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MEM23004A

Assignment 1

Apply Technical Mathematics

Section A - Assessment Information

Duration and/or due date: Week 4, Refer Canvas for Exact Date

Task Instructions

Summary and Purpose of Assessment:

This assignment in the unit of competency covers the application of mathematical analysis and graphical techniques to engineering problems. It includes exponential and logarithmic functions, sequences/series, trigonometric equations involving single and double angles, two dimensional vector analysis, number systems, complex numbers, determinants and matrices.

You must demonstrate an understanding of:

 Technical mathematical techniques required for an engineering application

 How to apply technical mathematical techniques to engineering application

What and where: This is a computer based individual assessment. However collaboration is encouraged for completion. OBSERVATION OF TEACHER DURING CLASS TIME IS MANDATORY FOR SATISFACTORY COMPLETION.

How: You will be assessed according to the criteria outlined in the assessment below. Please see below “Additional Instructions to Students”.

Conditions for assessment

Refer below

Instructions on submitting your knowledge assessment

Instructions to Students:

1. Students must submit an electronic copy of this assignment via RMIT CANVAS before its due date.

2. Students found in breach of assessment conditions can be charged with academic misconduct, have their results cancelled, be excluded from the program and receive other penalties. Penalties can also apply if a student’s test material is copied by others.

3. Plagiarism is the presentation of the work, idea or creation of another person as though it is one’s own. It is a form of cheating and is a very serious academic offence that may lead to expulsion from the University. Plagiarised material can be drawn from, and presented in, written, graphic and visual form, including electronic data, and oral presentations. Plagiarism occurs when the origin of the material used is not appropriately cited.

4. RMIT special consideration is to enable you to maintain your academic progress despite adverse circumstances. The process for special consideration can be found at https://www.rmit.edu.au/students/student-essentials/assessment-and-exams/assessment/special-consideration

5. Students with a disability or long-term medical or mental health condition can apply for adjustments to their study and assessment conditions (Reasonable Adjustments and Equitable Assessment Arrangements) by registering with Equitable Learning Services (ELS) at https://www.rmit.edu.au/students/support-and-facilities/student-support/equitable-learning-services

Additional Instructions:

1. Performance requirement

a. Attempt all questions. OBSERVATION OF TEACHER DURING CLASS TIME IS MANDATORY FOR SATISFACTORY COMPLETION OF THIS ASSESSMENT

b. Satisfactory (S) performance this assessment – MUST ANSWER ALL QUESTIONS SATISFACTORILY

c. Not Yet Satisfactory (NYS) performance – ONE OR MORE QUESTIONS ANSWERED UNSATISFACTORILY

2. To be deemed competent in this course you will need to gain Satisfactory (S) result in all of the assessments (all three).

2. Late submission approval will be in line with RMIT policy Application for extension of submittable work (7 calendar days or less) form.

3. Special consideration for assessment Application for special consideration form.

4. If a student’s result is NYS: feedback and agreed deadline date for the student to demonstrate competency will be advised.

5. The date(s) must be within enrolment dates for this competency otherwise the student will be given a final result of NYS and the student may need to re-enrol/ repeat this course.

Note: Use computer software application to find and validate your answers or drawing graphs before the submission

This assignment covers PC 1.1, 1.2, 1.3, 2.1, 2.3, 2.4, 2.5

Section B – Student Answer Sheet

Q1:

The pressure drop P in pounds per square inch (psi) in a particular oil reservoir is a function of the number of years t that the reservoir has been in operation. The pressure drop is approximated by the equation P  150t  20t 2  t 3 .

(a) By using MATLAB, Excel, CAS calculator or an appropriate standard engineering software, find the number of years for the pressure to drop 400 psi.

(b) By using MATLAB, Excel, CAS calculator or an appropriate standard engineering software, sketch the graph of pressure versus number of years between 0 to 10 years.

PC 1.1, 1.2, 1.3, 2.1, 2.3, 2.4, 2.5

A:

Exponentials/Logarithms

Q2

You are using an excavator on a cold winter day (20ºF outside) and the engine overheats (at about 220 ºF). When you turn off the engine, it begins to cool down. The temperature T of the engine t minutes after you park satisfies the equation tTe 0.1120020log.

(a) Solve the equation for T.

(b) Use part (a) and MATLAB, Excel, CAS calculator or an appropriate standard engineering software to find the temperature of the engine between 1 to 20 minutes.

PC 1.1, 1.2, 1.3, 2.1, 2.3, 2.4, 2.5A:

Quadratic Equations

Q3

The volume of water in a tank, V m3, over a 10 month period is given by the function , where t is in months and t ∈ [0, 10].

Use an appropriate standard engineering software such as MATLAB, CAS calculator, programmable calculator, Excel software, to find the volume of water in the tank after 10 months.

Use an appropriate standard engineering software such as MATLAB, CAS calculator, programmable calculator, Excel software, to solve and analyse this problem mathematically, including graphing of the function required for this engineering application.

PC 1.1, 1.2, 1.3, 2.1, 2.3, 2.4, 2.5

A:

Exponential/Logarithmic Functions

Q4

Use an appropriate standard engineering software or MATLAB to solve and determine