It means that y is a function of k.
To find the constant of variation ( k ) for an inverse variation, use the formula ( y = \frac{k}{x} ), where ( y ) and ( x ) are known values. Rearranging gives ( k = y \cdot x ). Once you have ( k ), you can write the equation for the inverse variation as ( y = \frac{k}{x} ). For example, if ( k = 12 ), the equation would be ( y = \frac{12}{x} ).
The constant variation for the relationship ( y = kx ) indicates that ( y ) varies directly with ( x ), where ( k ) is the constant of variation. This means that for any change in ( x ), ( y ) changes by a proportional amount determined by ( k ). If ( k ) is positive, ( y ) increases as ( x ) increases; if ( k ) is negative, ( y ) decreases as ( x ) increases. The value of ( k ) represents the rate of change between ( y ) and ( x ).
If ( y ) varies inversely as ( x ), this means ( y = \frac{k}{x} ) for some constant ( k ). Given that ( y = 24 ) when ( x = 8 ), we can find ( k ) by substituting these values: ( 24 = \frac{k}{8} ) which gives ( k = 192 ). Now, to find ( y ) when ( x = 4 ), we use the equation ( y = \frac{192}{4} ), resulting in ( y = 48 ).
A variable, Y, is inversely proportional to another variable, X if XY = k for some positive constant k. An equivalent formulation is Y = k/X. What this means is that if you double X, then Y is halved. If you treble X then Y is reduced to a third etc.
If the line ( De ) is parallel to the ( xy )-plane, it means that the value of ( y ) remains constant along that line. Therefore, ( y ) can take any specific value, but it does not change as ( x ) varies. In mathematical terms, this means ( y = k ) for some constant ( k ).
y means and
Using the distance formula it is the square root of: (h-x)^2 +(k-y)^2
Formula of a circle in a Cartesian plane: (x-h)^2+ (y-k)^2 = r^2 where the center is at (h,k) and the radius is r.
Equations: y = 3x +1 and x^2 +y^2 = k If: y = 3x +1 then y^2 = 9x^2 +6x +1 If: x^2 +y^2 = k then y^2 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant formula: k = 1/10 Using the quadratic equation formula: x = -3/10 By substitution: y = 1/10
To find the constant of variation ( k ) for an inverse variation, use the formula ( y = \frac{k}{x} ), where ( y ) and ( x ) are known values. Rearranging gives ( k = y \cdot x ). Once you have ( k ), you can write the equation for the inverse variation as ( y = \frac{k}{x} ). For example, if ( k = 12 ), the equation would be ( y = \frac{12}{x} ).
It is a straight line through the origin and, if k > 0 reflects a direct relationship between x and y. This means that each unit increase in x is associated with y increasing by k. If k < 0 it reflects a direct but negative relationship and this means that each unit increase in x is associated with y decreasing by k. If k = 0 then the result is the x-axis. This means that changes in x are not associated with changes in y. None of the above imply causation.
The constant variation for the relationship ( y = kx ) indicates that ( y ) varies directly with ( x ), where ( k ) is the constant of variation. This means that for any change in ( x ), ( y ) changes by a proportional amount determined by ( k ). If ( k ) is positive, ( y ) increases as ( x ) increases; if ( k ) is negative, ( y ) decreases as ( x ) increases. The value of ( k ) represents the rate of change between ( y ) and ( x ).
If: y = x^2 -2x -7 and y = 2x +k Then: x^2 -2x -7 = 2x +K Transposing terms: x^2 -4x +(-7 -k) = 0 Using the discriminant formula: 4^2 -4*1*(-7 -k) = 0 => k = -11 Using the quadratic equation formula: x^2 -4x +4 = 0 => x = 2 By substitution: y = -7 Therefore the values of the variables are: k = -11, x = 2 and y = -7
If ( y ) varies inversely as ( x ), this means ( y = \frac{k}{x} ) for some constant ( k ). Given that ( y = 24 ) when ( x = 8 ), we can find ( k ) by substituting these values: ( 24 = \frac{k}{8} ) which gives ( k = 192 ). Now, to find ( y ) when ( x = 4 ), we use the equation ( y = \frac{192}{4} ), resulting in ( y = 48 ).
Formula of a circle in a Cartesian plane: (x-h)^2+ (y-k)^2 = r^2 where the center is at (h,k) and the radius is r.
It means: And what are you doing right now?
A variable, Y, is inversely proportional to another variable, X if XY = k for some positive constant k. An equivalent formulation is Y = k/X. What this means is that if you double X, then Y is halved. If you treble X then Y is reduced to a third etc.