# The A to Z of mathematics a basic guide - Sidebotham T.H.

ISBN 0-471-15045-2

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, , distance , distance

distance = speed x time, speed = , time =-

time speed

Example. Amanda runs the 100 meters in 12.9 seconds. Find her speed in meters/ second and in kilometers/hour, assuming she runs at a constant speed throughout.

Solution. Write

distance

Speed = —;--------

time

100

= Substituting distance = 100, time = 12.9

= 7.75 (to 2 dp)

Amanda’s speed is 7.75 meters/second.

Now write

Speed = 7.75x3.6 1 meter/second = 3.6 kilometers/hour

= 27.9

Amanda’s speed is 27.9 kilometers/hour.

Reference: Displacement.

VELOCITY-TIME GRAPHS

Reference: Acceleration.

VERTEX

Reference: Edge.

VERTICAL

Reference: Horizontal.

VERTICALLY OPPOSITE ANGLES

469

VERTICAL LINE TEST

Reference: Correspondence.

VERTICAL PLANE

Reference: Inclined Plane.

VERTICALLY OPPOSITE ANGLES

When two straight lines intersect at a vertex there are two pairs of congruent angles. Angles at the vertex that are opposite each other are called vertically opposite angles, and are equal in size. In this geometry theorem, “vertically” has no reference to the word vertical, but is derived from the word vertex (see figure a):

Angle a = angle b and Angle c = angle d

(a)

Example. Figure b shows an open pair of scissors. If angle x = 47°, find the size of angle y.

(b)

Solution. Write

y = 47° Vertically opposite angles are equal Reference: Geometry Theorems.

470 VOLUME VOLUME

The volume of a solid shape is a measure of the three-dimensional space it occupies. It is measured in cubic units, which is written as units3. We can find the volume of a solid shape, say a cuboid, by counting the number of cubes that its three-dimensional space occupies. The volume of a cuboid measuring 3 cm by 2 cm by 3 cm can be found by counting the number of cubic centimeters (abbreviated cm3) it occupies. There are three layers of cubes, and in each layer there are six cubes, so the volume of the cuboid is 6 + 6 + 6 = 18 cm3.

length

Alternatively, the volume of the cuboid can be found using the formula (see the figure)

Volume = length x width x height

= 3x2x3 Substituting length = 3, width = 2,

and height = 3

= 18 cm3

For examples of finding the volumes of well-known solids see the respective entries. The units commonly used for volume are

♦ Cubic millimeter, mm3

♦ Cubic centimeter, cm3

♦ Cubic meter, m3

The relationships between these units are

1000 mm3 = 1 cm3

1,000,000 cm3 = 1 m3

When we are finding the volume of liquid that a vessel holds we say we are finding the capacity of the vessel.

References: Capacity, Cube, Cuboid, Metric Units.

WEST

Reference: East.

WHOLE NUMBERS

Reference: Integers.

WIDTH

Reference: Breadth.

471

X-AXIS

Reference: Cartesian Coordinates.

XCOORDINATE

Reference: Cartesian Coordinates.

472

Y

Y = MX+ C

References: Cartesian Coordinates, Gradient-Intercept Form, Graphs. YARD

Reference: Imperial System of Units.

473

z

ZENO’S PARADOX

Reference: Paradox.

474

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