Miraculous Mathematics World MMW

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GOOD DAY EVERYONE.

TODAY, WE WILL BE TALKING ABOUT PYTHAGORAS THEOREM. YOU KNOW MIRACULOUS TO ALWAYS BRING OUT SOMETHING NEW.

BELOW IS THE LATEST FORMULA/ THEOREM, PLEASE ONLY FOR OBJECTIVE QUESTIONS AND NOT THEORY BECAUSE IT MY INNOVATION AND NOT MATHEMATICS ASSOCIATION OF NIGERIA [ MAN ].

View the pictures and get the solutions. Try with any other questions of your choice.

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ENJOY.....

THE POWER OF TWO { SQUARE}
Goodday everyone, today we shall be talking about two as a power, that is the square of a number.
Conventionally, calculating the square of a number is multiplying the number by itself.
E.g 5^2 = 5×5 = 25
n^2 = n × n
There exist another method below by which one can calculate the square of a number without multiplying it by itself.
NEW METHOD:
The new method is multiplying the number by the square (which is 2) and add the product of the number and their difference ( difference between the number and the square which is 2).

MATHEMATICAL PROOF ABOUT THE FORMULA
Considering, n^2 = ( n × 2 ) + [ n × ( n - 2 ) ]
= 2n + [ n^2 - 2n ]
= 2n + n^2 - 2n
= n^2 + 2n - 2n
= n^2
Therefore, n^2 = n^2 Mathematically proven...
E.g
5^2 = ( 5 × 2 ) + [ 5 × ( 5 -2 ) ]
= 10 + ( 5 × 3 )
= 10 + 15
= 25.
NOTE : IT IS APPLICABLE TO ALL NUMBERS.
TRY THIS METHOD WITH LARGER NUMBERS AND YOU WILL GET SAME RESULT AS THE NORMAL METHOD.
THANKS.
BY : OMIJIE MIRACLE.
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Good day everyone
Today we shall be talking about ......
SHAPES
THE SQUARE.

A square is a shape with
four straight lines. It has its four sides equal, thereby making the length and breadth equal.
From the above explanation, we have the length= breadth.
Meaning all squares must have their area to be a perfect square.
Mathematically,Area = L × B
Area = Perfect square ( because the L = B ).
For instance, when asked to calculate the area of a square when either the length or breadth is given, simply square the value to get the area.

E.g Find the area of a square whose length is 4cm.

Solution.
Recall from the above method,
A = L^2
A = 4^2
A = 16cm square.

Also, to find the length and breadth of a square when the area is given, simply find the square root of the area, ( because the length = the breadth ).

E.g Find the length and breadth of a square that has its area as 64cm square.

Solution.
Area = Length × Breadth ( Recall that Length = Breadth)
A = L^2
64 = L^2
√64 = √L^2
√64 = L
8 = L
L = 8cm.
Therefore the length = 8cm and the Breadth = 8cm.

But for short, you need not to go through this steps.

Solution.
A = L × B
( Recall from the above explanation )
√A = L
√64 = 8.
Recall that The Length = The Breadth
Therefore, the Length and Breadth of the square is 8cm each.
Length = 8cm and Breadth = 8cm.
That of the perimeter of a square will soon be out. Thanks...

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BY : OMIJIE MIRACLE.
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GOOD DAY EVERYONE
Today we shall be talking about percentage error
PERCENTAGE ERROR
Formula : percentage error = (Error made / Actual measurement) × 100.
Yes correct, but that has been the formula we have been using.
There is a new formula that can be used to solve problems on percentage error.
NOTE THAT : THIS FORMULA IS NOT FROM ANY TEXTBOOK OR MATERIAL.
Infact the formula will be derived below but also note that it is from the first formula.
NEW FORMULA:
Percentage Error = ( Error made / Actual measurement ) × 100.
Let Error made = E
Actual measurement = M
Percentage Error = ℅E
%E = ( E / M ) × 100
℅E = ( E × 100 ) /M
%E × M = 100E
(%E × M) / 100 = E
E = (%E × M) / 100 ( Re-arrangement)
E = %E × ( M / 100 )
E= %E × 0.0M
%E = E / 0.0M .
Simplifying ( E / 0.0M ), we have it to be = E × ( 1/0.0M). Yet again, simplifying ( 1 / 0.0M ), we have it to be = ( 100 / M ).
So, ( E / 0.0M ) = ( E ) × ( 100 / M ).
Therefore,
℅E = E × ( 100 / M )
%E = E × ( 100 / M )
I would like my formula to have a square root, so introducing a square root, I would have to multiply by 10
%E = E × ( 100 / M )
%E = ( 10 × E ) × ( √100/M ) ( Note only 100 is inside the square root).
THEREFORE ,
%E = 10E( √100/M ).

