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

Extracts from this document...

Introduction

1.

Question:

Trigonometry can be used to solve problems instead of constructing a scale diagram.

A man leaves a point walking at 6kmh on a bearing of 80o. A cyclist leaves the same point at the same time on a bearing of 120o travelling at a speed of 17kmh. Calculate their distance apart after 4 hours using trigonometry.        (6)

Answer:

image10.png

Figure 01

As shown in the figure 01, let’s take ‘A’ as the starting point.

After 4hrs the man is at point M and cyclist at point C

Distance travelled by the man after 4hrs                

image00.png

Distance travelled by the cyclist after 4hrs        

image00.png

Now let’s consider the

 triangle

Using the information in the question, the application of the Cosine rule would seem

...read more.

Middle

cm

a)  Using Excel verify this is true.

(2)

b)  Add the appropriate trend line.

(1)

c)  Display the equation of this trend line.

(1)

Answer:

image11.png

(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

image02.png

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

.04

.05

0.8

0.7995

0.8023

According to the above table

...read more.

Conclusion

"c15">Answer:

Angular displacement

 is given by function of

 by following equation

image03.png

(a).Then Angular velocity

, is given by

image03.png

image03.png

Angular velocity of the disc after 1.5s
image03.png

image00.png

(b).Then Angular acceleration

, is given by

image03.png

image04.png

Angular acceleration of the disc after 1.5s

image04.png

image00.png

(c).When angular velocity becomes zero for the first time whereimage00.png

image05.png

image06.png

image00.png

image00.png

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

done  v2p dv

(4)

v1

Note:  1

dx

 ln x

x

Answer:

Gas expands according to the law of

Where k is constant

When  image00.png

 ,

When gas expands work done is given by

image07.png

But

image03.png

image08.png

image01.png

image09.png

image00.png

...read more.

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