Calculus

A Straight line !!!!

6x + 2y = 8

Algebriacally rearrange

2y = -6x + 8

y = -3x + 4

It is now in the straight line form of y = mx + c ,

The gradient'slope is '-3' and the y-intercept is '+4'.

x^(2) + y^(2) = 36 = 6^(2)

The graph is a circle of radius '6' , centred on the origin (0,0).

CosX = Sin2x

Using Trog. Identityt

CosX = 2SinXCosX

CosX cancels down to '1'

Hence

CosX/CosX = 2 SinX

1 = 2SinX

SinX = 1/2 = 0.5

SinX = 0.5

X = Sin^(-1) 0,5

X = 30 degrees = pi/6 radians

Cos (x) = -Sin(x)

1 = -Sin(x) / Cos (x)

1 = -Tan(x)

Tan(x) = -1

x = Tan^-1(-1(

x = -45 degrees = - pi /4 , 3pi/4, 5pi/4 ....

If you mean y = Sin(pi(x))

Then

Use the chain rule

dy/dx = dy/du X du/dx

Let

pi(x) = u

y = Sin (u)

dy/du = Cos(u)

u = pi(x)

du/dx = pi

Combining

dy/dx = pi Cos(u) = piCos (pi(x)). The answer!!!!!

Oh, isn't pi just a delightful number? Let's paint a picture with its first 35 digits: 3.1415926535897932384626433832795028. Just like adding happy little trees to a landscape, each digit of pi adds to the beauty and mystery of mathematics. Keep exploring and discovering, my friend.

974 x 7 = 6818

'x^(2)' looks like a bowl on a graph.

'-x^(2)' looks like an upturned bowl, or an umbrella.

Very simple: it is 1.6989700043 to be exact. You can test this because log50 means we assume the natural log (base 10), if you test 10 to the exponent of 1.6989700043 you should render 50 as your result :D

To convert a decimal into a fraction, write the decimal number over one like this: .52/1. Next, remove the decimal point and add as many zeroes to the bottom number as there were numbers after the decimal: .52/1 would now be 52/100. The last step is to simplify the fraction: 53/100 = 26/50 = 13/25. The fraction equivalent of .52 is 13/25.

y = Sin(x)

dy/dx = Cos(x)

10^3(8.75) would equal 10^26.25 which would equal: {| |- | 1.77828E+26 |}

x times 1 is x. Anything times 1 is still that same anything.

To graph the equation y - x + 3, we can first rearrange it into slope-intercept form, y = x - 3. This equation represents a line with a slope of 1 and a y-intercept of -3. To graph it, start by plotting the y-intercept at (0, -3), then use the slope to find another point, such as moving up 1 unit and to the right 1 unit. Connect these points with a straight line to complete the graph.

To calculate 10 percent of 6000, you first convert 10 percent to a decimal by dividing it by 100, which equals 0.10. Then, you multiply 0.10 by 6000 to find the answer. Therefore, 10 percent of 6000 is 600.

In Maths double sign symbols can be tabled as

• • = +
• • = -

• • = -
• • = +

NB If no symbol is given in front of a number, then read it as plus(+).

The word 'Mathemetics' comes from Classical Greece, and means 'to learn'.

Think of it as a puzzle , like a crossword puzlle, to be solved. However, there are a set of rules that you must follows in finding solutions, that are different from a crossword puzzle.

Board ganes, like Chess, or Snakes and Ladders have their own set of rules to follow in order to play the game fairly. Maths is the same, its just another different set of rules.

By Simultaneous Equations. Assuming you mean

5x + 3y + 20 = 0

2x - y - 14 = 0.

We will eliminate 'y' by multiplying the bottom eq'n by '3' and then adding.

Hence

5x + 3y + 20 = 0

6x - 3y -42 = 0

Add

11x -22 = 0

11x = 22

x = 22/11

x = 2

when x= 2

2(2) - y - 14 =0

4 - y - 14 = 0

-y - 10 = 0

y = -10

So the point of intersection in ( x.y.) form is ( 2, -10).

y varies as 1/x^(2)

y = k X 1/^(2)

y = k/x^(2)

k = y x^(2)

When y = 4 & x = 3

Then

k = 4(3^(2))

k = 4(9)

k = 36 (The constant of proportionality

Hence the general equation is

y = 36/x^(2)

When x = 2

y = 36/2^(2)

y = 36 /4

y = 9 The answer!!!!!

f'(x) = x^(3) / 3

Hence

f(x) = 3x^(2) / 3 +C

f(x) = x^(2) + C ' The '3' cancels out. The 'C' is a constant that comes with antoderivation.

It is a branch of maths that involves Calculating rates of change and irregular.curved volumes.

'The word 'Calculus' is Latin and means 'stones'. Where the ancients would have used stones/pebbles to make calculations.

Composite, because it can be divided by '2'.

NB All even numbers , except '2', are composite, therefore NOT prime.

All prime numbers are odd number, except '2'. However, not all odd numbers are prime numbers.

All EVEN numbers end in 0,2,4,6,8

All ODD numbers end in 1,3,5,7,9.

Since '76' ends in '6' , then it is an even number, hence composite.

64x^(2) - 5 = 11

Equate to zero , by subtracting '11' from both sides.

Hence

64x^(2) - 16 = 0

Algebraically rearrange

(8x)^(2) - 4^(2) = 0

We now have two squared terms with a negative between them. This factors to :-

(8x - 4)(8x + 4) = 0 Note the different signs in each brackets.

Hence

8x - 4 = 0

8x = 4

x - 4/8

x = 1/2

&

8x + 4 = 0

8x = -4

x = -4/8

x = -1/2

So the two solutions are x = 1/2 & x = -1/2

NB Twosquared terms with a POSITIVE(+) between them , does NOT factor.

The expression "8x for each value of x" means that you are multiplying the value of x by 8. This indicates that for every possible value of x, you will multiply that value by 8. For example, if x is 2, then 8 multiplied by 2 equals 16. This expression represents a linear relationship where the output is 8 times the input value of x.

One highly recommended textbook for learning advanced calculus is "Advanced Calculus" by Gerald B. Folland.