Calculus

41 - y = 4y + 6

41 = 5y + 6


35 = 5y


7 = y

x=5

9

No

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

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

If: x = 7

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

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

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

The first successful English colony in America was established in 1607

5.34 x 9.4 = 50.19600

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

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

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.

9

method in wrinting a set

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

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.

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

If: 10x+7 = 5x+22

Then: 10x-5x = 22-7

And: 5x = 15

So: x = 3

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

==========

No real roots.

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.

Yes, It is a solution (a+)