Warning (2): file_get_contents(): https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ed%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22italic%22%3Emass%3C%2Fmi%3E%3Cmi+mathvariant%3D%22italic%22%3Evolume%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22italic%22%3Ekg%3C%2Fmi%3E%3Cmsup%3E%3Cmrow%3E%3Cmo%3E%28%3C%2Fmo%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmo%3E%29%3C%2Fmo%3E%3C%2Fmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi+mathvariant%3D%22italic%22%3Ekg%3C%2Fmi%3E%3Cmsup%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ev%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22italic%22%3Edistance%3C%2Fmi%3E%3Cmi+mathvariant%3D%22italic%22%3Etime%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22italic%22%3Ems%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ea%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22italic%22%3Evelocity%3C%2Fmi%3E%3Cmi+mathvariant%3D%22italic%22%3Etime%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22italic%22%3Ems%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmi%3Es%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22italic%22%3Ems%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents() [function.file-get-contents]: https:// wrapper is disabled in the server configuration by allow_url_fopen=0 [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Warning (2): file_get_contents(https://www.wiris.net/demo/editor/render.png?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EP%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3E%3C%2Fmi%3E%3Cmfrac%3E%3Cmi+mathvariant%3D%22italic%22%3Eforce%3C%2Fmi%3E%3Cmi+mathvariant%3D%22italic%22%3Earea%3C%2Fmi%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmfrac%3E%3Cmrow%3E%3Cmi+mathvariant%3D%22italic%22%3Ekg%3C%2Fmi%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22italic%22%3Ems%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmsup%3E%3Cmi%3Em%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmfrac%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22italic%22%3Ekg+ms%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E1%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmsup%3E%3Cmi%3Es%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3Cmi+mathvariant%3D%22italic%22%3Eor%3C%2Fmi%3E%3Cmsup%3E%3Cmi+mathvariant%3D%22italic%22%3ENm%3C%2Fmi%3E%3Cmrow%3E%3Cmo%3E-%3C%2Fmo%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmsup%3E%3C%2Fmath%3E) [function.file-get-contents]: failed to open stream: no suitable wrapper could be found [ROOT/vendors/mathml_to_image.php, line 6]
file_get_contents - [internal], line ??
grabDataImage - ROOT/vendors/mathml_to_image.php, line 6
string_between - ROOT/vendors/mathml_to_image.php, line 30
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
string_between - ROOT/vendors/mathml_to_image.php, line 34
math_to_image - ROOT/vendors/mathml_to_image.php, line 51
TopicsController::viewOnSearchTopic() - APP/Controller/TopicsController.php, line 98
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 490
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 191
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 165
[main] - APP/webroot/index.php, line 108
Fundamental units are those which are neither derived from one another nor can be dissolved. Eg. Units of mass, there are 7 basic units of measurement.
Systems of units:-
CGS system:- in which units of length, mass and time, in cm, gram & seconds.
FPS:- in which fundamental meter, units in foot, kilogram, pound & second.
MKS:- meter, kilogram & second.
SI unit:-
In SI system (System international d units)
SI units for seven basic quantities:-
Name of quantity
Symbol
Name of SI unit
Symbol for SI unit
Length
L
Meter
M
Mass
M
Kilogram
Kg
Time
t
Second
S
Temperature
T
Kelvin
K
Electric current
I
Ampere
A
Luminous intensity
Iv
Candela
Cd
Quantity of matter
N
Mole
Mol
Derived units:- these are obtained from basic units:-
There are:-
Area = length x breadth = m x m = m2
Volume:- V = length x breadth x height
= m x m x m = m3
iii. Density (d) =
iv) Velocity (v)
v) Acceleration (a)
vi) Force (f) f = mass x acceleration = kg ms-2 unit of force = Newton
(vii) Pressure
Its unit is also called as Pascal (Pa)
Symbols of commonly used prefixes in power of ten
Deci. (d) 10-1
Deca. (da) 101
Conti. (c) 10-1
Hecto. (h) 102
Milli. (m) 10-3
Kilo. (K) 103
Micro. (µ)10-6
Mega. (M) 106
Mono. (η) 10-9
Giga (G) 109
Pico (P) 10-12
Tetra (T) 1012
Fento (f) 10-15
Peta (P) 1015
Alto (a) 10-18
Exa (E) 1015
Zepto (z) 10-21
Zeta (Z) 1021
Yocto (y) 10-24
Yotta (Y) 1024
Some other inter conversions:-
1 mile = 1.6 km = 1.6 x 103 m
1 hour = 60 x 60 = 3600 s
1 foot = 12 inches
1 inch = 2.5 x 10-2m = 2.5 cm
1 pound = 0.453 kg = 453 g
1 m3 = 100 x 100 x 100 cm3
1 m3 = 106 cm3
Mass and weight:-
Mass:- mass of a substance is the amount of matter present in it and it is constant.
Weight:- it’s the force exerted by gravity on an object. It may vary from one place to another.
Significant figures (S.F)
The significant figures in any number are all the certain digits with last digit uncertain or doubtful.
Rules for reporting S.F:-
All non-zero digits in a number are significant.
The zeros between two non-zero digits are always significant.
The zeros written to the L.H.S of first non-zero digit in a number are not significant.
All the zeros placed on right of decimal point are significant.
Note:- if any number ends in zero without any decimal, then zeros may or may not be significant.
Example:- in (i) 44.3 S.F 3
(ii) 5.243 S.F 4
(iii) 44.2 S.F 3
6.01 has 3 S.F
6.001 has 4 S.F
0.523 has 3 S.F
0.002 has 1 S.F
0.016 has 2 S.F
11.0 has 3 S.F
15.00 has 4 S.F
16.000 has 5 S.F
The no. 25000 may have 2,3,4 or 5 S.F so to remove this confusion scientific notation is used i.e. N x 104
Where N => a no. with single non-zero digit to the left of decimal point.
SureDen