Hence, the slope are different, neither parallel nor perpendicular. There will intersects at a point. Graph is as follows:
c) 4x – 7y = 10, has slope = 4/7, 7x + 4y = 1 has slope = -7/4. The slope are negative reciprocals, so the line are perpendicular.
Graph is as follows:
Questions 2. A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by. What is the height of the building? What is the maximum height reached by the ball? How long does it take to reach maximum height? Also, find a rigorous algebraic solution for the problem. [Suggestion: go to desmos/calculator and write
and observe the answers.] Answers Since h(t) = -4 2 + 24t + 8, at the top before throwing, the t = 0 the height is 8 meters. For maximum height, we need to differentiate the given function with regard to the time and put it to 0. Hence, the differentiation are:
d ( h ( t )) dt =
d (−4 t 2 + 24 t + 8 ) dt = d (−4 t
2 )
dt +
d ( 24 t ) dt +
d ( 8 ) dt = - (2 * 4) t + 24 + 0 = -9 + 24
Since d ( dth ( t ))= 0 , hence, - 9 + 24 = 0, => t = 2,
The maximum time to reach the maximum height is at t = 2 sec. Put t into the function h (2) = -4 * 2 2 + 24 * 2 + 8 = 37. Hence, the maximum height is 37 meters. The graphs is showing below:
References
Abramson, J. (2017). Algebra and trigonometry. OpenStax, TX: Rice University. Retrieved
from openstax/details/books/algebra-and-trigonometry
Desmos. (2017, May 09). Desmos graphics calculator. desmos/calculator?
lang=en
Written Assignment Unit 2
Course: College Algebra (MATH 1201 )
University: University of the People
