Expressions and formulae - EDUSPORTSTZ

## Sunday, 30 April 2017

We have already seen that and are examples of formulae. There are many others that we use regularly in other subjects. Sometimes we have to construct our own formula:

# Example

A taxi firm charges per mile plus a fixed charge of . Write down a formula for the cost of hiring this taxi to travel miles.

# Solution

• It costs to travel mile.
• It costs to travel miles.
• It costs to travel miles.
So travelling for miles will cost .
The formula is .
Note: .
QQuestion
A rectangle has a width of and a length of . Write down a formula for the perimeter in terms of .

# Substitution

To recap, the cost of hiring this taxi to travel miles, when a taxi firm charges per mile plus a fixed charge of is:- To find the cost of the taxi for a journey of miles, replace with .   # Changing the subject of a formula

The formula for finding the circumference of a circle is . So it is easy to find the circumference if we know the radius.
What happens, though, if we know the circumference but want to know the radius?
In this case we can rearrange to make r the subject of the formula. , so we divide both sides by  or QQuestion
The equation of a straight line is Rearrange the formula to make the subject.

# Changing the subject of a formula

We may know the area of a circle and be required to find the radius. To do this, we can rearrange the formula to make the radius the subject.
The area of a circle (A) is . So: We will now rearrange the formula to make the subject.
A = Start by dividing both sides by . Then take the square root of both sides. or QQuestion
The formula for the volume (V) of a sphere is: Rearrange the formula to make the subject.

QQuestion
A circular pond is surrounded by a square lawn.
The area (A) of the lawn is: Rearrange the formula to make the subject
QQuestion
This triangle and rectangle have equal perimeters. This means that .
Rearrange the formula to make the subject.