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 – ENGINEERING MATHEMATICS I
Coursework Set 1
Instructions:
a) Work in groups of 2–3 members.
b) Each group must include members from different programmes (BELE, BCCE, BBI).
c) Clearly list each member’s 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 𝑅𝐿. The source voltage is 𝑉 and its
internal resistance is 𝑅𝑆. Calculate the value of 𝑅𝐿 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) 𝑦 =
𝑥2−𝑥−6
𝑥+ 1
5 Marks
(ii)𝑦 =
𝑥−1
𝑥2−4
5 Marks
4. Given the system of linear equations
4𝑥 − 5𝑦 + 7𝑧 = −14
9𝑥 + 2𝑦 − 3𝑧 = 47
𝑥 − 𝑦 − 5𝑧 = 11
Solve the equation using
(i) Crammer’s rule
5 Marks
(ii)Gauss elimination method
5 Marks
5. (a) Sketch graphs of the following functions
(i) 𝑓(𝑥) =
𝑥
|𝑥|
2 Marks
(ii) 𝑓(𝑥) = √4 − 𝑥2
2 Marks
(iii)𝑓(𝑥) = {𝑥2,
𝑥 > 1
2,
𝑥 ≤ 1
2 Marks
(b) An open box is to be made from an 8𝑐𝑚 × 15𝑐𝑚 piece of sheet metal by cutting out
squares with sides of length 𝑥 from each of the four corners and bending up the sides.
Express the volume 𝑉 of the box as a function 𝑥, and state the domain and range of the
function.
4 Marks
6. Evaluate the following integrals
(i) ∫
sin^2 3𝑥 cos 3𝑥 𝑑𝑥
𝜋 2
⁄
0
4 Marks
(ii) ∫
cos 2𝑥
√7−3 sin 2𝑥 𝑑𝑥
𝜋 4
⁄
0
4 Marks
(iii)∫
𝑥2
√4−3𝑥 𝑑𝑥
1
0
4 Marks
(iv) ∫ √tan 𝑥 sec^2 𝑥 𝑑𝑥
4 Marks
(v) ∫ 𝑒𝑎𝑥 cos 𝑏𝑥 𝑑𝑥
4 Marks
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Answer
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Step 1I will solve the first problem here.
The source voltage is $V$, and its internal resistance is $R\_S$.
**EMT^1101 Assignment Problem 1:**
Step 2
V_{RL} = V \cdot \frac{R\_L}{R\_S + R\_L}
The formula for power is given by: Using Ohm's Law, we can write:
Final Answer
The value of $R\_L$ that results in the maximum power being transferred from the voltage source to the load resistor is $R\_L = R\_S$.
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