Calculus

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.

That is 2.333 ounces

Ah, surds are like little puzzles in mathematics that help us solve real-world problems with precision and accuracy. You might not realize it, but they are used in various fields like engineering, architecture, physics, and even computer science. Embrace the beauty of surds, my friend, for they are the key to unlocking the mysteries of the world around us.

Oh, dude, math time! So, like, 56 times 6 equals 336. Boom, there you go. Math wizardry at its finest.

The volume of a cylinder is given by the equation V=2*pi*r*h

V=volume

r=radius

h=height

Since the height and volume are given in this case, rearranging the equation will show that r= V / (2*pi*h). With that equation you can find the radius of any cylinder with known volume and height.

Well, isn't that a happy little question! When you multiply 20 by 0, you get 0. It's like having 20 friends over for a painting party, but if no one shows up, you still have a peaceful time painting by yourself.

Oh, dude, molecule x-y-x has a linear shape with bond angles of 180 degrees. It's like a straight line, you know? So, if you're ever in a geometry competition and they ask about x-y-x, just remember it's as straight as a ruler.

To factor the expression x^3 + 5x^2 + 6x, we first look for common factors among the terms, which is x. Factoring out x gives us x(x^2 + 5x + 6). Next, we factor the quadratic expression x^2 + 5x + 6 by finding two numbers that multiply to 6 and add up to 5, which are 2 and 3. Therefore, the factored form of x^3 + 5x^2 + 6x is x(x + 2)(x + 3).

C equals the speed of light in a vacuum, which is approximately 299,792,458 meters per second. So if you're looking for a simple answer, there you have it. Just remember, I'm not here to hold your hand through the world of physics, honey.

0

Y is the output and X is the input.

one hundred seventy-five million

The highest number ever counted to is theoretically infinite. In mathematics, there is no limit to how high a number can be counted. However, in practical terms, the highest number ever counted to by a human or a computer is limited by time and resources. The largest number typically used in mathematics and science is known as Graham's number, a number so large it cannot be expressed using standard notation.

Ah, a half power is like giving x a gentle hug and telling it to take a deep breath. It means finding the square root of x, which is like finding the number that, when multiplied by itself, equals x. So, x to the half power is just a way of saying the square root of x, allowing us to simplify and understand things in a beautiful way.

To multiply 2x by 2y, you would use the distributive property of multiplication over addition. This means you would multiply each term in the first expression by each term in the second expression. In this case, 2x * 2y would result in 4xy, as 2 * 2 equals 4 and x * y equals xy.

Oh, absolutely! When we talk about x to the power of 2, we're simply saying x multiplied by itself, which is the same as x squared. It's like painting a beautiful little tree with just a few brushstrokes - different ways of saying the same thing, but all leading to a lovely result.