Algebra

sqrt(66) = sqrt(2 x 3 x 11) =

sqrt(2) X sqrt(3) X sqrt(11) or

2^(1/2) X 3^(1/2) X 11^(1/2) = 66^(1/2)

Since 2.3. & 11 are all prime number , their square roots are Irrational. Hence sqrt(66) is also irrational .

5

There are 48 years between 1964 to 2012. This is because 2012-1964=48.

Yes and they add up to 11x

In this simple construction, the horizontal and vertical lines are evident. The red line terminates at the middle of three closely spaced collinear points, which is equidistant from the other two. The red angle measures approximately 70.002°. Angles with values ​​very close to 8, 38, 134, and 46 degrees are also formed in the same construction.

6/11 - 1/2 =

12/22 - 11/22

1/22 The answer!!!!!

y = x - 4

x^(2) + y^(2) = 8

Hence

y^(2) = 8 - x^(2)

Square up the linear eq'n and substitute

Hence

y^(2) = ( x - 4)^(2)

NB Notice the RHS is wholly squared , not individual terms.

Substitute ; this eliminates 'y'

( x - 4)^(2) = 8 - x^(2)

Square out the brackets

x^(2) - 8x + 16 = 8 - x^(2)

Collect terms

2x^(2) -8x +8 = 0

Factor

2(x^(2) - 4x + 4) = 0

(x- 2)(x - 2) = 0

Hence x = 2 ( The 'x' coordinate) .

Substitute into either eq;n for 'y'

y = 2 - 4

y = -2

Hence

( x,y) = ( 2,-2) ; The point of contact of the tangent and the curve.

-2

2^(3) X 2^(2( X 2^(-1)

Per the law of indices .

When the coefficient is the same , '2' in this case, you add the indices.

Hence

2^(3 + 2 + -1)

2^(5 - 1)

2^(4) = 16

Verification

2&(3) = 8

2^(2( = 4

2^(-1( = 1/2

Hence

8 x 4 X 1/2 =

32 x 1/2 = 16

NB Laws of indices/

When the coefficient is the same in ALL cases.

#1 a^(n) X a^(m) = a^(n+m) ; Add the indices

#2 a^(n) divide a^(m) = a^(n-m) ; Subtract the indices )

#3 [a^(n)]^(m) = a^(nm( ; 'nesting' multiply the indices.

NB you cannot use these laws for different coefficients

e.g. a^(n) X b^(n) NOT allowed/.

e.g.

2^(2) X 3^(2) is NOT [2x3] ^(2 + 2)

Oh, what a happy little question! When you have 2 to the power of -6, it means you're taking the reciprocal of 2 to the power of 6. So, 2 to the negative 6th power is 1 over 2 to the 6th power, which simplifies to 1 over 64. Just a little fraction painting to brighten your day!

Oh, what a happy little question! When we have a number raised to a negative power, we can simply move it to the denominator to make it positive. So, 6 to the negative 4th power is the same as 1 over 6 to the 4th power, which simplifies to 1 over 1296. Just a little math magic to brighten your day!

You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.

You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.

You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.

You get the largest area with a circle. Divide the perimeter by (2 x pi), then calculate the area with the formula pi x radius2.

2 miles + 327 yards = 2*5280 + 327*3 = 10560 + 981 = 11541 feet

Y Axis - Forward and Backward

X Axis - Left and Right

Z Axis - Physical UP and Down

4x + 2y = 12

Rearrange into straight line equation ( y = mx + c)

Where 'm' is the slope/gradient.

Hence

2y = -4x + 12

y = -2x + 6

Hence '-2' is the gradient /slope.

A number that can vary.

Human height can vary between say 4 feet and 7 feet .

-x -2 = 1 - 2x

Add 'x' to both sides ( preserve equality ; balance)

-2 = 1 - x

Add '2' to both sides

0 = 3 -x

Add 'x' to both sides

x = 3 The Answer !!!!!

NB When said as 'adding/subtracting etc., to both sides', this is to preserve equality (=), so the eq'n remains 'balanced', just like a weigh scales.

e.g. with numbers.

5 = 3 + 2 , however, 5 - 2 = 3 ( same difference!!!!!).

3×9= 27

1×27

Please there is your answer.

God bless you!

The ancient civilisations, 4000 years ago, Sumerians, calculated 'pi' to be 3.141592.....

The story goes ; A donkey on a tether ( radius) was driven around in a circle (Circumference) to drive water up from a well.

They noticed that however, long the tether (radius) was , the correspodning circle(circumference) was always in the same ratio. ; pi = 3.141592.....

This can be mathematically expressed as

Circumference is directly proportional to the diameter.

or

'C' is directly proportional to 'd '

This can be equated with a constant

C = k d

Algebraically rearranged as

k = C/d

Whatever the dimensions of a given circle were/are 'k', the constant, was always found to be 3.141592....

Much later after the Sumerians, the Classical Greeks, gave the name 'pi' to this constant. 'pi' being the lower case classical Greek letter 'p' and refers to **P**roportion.

Hence 'pi' , today is used as this constant of proportion for circles.

'pi' is an irrational number, which means in casual terms, the decimal digits go to infinity and there is no regular order in the decimal digits.

On 'Supa-Dupa' computers' pi' has been calculated to some 50 billion places and still going.

NB Remember the circle equations.

C = pi d

C = 2 pi r ( d = 2r)

A(area) = pi r^(2)

When learning circle calculations you are probably given pi as 3.14, or .3.1416. or 22/7, but these are only approximate values, and NOT exact values.

Hope that helps!!!!!

Circumference equals the diameter multiplied to 'pi'.

Algebraically it is written as

C = pi d

NB 'pi' is an irrational number , of the value 3.141592.... Approximated to 3.14 or 3.1416

The right angle (90 degree angle).

3.41 x 1,3019234 /12347 x 8 + 13- 1804351 x 235-135425 x2 105 + 1- 1243818723847= 68935013828483769314151163591716 The hardest math problem is the one that you don't understand an therefore can't do.

NO!!!

Because it is an equation, because it contains an 'equals(=)'.

A mathematical expression does NOT contain an 'wquals'.

hypotenuse lit. 'stretching under'. It refers to how the hypotenuse "stretches under" the right angle. ( From Classical Greek).

It is the line opposite the right angle in a triangle.

It is 50000000.