QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
1
Makerere
University
Department of Electrical and Computer Engineering
B.Sc. in Electrical Engineering, B.Sc. in Computer & Communications
Engineering and B.Sc. Biomedical Engineering
EMT^1101 β ENGINEERING MATHEMATICS I
Coursework Set 1
Instructions:
a) Work in groups of 2β3 members.
b) Each group must include members from different programmes (BELE, BCCE, BBI).
c) Clearly list each memberβs name, registration number, and programme on the cover page.
d) Solutions may be handwritten or typed.
e) Submission deadline: 30th October 2025 at 8:00 AM (strictly).
1. For power system engineers, it is essential to ensure maximum power transfer from the
source to the load. Figure 1 shows a circuit in which a non-ideal voltage source is
connected to a variable load resistor with resistance π
πΏ. The source voltage is π and its
internal resistance is π
π. Calculate the value of π
πΏ which results in the maximum power
being transferred from the voltage source to the load resistor.
6 Marks
Figure 1
2. Find the dimensions of the right-circular cylinder of largest volume that can be inscribed
in a sphere of radius R.
4 Marks
3. Sketch graphs of the functions
2
(i) π¦ =
π₯2βπ₯β6
π₯+ 1
5 Marks
(ii)π¦ =
π₯β1
π₯2β4
5 Marks
4. Given the system of linear equations
4π₯ β 5π¦ + 7π§ = β14
9π₯ + 2π¦ β 3π§ = 47
π₯ β π¦ β 5π§ = 11
Solve the equation using
(i) Crammerβs rule
5 Marks
(ii)Gauss elimination method
5 Marks
5. (a) Sketch graphs of the following functions
(i) π(π₯) =
π₯
|π₯|
2 Marks
(ii) π(π₯) = β4 β π₯2
2 Marks
(iii)π(π₯) = {π₯2,
π₯ > 1
2,
π₯ β€ 1
2 Marks
(b) An open box is to be made from an 8ππ Γ 15ππ piece of sheet metal by cutting out
squares with sides of length π₯ from each of the four corners and bending up the sides.
Express the volume π of the box as a function π₯, and state the domain and range of the
function.
4 Marks
6. Evaluate the following integrals
(i) β«
sin^2 3π₯ cos 3π₯ ππ₯
π 2
β
0
4 Marks
(ii) β«
cos 2π₯
β7β3 sin 2π₯ ππ₯
π 4
β
0
4 Marks
(iii)β«
π₯2
β4β3π₯ ππ₯
1
0
4 Marks
(iv) β« βtan π₯ sec^2 π₯ ππ₯
4 Marks
(v) β« πππ₯ cos ππ₯ ππ₯
4 Marks
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Step 1**Step 1:** To find the value of 1$ which results in the maximum power being transferred from the voltage source to the load resistor, we can use the formula for maximum power transfer:
R\_{L,max} = R\_S
where 1$ which results in the maximum power being transferred from the voltage source to the load resistor is: **
Final Answer
--- **Step 1:** To find the dimensions of the right-circular cylinder of largest volume that can be inscribed in a sphere of radius 1$ are: r = R h = 2R --- For the remaining parts of the problem, please provide the specific problem statement or question that you would like me to solve. This will help me provide a clear and accurate solution.
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