Maths Assignment - trigonometry, trend line, probability and calculus questions.

After 4hrs distance between the cyclist and man

2.

Question:

If experimental data doesn’t produce a straight trend line it doesn’t mean there isn’t a relationship. The use of software packages can allow quick and accurate testing of data to different trend lines so that a suitable relationship can be found if it exists.

Answer:

(a).As you can see in the graph the given data of pressure Vs altitude shows an exponential variation.

(b).The appropriate trend line is shown in dotted lines on the graph.

(c). Trend line equation is given by

3.

Question:

Probability can be used so that companies can decide on reasonable waiting times.

The waiting times for a bus are normally distributed with a standard deviation of 0.3 minutes. 80% of people waiting for a bus have to wait no more than 5 minutes. Calculate the mean average waiting time for one of these buses.        (3)

Answer:

Table 01: Cumulative probability for Z values

According to the above table

Z value corresponding to 0.8 cumulative probability is:  

Let

be the mean average waiting time for a buses

Then

4. 

Question:

Calculus is the study of how things change. It provides a framework for modelling systems in which there is change, and a way to deduce the predictions of such models.

Source:  http://www-math.mit.edu/~djk/calculus_beginners/chapter01/section02.html                                        

The angular displacement

 in radians of a rotating disc is given by

 where t is the time in seconds. Calculate:                

a)        The angular velocity of the disc after 1.5 seconds stating the units.        (3)        

b)        The angular acceleration of the disc after 1.5 seconds stating the units.        (3)        

c)        The first time when the angular velocity is zero.        (2)        

Answer:

Angular displacement

 is given by function of

 by following equation

(a).Then Angular velocity

, is given by

Angular velocity of the disc after 1.5s

(b).Then Angular acceleration

, is given by

Angular acceleration of the disc after 1.5s

(c).When angular velocity becomes zero for the first time where 

5.

Question:

A gas expands according to the law pv constant. When the volume is 2m3 the pressure is 240kPa. Calculate the work done as the gas expands from 1m3 to 4m3 given that work

Answer:

Gas expands according to the law of

Where k is constant

When  

 ,

When gas expands work done is given by

But