When someone asks for how much you weigh
• Person 1: How much do you weigh?
• Person 2: 700 N
• Person 1: ...
Factor theorem

P(x) = a(x)^3 + b(x)^2 +cx + d = (a-x) [a(x)^2 + bx +c]
P(x) = (x-a) Q(x) + R
P(a) = (a-a) Q(x) + R = R

Velocity-time graphs

Therefore,

tan(Θ) of a velocity-time graph = “opposite”/”adjacent”

= (m.s-1)/s

= m.s-2

= “acceleration”

Note: Words have been placed in quotation marks to indicate words instead of pronumerals.

Brief description and comparison about number systems

A set (or group) of symbols that can be used to indicate magnitude or quantity, operations applied to the symbols and instructions of the applications of the operations for the symbols are, together, known as a number system

Two number systems are the real number system and the complex number system.

1. The real number system includes Q and Q’
2. The complex number system includes Polar Numbers

Other notes:

• The pronumeral (or symbol) “i” has a value of the square root of -1.
• i^2 = -1
Trigonometric ratios and transpositions of equations

1.

sin(Θ) = opposite/hypotenuse = a

therefore, sin-1(a) = Θ

2.

therefore, cos-1(a) = Θ

3.

therefore, tan-1(a) = Θ

Thermal diffusivity

Conduction is the transfer of heat energy from particle to particle in a substance. Convection is the transfer of heat energy by movement of particles (vector components). In convection, the more heat energy a particle has, the more it moves; noting that convection currents of higher heat energy usually rise and convection currents of lower heat energy usually move to lower areas.

Thermal diffusivity is the measurement of thermal inertia, which is the convection of heat energy throughout the substance. Thermal diffusivity can be measured using the equation

α = k/(pcp)

In this equation α represents the thermal diffusivity (the quotient), k represents the thermal conductivity, ρ represents density, and cP represents specific heat capacity. Thermal conductivity is measured in the SI derived physical quantity of W/(m × K); density in the derived physical quantity of kg/m3.

Volumetric heat capacity is measured in the derived physical quantity of J/(kg × K) and is represented by the denominator of pcp.

Force

F = ma

where,

• F represents force
• m represents mass
• a represents acceleration
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