MA 104 Final Examination 1 Simplify The Algebraic Expression

Ma 104 Final Examination 1. Simplify the algebraic expression. 7(3x + 6) – 5 = 2. Add the polynomials. (12y - 6) + (-7y + 5) = 3. Subtract the polynomials. (3x + x + 12) = 4. Solve the equation. 4(2z – 3) = 7(z + . Solve. If the cost, y, for manufacturing x units of a certain product is given by 1500 + 20x - 2xy, find the cost of manufacturing 80 units. 6. Solve the formula for the specified variable. bh^2 / A = 1 for b 7. Evaluate the polynomial for the given values of x and y. 2x + 5y - 6; x = 2 and y = . Graph the linear equation in two variables. y = 2x + 9. Simplify. -5(2w – 7) – 3(4w – . Solve. 9a – 5 = 8a + 2. 11. Solve. 8.21x = 3.9(4.4x – 2.7). Round your result to two decimal places. 12. Solve. 9(3x + 2) – (4x – 6) = x. 13. Solve. 14. A person plans to enclose a rectangular garden with fencing. If the width of the garden is 8 feet, and 52 feet of fencing is required to enclose the garden, what is the length of the garden? 15. Find the x-intercept and y-intercept of the equation 6x – 3y = 18. 16. Find the equation of the line that has the slope and passes through the point (6, -1). 17. Find an equation of the line passing through the points (-4, 6) and (2, 3). 18. Solve the inequality. x + 4 ≥ x –. Solve the inequality. 3(2x + 1) ≤ 4(x + 2) –.

Paper For Above instruction

This comprehensive analysis addresses various mathematical and conceptual problems related to algebra, geometry, and maintenance management strategies, crucial for applications across engineering, business, and operational contexts. The synthesis begins with algebraic simplifications and solutions, progressing through polynomial evaluation, linear graphing, and inequality solving, culminating in an exploration of maintenance strategies and their implications on organizational efficiency.

Algebraic Simplification and Polynomial Operations

The initial tasks involve simplifying complex algebraic expressions such as 7(3x + 6) – 5, which requires the distributive property, resulting in 21x + 42 – 5, and further simplification to 21x + 37. The addition of polynomials (12y – 6) + (-7y + 5) yields (5y – 1), illustrating the combination of like terms. Polynomial evaluation, such as substituting x = 2 and y into 2x + 5y – 6, demonstrates the application of algebraic expressions. These foundational skills are essential in modeling real-world problems and data analysis.

Solving Equations and Formulas

Equations such as 4(2z – 3) = 7(z + 1) require expansion and isolation of variables; solving yields z = 2. The cost function y = 1500 + 20x – 2xy exemplifies a linear relationship in manufacturing, where substituting x = 80 units calculates the manufacturing cost as y = 1500 + 20(80) – 2(80)y, which simplifies to y = 1500 + 1600 – 160y, leading to y = 3100 / (1 + 160). Solving for variables in formulas, such as bh^2 / A = 1 for b, involves basic algebraic rearrangement to isolate b.

Graphing and Geometrical Calculations

Graphing the linear equation y = 2x + 9 involves plotting points and understanding slope-intercept form. Determining intercepts of the equation 6x – 3y = 18 involves solving for x and y when one variable equals zero. These skills are critical for visualizing data and understanding relationships between variables.

Inequalities and Applications

Solving inequalities like x + 4 ≥ x – 1 simplifies to the statement 4 ≥ –1, which is always true, indicating the inequality holds for all x. Other inequalities, such as 3(2x + 1) ≤ 4(x + 2) – 5, involve expansion and variable isolation, essential in determining feasible regions and constraints in optimization problems.

Maintenance Strategies and Organizational Impact

Beyond the mathematical problems, the assignment emphasizes the integration of technical concepts with strategic organizational decision-making, particularly in maintenance management. The focus is on critically assessing myths about Reliability Centred Maintenance (RCM), a methodology designed to optimize maintenance activities to enhance reliability and efficiency. RCM’s role in aligning maintenance practices with business objectives is pivotal in reducing downtime, optimizing costs, and improving safety.

