Calculus

The first successful English colony in America was established in 1607

41 - y = 4y + 6

41 = 5y + 6


35 = 5y


7 = y

X/-5 + 4 = 24

multiply through by -5

X - 20 = -120

add 20 to each side

X = -100

check

-100/-5 + 4 = 24

20 + 4 = 24

checks

No

9

Convert the equation into y = mx + b form:

2x + 3y = 6

-2x -2x

3y = 6 - 2x

Divide both sides by 3:

y = 2- 2/3x

If we move the terms around to put in in y = mx + b:

y = -2/3x + 2

m is the slope, so the slope is -2/3

x=5

9

If: x = 7

Then: y = (2*7)+3 = 17

And: 5x+y = (5*7)+17 = 52

Use natural logs.

5^(8-2X) = 25

ln5^(8-2X) = ln25

8-2X ln5 = ln25

8-2X = ln25/ln5

8-2X = 2

subtract 8 from each side

-2X = -6

divide each side by -2

X = 3

check

5^(8-3(2)) = 25

5^2 = 25

25 = 25

checks

4 e - 9 = 19

+ 9 = + 9 Inverse of -9

---------------------

4 e +0 = 38 -9+9 cancels

----- -------

4 4 Divide 4 to both sides

----------------------

e = 9.5 OR 9 R2

Writing equations in questions is problematic - some symbols regularly get eliminated.The integral of e to the power x is: e to the power x + C

If your expression contains no variables, for example e times e, or e to the power e, then the entire expression is a constant; in this case, the integral is this constant times x + C.

The slope of the line that represents the graph of that equation is 15.

The amplitude is 1.

method in wrinting a set

(8+5)*5-8-8=49

No real roots.

When an equation has two variables, there are an infinite number of (x,y) pairs

that solve it. The equation can be graphed as a straight, curved, or wiggly line,

and every point on the line is a solution of the equation.

There's no single (x,y) point until you have two separate equations. Then

the solution is the point ... or few points ... where their graphs intersect.

375 million

X2 + 2X - 4 = 0

Use the discriminant to find out.

b2 - 4ac

a = 1

b = 2

c = - 4

22 - 4(1)(- 4)

4 + 16 = 20 > 1

=============so,

Two real solutions.

Why not? Just a second integration. Drop the constant.

int[- cos(x)] dx

the negative implies - 1 and can be brought out side the integrand

- int[cos(x)] dx

= - sin(x) + C

==========

If: 10x+7 = 5x+22

Then: 10x-5x = 22-7

And: 5x = 15

So: x = 3

Fourier analysis began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions.

The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in Fourier analysis.

Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation.

If you want to find out more, look up fourier synthesis and the fourier transform.

1 millimetre = 0.1 centimetre.

first:you find the gcm(greatest common factor)wich is the lowest number that can go evenly into the numerator and the denominator.

next:you devide both the numerator and the denominator by that gcm(greatest common factor)and walla!