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A dimensional equation is one in which the units of measurement and their powers are used rather than their actual numeric values.
For example, consider an object under constant acceleration:
let u denote its initial velocity
v denote its final velocity
a the acceleration
and t the time between the initial and final points of time.
Then v = u +at
The dimensional equation is
[LT-1] = [LT-1] + [LT-2][T]
L represents a dimension of length
T represents a dimension of time
M, which does not appear here, would represent mass.
Only terms with the same dimensions may be added or subtracted.
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Can dimensional analysis be used to check equation validity?
Yes.
What are the used of dimensional equation?
A dimensional check in an equation can provide a quick check about the possible correctness of the equation. For example, if you are supposed to calculate a speed, the dimensions of the result MUST be of the form [distance] / [time] (or something that you can simplify to distance/time). If it doesn't, the formula is wrong. If it does, it MIGHT be correct.
What satisfies an equation in two variables?
An ordered pair or coordinates of a point in 2-dimensional space.
What is the geometrical representation of a linear equation?
A line, "living" in N-dimensional space, where N is the number of variables.
What is -2x-3y plus 5z equals 7?
It is the equation of a line in 3-dimensional space.
Can dimensional analysis be used to check equation validity?
Yes.
What is -3x-5y equals 21?
It is a linear equation in two dimensional space. Such an equation defines a line in 2-d
What is an ordered pair that makes an equation in two variables true is called?
A solution (in 2-dimensional space).A solution (in 2-dimensional space).A solution (in 2-dimensional space).A solution (in 2-dimensional space).
What are the used of dimensional equation?
A dimensional check in an equation can provide a quick check about the possible correctness of the equation. For example, if you are supposed to calculate a speed, the dimensions of the result MUST be of the form [distance] / [time] (or something that you can simplify to distance/time). If it doesn't, the formula is wrong. If it does, it MIGHT be correct.
Is it true that dimensional analysis can tell whether an equation is physically correct?
yes
What is the equation for volume on a triangle?
Since a triangle is two-dimensional, it cannot have volume.
What are the examples of three unknown equation?
The location of a point in 3-dimensional space.
What is 5cm3 x 15cm3 plus 103 equals?
An equation in 6 dimensional space!
What satisfies an equation in two variables?
An ordered pair or coordinates of a point in 2-dimensional space.
What is the geometrical representation of a linear equation?
A line, "living" in N-dimensional space, where N is the number of variables.
What is -2x-3y plus 5z equals 7?
It is the equation of a line in 3-dimensional space.
What are the different kinds of linear equation?
There can be linear equations with 1, 2, ... variables. Each of these is different since an equation with n variables belongs to n-dimensional space.