NEW FORMULA :
%E = 10E ( √ 100 / M ).

Therefore,
Percentage error = (Error made / Actual Measurement) × 100 is = percentage error = (10× Error made) × ( √ 100 / Actual Measurement).
MATHEMATICALLY PROVEN...
BY : OMIJIE MIRACLE

An example is given below
Example:
A boy measured a stick to be 7cm instead of 9cm. Calculate the percentage error.
SOLUTION...
First Formula:
Percentage Error = ( Error made / Actual measurement ) × 100
Error made = ( 9 - 7 ) cm = 2 cm
Percentage error = ( 2 / 9 ) × 100
Percentage error = 22.22%

Using the New Formula
Error made = ( 9 - 7 )cm = 2 cm
Percentage Error = ( 10 × Error made ) × ( √ 100 / Actual Measurement )
Percentage Error = ( 10 × 2 ) × ( √ 100 / 9 )
Percentage Error = 22.22%
First formula = New Formula
22.22% = 22.22%
NOTE IN USING THE SECOND FORMULA, WE NEED TO BE CAREFUL WITH THE SQUARE ROOT. THIS WILL LEAD US TO THE NEXT SECTION.

NOTE / FACT
~ ( √ 100 / M ) IS NOT = √ ( 100 / M )
LET M = 10
( √ 100 / 10 ) IS NOT = √ ( 100 / 10 )
1 IS NOT = 3.16227

MATHEMATICALLY PROVEN

~( 1 / 0.0M ) IS = ( 100 / M )
LET M = 2
( 1 / 0.02 ) IS = ( 100 / 2
)
50 IS = 50
MATHEMATICALLY PROVEN.

IF YOU HAVE ANY QUESTIONS, YOU CAN ASK.
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THANK YOU.
BY : OMIJIE MIRACLE

GOOD EVENING ALL
Today we will be talking about Surd. I will teach how to answer surd question [ especially obj questions]. So let's get started

SURD
√a × √a = a
√5 × √5. = 5.
To answer surd questions like this especially objective save yourself the stress of multiplying any figure if the figures are the same just pick one out.
But if the figures they are different just go ahead and multiply them out.

RATIONALIZATION OF SURD PART |


Again, to rationalize surd [ especially objective questions], if the figures are the same just pick the denominator.
For instance,
Rationalize a/√a. Then the solution to the question is [ a / ( the value or number inside the square root)] × √a,
i.e [(a / a) × √a] = √a.
Or simply pick the denominator.
E.g 5 / √5 = √5
Remember the figures must be the same.

RATIONALIZATION OF SURD PART ||
Before working on complex surds, let's work on inverse surd. In this case to rationalize inverse surd we have, inverse of a single surd = [ the denominator / the number in the square root].
For instance, Rationalize
1 / √a.
From the above explanation , it will be
1 / √a = √a / a.
E.g 1 / √5 = √5 / 5
Recall that : it is to make you' fast in answering surd questions like this.
Note especially objective question.
RATIONALIZATION OF SURD PART|||
In this section we shall be dealing more on numbers greater than one unlike the other previous section.
To rationalize surd in the form of 2 / √a.
The solution is
2 / √a = [ the numerator/ the number in the square root] × √a
Therefore
2 / √a = [(2 / a)]× √a.
= [(2√a) / a]
E.g Rationalize 2 / √5
From the above explanation
2 / √5 = [(2 / 5) × √5 ]
=(2√5)/5.
NOTE: IT IS APPLICABLE TO ALL NUMBERS

RATIONALIZATION OF SURD
PART |||
In this section we will be dealing with more complex surd. Surd in the form of
1 / 2√a.
To rationalize this surd will take us through one to two steps.h
For instance, rationalize 1 / 2√a.
1 / 2√a = [( The numerator) / (the coefficient of the square roof × value inside square root)].
From the above explanation, we have,
1 / 2√a = [(1) / ( 2 × a)] × √a
= √a / 2a.
E.g Rationalize
1 / 2√5 = [(1) / ( 2 × 5 )] × √5
= (1 × √5) / 10 = √5 / 10.
NOTE T