Simply Maths

25/12/2018

Use your DIY skills to create your own energy

25/11/2018

Thought of a lovely exponential problem this morning.
Wishing everyone a lovely holiday and blessed Christmas.

16/09/2018

26/10/2017

Taking exponential rules a little further:

The square root of a = a^(1/2)

The square root of (-25)
= the square root of ( 25.-1)
= the square root of (25) . the square root of (-1)
= 5. square root of (-1)

26/10/2017

A few critically important rules and applications:

(6)^n = (2 . 3)^n = 2^n . 3^n

Also:
(6ab - 2xy)/ 2ay
= 6ab/ 2ay - 2xy/2ay
= 3b/y - x/a

Also:
a^(n + 2)/ a^(n + 1)
= a^(n + 2). a^(-n -1)
= a^(n +2 - n -1)
= a^1
= a

26/10/2017

Good morning everyone.
During an interesting session with a grade 10 student, she immediately pointed out, when I mentioned log calculations, that it is also required in financial maths where compound interest is applicable. In the example below one needs logs to calculate the period as follows:

A = P ( 1 + i ) ^n
A/P = ( 1 + i ) ^n
n = log A/P / log (1 + i )

Thanks. That was appreciated.

19/10/2017

Determined that the present Maths cirriculum does not spend much time, if any, on logs.

Look at the following example:

7^x = 2401. (^ means to the power of)
The easy solution can be obtained by using logs as follows:

x.log7 = log2401
x = log2401/ log7
= 4

Where this procedure is also required, is in financial maths in calculating the period over which an original amount P grows to a quantity of P determined at a monthly or annual compound interest at a given interest rate.

Should you like to see an example, let me know, and I shall post it.

Have a blessed day.

11/10/2017

Today, a little information with regards to logs.

If log 1000 = 3, it is of course to the base 10.

This means that 10 to the power 3 = 1000.

Ok, now change the log to base 2.

It is logical that the new log will have to be a higher number.

An easy way to do conversions, is to multiply the answer with the following factor:

(Log 10/ Log 2), which should be 3.322 if my memory does not deceive me.

This factor calculation can be adapted for any log base change.

24/09/2017

2^2011.5^2007
= 2^3.2^2008.5^-1.5^2008
= 2^3.5^-1.2^2008.5^2008
= 8/5. (2.5)^2008
= 1,6x10^2008
= RHS

16/09/2017

An interesting problem to solve:

Prove that 2^2011 x 5^2007 = 1.6 x 10^2008

Where ^ means "to the power of".

04/09/2017

On the previous question relating to the area of the triangle:

I refer to the circle theorim that states that the angle subtended at the centre of the circle is twice the size of the angle subtended at the perimeter.

Should the base of the triangle then be the diameter, the radius would equal 5.

Therefore, the maximum height of the triangle can only equal the radius, which is 5.

Therefore the triangle cannot exist.