# Engineering Mathematics: Solved Problems and Examples

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This article provides solved problems and examples on various topics in Engineering Mathematics, including sinusoidal functions, aeroplane velocity, derivatives, and work done. It also includes compound angle identities and critical points.

## Engineering Mathematics: Solved Problems and Examples

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ENGINEERING MATHEMATICS
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Q1. What is the period of sinusoidal function y=4sin (-2x+7)-1
Answer: The period is determined using the formula 2 π
¿ b¿¿ , replacing b with -2 in the period
formula
Period= 2 π
¿2¿ ¿, solving the equation
The absolute value is determined by the distance between zero and a number thus the distance
between -2 and 0 is 2
The common factor will cancel out 2 π
2 . Diving π by 1, we get π
The period of the sinusoidal wave is thus π
Q2. Consider an aeroplane is pointing towards South and flying with an airspeed of 120 m/s.
Simultaneously there is a steady wind blowing due West with a constant speed of 40 m/s.
a) Make a sketch that shows how to find the resultant velocity of the plane
cos θ= 40
126.49
θ=71.56 °
tanθ= 120
40 , θ=251.56 ° whichis the direction angle
b) What is the resultant speed of the aeroplane?
126.49 m/s
Q3.1. If f(x) =x3-9x, what is the average rate of change of f over the interval [1, 6]?
The average rate of change of a function is established by evaluating the change in the
values of y of the two pointes and then dividing the resultant by the change in the values of x of
the two points
f ( 0 ) f (6)
( 0 )(1)
Substituting the equation y=x3-9x for f (0) and f (6) and substituting the x in the function with the
corresponding values of x
{1 ¿ ¿=-8/-1=8
Q3.2 If f(x) =ln (x)/, find the rate of change of f(x) between 1 and 1.5
Answer: The average rate of change is determined by
f ( 1.5 ) f (1)
1.51 = ln ( 1.5 ) ln(1)
0.5 = ln(0.5)
0.5 =1.38629
Q3.3. What is the rate of change of the interval π x 4 π /3, for the function y=4 sin x-7
f ( 4 π /3 )f (π)
( 0 )(1) = 0.9692.624
1.047 =1.581

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