Calculus

x + 3y = 4

-x + 2y = -4

Simultan eous eq'ns.

Eliminate 'x' by adding. 4

Hence

5y = 0

y = 0

When y = 0

Substitute

x + 3(0) = 4

x + 0 = 4

x = 4

So the answer as a coordinate pairs is ( x,y) = ( 4,0)

The equation ( \log_A 6 = B ) can be rewritten using exponents as ( A^B = 6 ). If we also have ( a^b = c ), we can express ( A ) as ( a ), ( B ) as ( b ), and ( 6 ) as ( c ). Thus, ( a = A ), ( b = B ), and ( c = 6 ).

ax - x = c

Factor 'x'

Hence

x(a - 1) = c (NB '1' is ONE , not 'I'. )

Divide both sides by 'a-1'

Hence

x = c/(a-1)

Solved for 'x'.

The derivative of ( \ln x ) is ( \frac{1}{x} ) for ( x > 0 ). This means that as ( x ) increases, the slope of the tangent line to the curve ( y = \ln x ) at any point ( x ) is given by ( \frac{1}{x} ).

Yes, any second category space is a Baire space. A topological space is considered to be of second category if it cannot be expressed as a countable union of nowhere dense sets. Baire spaces are defined by the property that the intersection of countably many dense open sets is dense. Therefore, since second category spaces avoid being decomposed into countable unions of nowhere dense sets, they satisfy the conditions to be classified as Baire spaces.

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Given a complex number z = a + bi, the conjugate z* = a - bi, so z + z*= a + bi + a - bi = 2*a. Note that a and b are both real numbers, and i is the imaginary unit: +sqrt(-1).

Non-exact differential equations are commonly applied in various fields such as physics, engineering, and economics. They can model systems where the relationship between variables is not straightforward, such as in fluid dynamics, where viscosity and turbulence complicate the equations. Additionally, they are used in control theory to describe dynamic systems that do not follow exact relationships, and in thermodynamics to analyze processes that involve non-conservative forces. Their solutions often provide insights into complex phenomena that require approximations or numerical methods.

Derivative classification involves incorporating classified information into new documents or materials. Criminal sanctions related to derivative classification can include fines, imprisonment, or both, depending on the severity of the violation. Additionally, individuals may face disciplinary actions, such as loss of security clearance or employment termination. It's essential for those handling classified information to understand and adhere to proper classification protocols to avoid these sanctions.

Authorized sources for derivative classification include official documents such as classified reports, intelligence assessments, and policy directives that contain classified information. Additionally, guidance from the originating agency, classification guides, and established standards for classification can serve as authorized sources. It's essential for individuals engaged in derivative classification to refer to these sources to ensure compliance with security protocols and maintain the integrity of classified information.

You cannot !!!

'cm'(centimetree) is a measure of LENGTH

'm^(3)' ( cubic metre) is a measure of VOLUME.

You need two more linear dimensions to convert to ccubic metre.

3x^(2) - 24x + 48

Factor out '3'

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

3(x - 4)(x - 4)

Fullt factored.

3^(2) + x = 25

9 + x = 25

x = 25 - 9

x = 16

Cricondentherm is the highest temperature at which a mixture of hydrocarbons can exist as a liquid and gas in equilibrium, while cricondenbar is the highest pressure at which the same equilibrium occurs. These terms are crucial in thermodynamics and petroleum engineering, particularly in understanding phase behavior of hydrocarbons. The hydrocarbon critical point is the specific temperature and pressure at which a pure hydrocarbon transitions into a supercritical fluid, exhibiting properties of both liquid and gas. Together, these concepts help in the design and optimization of processes involving hydrocarbon extraction and processing.

x^(4) dx =

x^(5) /5 [2,4] =>

4^(5)/5 - 2^(5)/5 =>

2^(10) / 5 - 2^(5) / 5

[2^(10) - 2^(5) ] / 5 =

[1024 - 32] / 5 =

992/5 = 198.4

x^(2) - 10x + 24

Since the coefficient of 'x^(2)' is '1', ; number not shownl we look at the constant '24'.

Write down all the factors of '24'. They are 1,2,3,4,6,8,12,& 24.

From this list we need to select two numbers that add to '10' and multiply to '24'.

The possibilities of addition ARE 4 + 6, 2+ 8 , & 12 -2.

However, only 4 + 6 = 10 & -4 x -6 = 24 , but -12 X 2 = -24 (Not +24).

So the only pair are '4' & '6'.

Set up factor brackets;)

(x 4)(x 6)

Since ;24; is positive (+) then the signs in the brackets are both the same. They can be either '+' or '-' .

Since the coefficient of 'x' is '-10' , then the signs are negative(-).

So fully factored it is

( x - 4)(x - 6)

An authorized source for derivative classification is any official document or information that has been classified by an original classification authority, and which provides the basis for deriving new classified information. This includes previously classified documents, reports, and other materials that contain sensitive data. Derivative classifiers must ensure that the new classification aligns with the original classification guidance, adhering to established policies and procedures. Examples include classified reports, intelligence assessments, and government publications that provide the necessary context for classification.

30

Let y = 5x

Then think y = 5x^(1)

Differentioation at its most simplistic is to move the exponential to be a coefficient. Then taking the original expoential subtract '1' from it , and use the answer as the new expoential .

Algebraically

y = Ax^(n)

dy/dx = Anx^(n-1)

So for the above example

y = 5x^(1)

dy/dx = 5(1)x^(1-1)

dy/dx = 5(1)x^(0)

Now any value to the power of '0' equa; '1'.

Hence

dy/dx = 5(1)(1)

dy/dx = 5 The answer.

Undefined: You cannot divide by zero

y = x^(1/2) (NB power of '1/2' mean the 'square root'.

Hence

dy/dx = (1/2)x^(-1/2)

or

dy/dx = 1/ [2x^(1/2)]

Remember SecX = 1/CosX

Substitute

SinX X 1 /CosX =

SinX / CosX =

TanX

A 9-sided polygon, is named 'Nonagon'.

The number of diagonals are '9'

From any one node, to the centre of the opposite side.

Since there are 9 nodes and 9 lines, then there will be 9 diagonals.

1

y + 1 = 0

y = -1

So it would be a straight line, parallel with the x-axis at y = -1.