You can write ordered pairs as ratios to determine if two sets of ordered pairs form a linear or non-linear relationship. In a table of x,y values, the ordered pairs are listed as the x value first, then the corresponding y value. Remove from the table and write as a ratio of x over y, (or y over x, if you like). In a linear relationship, all the ratios of x over y, (or y over x) are equivalent.
x = time, y = magnitude
They are proportional if a change in one of the quantities always and necessarily results in a proportional change in the other.So if you think of a simple equation, x = 2y then the quantities are proportional. If you double y then x is necessarily also doubled. If you triple y then x is also tripled. If you halve y then x is halved and so forth.However x = 2y + 1 is non proportional. This is because if, for example, you double y then x is increased but it is not exactly doubled and so the change is not in proportion. For example, in this equation, when y = 2 then x = 5. When y = 4 then x = 9. 9 is not the double of 5.
Given a unit circle (radius = 1) and a counterclockwise angle (theta) between the positive x axis, with the x-y coordinate of the point on the circle that the angle intersects, the three basic trigonometric ratios are... 1. sine (theta) is y 2. cosine (theta) is x 3. tangent (theta) is x / y
A set X is called a proper subset of a set Y if X is contained in Y but not equal to Y.
An identity is a statement which says two quantities are equal, like as x + y = y + x or sin (x + y ) = sin x cos y + cos x sin y .
A ratio is the quotient of two numbers or quantities giving their relative size. The ratio of x to y is written as x : y and is unchanged if both quantities are multiplied or divided by the same quantity. So 2 : 3 is the same as 6 : 9and 1 : 3/2.
Any two non-zero quantities are always proportional. If the two quantities are X and Y, they are proportional to X/Y.
You can write ordered pairs as ratios to determine if two sets of ordered pairs form a linear or non-linear relationship. In a table of x,y values, the ordered pairs are listed as the x value first, then the corresponding y value. Remove from the table and write as a ratio of x over y, (or y over x, if you like). In a linear relationship, all the ratios of x over y, (or y over x) are equivalent.
x = time, y = magnitude
When there is at least one pair of x and y whose ratio is different from the ratios for the others.
Two quantities are said to be in the Golden Ratio if the ratio of the larger to the smaller is the same as the ratio of their sum to the larger. Algebraically, if X and Y are the two quantities and X<Y, then Y/X = (X+Y)/Y This gives the ratio as 0.5*[1 + sqrt(5)] = 1.61803...
I Have No Clue, Please Help Me...? * * * * * It depends on the direction of the relationship. Consider y = x2 where x is a real number. The relationship from x to y is a function but the one in the opposite direction (x = sqrt(y) is not a function because it is a one-to-many mapping.
Two quantities are in a Golden Ratio if the ratio of the bigger quantity to the smaller quantity is the same as the ratio of the sum of the two quantities to the bigger quantity. In algebraic form, if the two quantities are x and y, and x is the bigger of the two, then they are in the Golden Ratio if x/y = (x+y)/x and that ratio is the Golden Ratio. which equals (1 + √5)/2.
As x increases, y decreases
They are proportional if a change in one of the quantities always and necessarily results in a proportional change in the other.So if you think of a simple equation, x = 2y then the quantities are proportional. If you double y then x is necessarily also doubled. If you triple y then x is also tripled. If you halve y then x is halved and so forth.However x = 2y + 1 is non proportional. This is because if, for example, you double y then x is increased but it is not exactly doubled and so the change is not in proportion. For example, in this equation, when y = 2 then x = 5. When y = 4 then x = 9. 9 is not the double of 5.
If there is any ratio like x:y , then x:y = x divided by y. if there are 2 ratios , x:y and a:b , then x:y / a:b = (x/y)/(a/b) = x/y * b/a = xb/ya.