basic_engineering_mathematics0

102 Basic Engineering Mathematics
Assignment 6
This assignment covers the material contained in
Chapters 12 and 13. The marks for each question are
shown in brackets at the end of each question.
1. Determine the gradient and intercept on the y-axis for
the following equations:
a) y =−5x + 2 (b) 3x + 2y + 1 = 0 (5)
2. The equation of a line is 2y = 4x + 7. A table of corresponding
values is produced and is as shown below.
Complete the table and plot a graph of y against x.
Determine the gradient of the graph. (6)
x −3 −2 −1 0 1 2 3
y −2.5 7.5
3. Plot the graphs y = 3x + 2 and y + x = 6 on the same
2
axes and determine the co-ordinates of their point of
intersection. (7)
4. The velocity v of a body over varying time intervals t
was measured as follows:
t seconds 2 5 7 10 14 17
v m/s 15.5 17.3 18.5 20.3 22.7 24.5
Plot a graph with velocity vertical and time horizontal.
Determine from the graph (a) the gradient, (b) the vertical
axis intercept, (c) the equation of the graph, (d) the
velocity after 12.5 s, and (e) the time when the velocity
is 18 m/s. (9)
5. Solve, correct to 1 decimal place, the quadratic equation
2x 2 − 6x − 9 = 0 by plotting values of x from x =−2to
x = 5 (7)
6. Plot the graph of y = x 3 + 4x 2 + x − 6 for values of x
between x =−4 and x = 2. Hence determine the roots
of the equation x 3 + 4x 2 + x − 6 = 0 (7)
7. Plot a graph of y = 2x 2 from x =−3tox =+3 and hence
solve the equations:
(a) 2x 2 − 8 = 0 (b) 2x 2 − 4x − 6 = 0 (9)