# 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:

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

Distance travelled by the cyclist after 4hrs

Now let’s consider the

triangle

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

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:

(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

.04 | .05 | |

0.8 | 0.7995 | 0.8023 |

According to the above table

Conclusion

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

done v2p dv | (4) | |

v1 | ||

Note: 1 | dx | ln x |

x |

Answer:

Gas expands according to the law of

Where k is constant

When

,

When gas expands work done is given by

But

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

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