# ENG1090: Let d be the last non-zero digit of your student number: Foundation Mathematics Assignment, MU, Malaysia

University |
Monash University (MU) |

**Assignment questions**

**Question 2.1**

Let d be the last non-zero digit of your student number. The average temperature of a machine (in celcius) is modelled by

T(t) = 5 sin(t/3) + d sin2(t/6) − d cos2(t/6),

where t is given in hour.

a) Simplify the expression T(t) into an equivalent form T(t), for constants D, E, k. Hint: use the power reduction formulas introduced in Lecture 4.

b) Identify the period of the function T(t), and provide a brief reason for your answer.

c) Determine the amplitude A and the principal angle α when T(t) is written as a sine function in phaseangle form T(t) = A sin. Justify your answers carefully.

**Question 2.2**

Radioactive materials, such as Plutonium-239, Radium-226, and others, decay exponentially. The amount of radioactive material present at time t can be described by R(t) = R0e kt, where t represents time (in years), and R(t) represents the amount of radioactive material present at time t. After 700 years, a sample of Plutonium-239 has decayed to 40% of its original mass.

Find the half-life of this sample of Plutonium-239, i.e., the amount of time it takes for Plutonium-239 to decay to half it original mask.

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