MNU 122
Tutorial 2&3.
Due Date 17/10/2022
Instructions.
Answer all questions.
All symbols have their usual meaning.
Show clearly how you came up with the answer.
Use the method in question.
Submit Hard copies in My office(LV 156) before 12:00 pm.
Maths Department ground floor.
Allocation points = 50 marks.
Questions.
1.You are working for ‘DOWN THE TOILET COMPANY’ that makes floats for ABC commodes.
The floating ball has a specific gravity of 0.6 and has a radius of 5.5 cm. You are asked to find
the depth to which the ball is submerged when floating in water. The equation that gives the
depth x to which the ball is submerged under water is given by
𝑥 3 − 0.165𝑥 2 + 3.993 × 10−4 = 0.
Use the bisection method of finding roots of equations to find the depth x to which the ball is
submerged under water. Conduct three iterations to estimate the root of the above equation.
Find the absolute relative approximate error at the end of each iteration, and the number of
significant digits at least correct at the end of each iteration.
2.Using the principle of Least squares method, fit an equation of the form 𝑦 = 𝑎𝑒 𝑏𝑥
to the data
x
1
2
3
4
y
1.65
2.7
4.5
7.35
3.Fit a curve of the form 𝑦 = 𝑎𝑥 𝑏 to the following data
Year (X)
1951
1952
1953
1954
Production 201
263
314
395
in tone (Y)
4. Let the system of equations be given by
1955
427
1956
504
(𝑎 > 0)
1957
612
2𝑥
2𝑥
−2𝑥
−𝑦
+2𝑦
+3𝑦
+3𝑧 = 5
+3𝑧 = 7
= −3
Apply Gaussian elimination method on the system above.
5.If P is the pull required to lift a load W by means of a pulley block, find a linear law of the form
𝑃 = 𝑚𝑊 + 𝐶, connecting P and W, using the following data
P (in kg.)
12
15
21
25
W (in kg.)
50
70
100
120
Compute P when W=150 KG.
END.