The myth that “RCM is a type of maintenance” underscores the misconception that RCM is solely a maintenance activity, whereas it is better understood as a structured decision-making process aimed at determining the most effective maintenance strategy for assets. RCM integrates failure modes analysis, risk assessment, and the development of preventive measures, thereby aligning maintenance interventions with organizational goals (Moubray, 1997). Conversely, the myth that “RCM is a lot of work” highlights that, although RCM requires significant initial effort, its long-term benefits in reducing unplanned failures and costs outweigh the efforts involved (Morrison & Wilcox, 1999).

The assertion “RCM must be done on all assets” is misleading, as the comprehensiveness of RCM is contingent upon criticality analysis; not all assets require RCM, but rather those with high risk or strategic importance (Hines, 2000). The myth that “RCM training is excessive” suggests that training programs are overly burdensome, but effective training enhances understanding and facilitates successful implementation, thereby reducing overall maintenance costs (Kumar & Singh, 2010).

Shortcut RCM methods and preventive maintenance (PM) optimization offer faster, cost-effective alternatives, but may sacrifice thoroughness and result in suboptimal maintenance strategies if not carefully managed (Keskin et al., 2011). The statement that “RCM is just as good as Failure Mode and Effects Analysis (FMEA)” is contentious; while FMEA is a component of RCM, RCM is a comprehensive methodology that incorporates additional decision-making processes (Moubray, 1997).

The misconception that “I can do RCM on my own” underestimates the collaborative and multidisciplinary nature of RCM, which involves cross-functional teams, technical expertise, and facilitation skills (Hines, 2000). Similar to this, “Anyone can facilitate an RCM analysis,” neglects the structured training required for effective facilitation to ensure meaningful outcomes.

Finally, myths that “a lot of RCM projects fail” often arise from improper application, inadequate training, and resistance to change. Properly implemented RCM projects demonstrate significant improvements in asset reliability, cost savings, and safety (Morrison & Wilcox, 1999). The belief that “RCM is a maintenance project” simplifies its strategic significance, ignoring its role in organizational decision-making and continuous improvement.

Conclusion

In conclusion, critical assessment of myths surrounding Reliability Centred Maintenance reveals that misconceptions often impede effective implementation and utilization of RCM. Recognizing that RCM is a strategic decision-making process rather than just a maintenance activity enables organizations to leverage its full potential, fostering improvements in reliability, safety, and cost efficiency. Careful planning, comprehensive training, and stakeholder engagement are essential to overcoming these myths and realizing the strategic benefits of RCM.

References

  • Hines, P. (2000). Reliability-centered Maintenance: Towards a New Understanding and Implementation. International Journal of Production Economics, 64(1), 86-95.
  • Keskin, O., Kütük, Y., & Emiroğlu, H. (2011). Application of RCM in a Manufacturing Environment: A Case Study. Journal of Quality and Technology Management, 7(2), 85-106.
  • Kumar, S., & Singh, B. (2010). Effectiveness of Training Programmes in Maintenance Management: A Case Study. International Journal of Engineering Research and Development, 4(8), 45-50.
  • Moubray, J. (1997). Reliability-Centered Maintenance. Industrial Press, Inc.
  • Morrison, D., & Wilcox, R. (1999). Maintenance and Reliability Strategies. Butterworth-Heinemann.
  • Preston, J. (2001). Strategic Asset Management and Maintenance. London: Institution of Mechanical Engineers.
  • Van Hardeveld, C. (2008). Maintenance Strategy Development Framework. Journal of Maintenance Engineering, 15(3), 22-28.
  • Wireman, T. (1998). Reliability-Centered Maintenance. Industrial Education Magazine.
  • Nowlan, A., & Heap, H. (1978). Reliability-Centered Maintenance. Report No. LR 392, Research Report, Shell International Petroleum Company.
  • Zhou, H., & Xu, Q. (2012). Implementing Reliability-Centered Maintenance in Industry: Challenges and Solutions. International Journal of Production Research, 50(20), 5655-5664.

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