Roots

Roots

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Exponents and Roots

Exam Prep Study Notes (Things to remember) 

Exponent

An exponent is the power or total number of times a given number or expression can be raised, and is often expressed as a raised symbol to the right side of the number or expression. E.g. x2, where 2 is exponent

Multiplying exponents

When multiplying like bases, you must add the exponents. e,g xa * xb = xa+b 

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Tips

Raise an exponent to another power

To raise an exponent to another power, multiply the exponents. e.g. (xa)b = xab

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Periodic compounding

The total accumulated value, including the principal sum plus compounded interest , is given by the formula:

where:

P is the original principal sum
P' is the new principal sum
r is the nominal annual interest rate
n is the compounding frequency
t is the overall length of time the interest is applied (expressed using the same time units as r, usually years).
 

Logarithmic formulae

logb(1) = 0
logb(b) = 1
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‹ Equations          up          Fractions and Decimals ›

 

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Cube

Cube

Regular hexahedron
Hexahedron.jpg
(Click here for rotating model)
Type
Platonic solid
Elements
F = 6, E = 12
V = 8 (χ = 2)
Faces by sides
6{4}
Conway notation
C
Face configuration
V3.3.3.3
Dihedral angle
90°
Cube vertfig.png
4.4.4
(Vertex figure)
Octahedron (vector).svg
Octahedron
(dual polyhedron)
Hexahedron flat color.svg
Net

Net of cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.

The cube is dual to the octahedron. It has cubical or octahedral symmetry.

The cube is the only convex polyhedron whose faces are all squares. Without the convex restriction, there's one more such figure, which is made out of 7 cubes; it can be formed by putting one cube in the center and attaching a congruent cube to each of its faces.

Video: Cubes - Faces, Vertices and Edges

Orthogonal projections

The cube has four special orthogonal .....

 

 

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