BREAKING

Search here

TUFOLLOW UWE MIONGONI MWA WANAOTUMIWA HABARI KILA SIKU

Sunday, 30 April 2017

30 April

Equeation

Solving equations

In equations a letter stands for an unknown number and you need find its value. You can solve equations with fractions. Trial and improvement involves substitution with different values.
30 April

Expressions and formulae


taxis
We have already seen that Equation: km = 1.6 times miles and Equation: C = pi times d 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 Equation: pounds 0.50 per mile plus a fixed charge of Equation: pounds 2.00 . Write down a formula for the cost Equation: C of hiring this taxi to travel Equation: n miles.

Solution

  • It costs Equation: pounds 2 + pounds 0.50 to travel Equation: 1 mile.
  • It costs Equation: pounds 2 + 2 times pounds 0.50 to travel Equation: 2 miles.
  • It costs Equation: pounds 2 + 3 times pounds 0.50 to travel Equation: 3 miles.
So travelling for Equation: n miles will cost Equation: pounds 2 + n times pounds 0.50 .
The formula is Equation: C = pounds 2 + (n times pounds 0.50) .
Note: Equation: pounds 0.50 = 50p .
QQuestion
A rectangle has a width of Equation: x and a length of Equation: 2x .
Diagram of a rectangle with the values 2x and x
Write down a formula for the perimeter Equation: P in terms of Equation: x .

Substitution

To recap, the cost Equation: C of hiring this taxi to travel Equation: n miles, when a taxi firm charges Equation: pounds 0.50 per mile plus a fixed charge of Equation: pounds 2.00 is:-
Equation: C = pounds 2 + (n times pounds 0.50)
To find the cost of the taxi for a journey of Equation: 20 miles, replace Equation: n with Equation: 20 .
Equation: C = pounds 2 + (20 times pounds 0.50)
Equation: C = pounds 2 + pounds 10
Equation: C = pounds 12 

Changing the subject of a formula

The formula for finding the circumference of a circle is Equation: C = 2 pi r . 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.
Equation: C = 2 pi r , so we divide both sides by Equation: 2 pi
Equation: frac {C} {2pi} = r
or
Equation: r = frac {C} {2pi}
QQuestion
The equation of a straight line is Equation: y = mx + c
Rearrange the formula to make Equation: c 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 Equation: pi{r}^{2} . So:
Equation: A = pi{r}^{2}
We will now rearrange the formula to make Equation: r the subject.
A = Equation: pi{r}^{2}
Start by dividing both sides by Equation: pi .
Equation:  frac {A} {pi} = {r}^{2}
Then take the square root of both sides.
Equation: sqrt{frac {A} {pi}} = r
or
Equation: r = sqrt{frac {A} {pi}}
QQuestion
The formula for the volume (V) of a sphere is:
Equation: V = frac{4}{3} pi {r}^{3}
Rearrange the formula to make Equation: r the subject.

QQuestion
A circular pond is surrounded by a square lawn.
The area (A) of the lawn is:
Equation: A = {4x}^{2} - pi{x}^{2}
Rearrange the formula to make Equation: x the subject
QQuestion
This triangle and rectangle have equal perimeters.
Triangle diagram with values 2x+1 and 5x. Rectangle diagram with values 3x and y
This means that Equation: 9x + 2 = 6x + 2y .
Rearrange the formula to make Equation: x the subject.