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Mathematics Assignment - Math Problem Example

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Download file to see previous pages 1 m3 = 100 cm3 = 0.86 tonnes
Then, divide both sides by 10
10 Cubic cms = 0.086 tonnes
(b) What volume of soil weighs 3 kg
1 ton = 1000 kg
Then,
0.86 tonnes = 860 kg = 1 m3
So,
1 m3 = 860 kg
Multiply both sides by 3/860
3/860 m3 = (3*860) / 860 kg
0.0035 m3 = 3 kg
14. If 10 men take 3 days to complete a task
(a) How long will it take 6 men to complete the task
10*3 = 6*x
30/6 = x = 5
(b) If the task is to be completed in two days how many men are required
10*3 = x*2
X = 30/2 = 15
15. Draw the graph of 5x + 2y 10 = 0 and determine the x and y intercepts
When x=0,
5(0) + 2y = 10
Y= 10/2 = 5
(x,y) = (0,5)
Similarly, when y=0.
5x + 2(0) = 10
X = 10/5 = 2
(x,y) = (2,0)
16. The distance travelled by a train and the corresponding times are given by
Time, hrs 0 0.5 1.5 2.5
Distance, kms 0 38 114 190
Plot the graph of distance as a function of time and determine the equation of the line.
Equation of the line,
y = mx +c
Where,
c = y-intercept &
m = slope of the line =
here, as the graph shows c = 0,
whereas, let us consider (0,0) and (0.5,38) to determine m.
m = (38 - 0) / (0.5 - 0) = 76
So, the equation of the line is:
y = 76x + 0
or
y = 76x
17. A ball is thrown upward with an initial velocity 55 m/sec. The speed of the ball decreases uniformly with time and after 5 secs its velocity is 6 m/sec.
(a) Determine the equation relating the velocity of the ball and time.
Here, there are 2 coordinates given, i.e. (55,0) and (6,5) considering time is plotted on the y-axis.
As per the graph in part b, c (y-intercept) = 5.6 and m = (5-0)/(6-55) = -5/49
Therefore, the equation will be,
+ 5.6
Or
49y +5x = 274.4
(b) Draw the graph of this equation.
(c) Determine the time at which the...
The negative velocity in this example would be a hypothetical state to achieve. The equation for such a case will be bound by constraints, ensuring no negative values can be put in for time and velocity.
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