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The statement " y varies inversely as x means that when x increases, y decreases by the same factor.In other words, the expression xy is constant:
xy = k
where k is the constant of variation.
We can also express the relationship between x and yas:
y = k / x
where k is the constant of variation.
Example 1: If y varies inversely as x , and y = 6 when x = , write an equation describing this inverse variation.
k = (6) = 8
xy = 8 or y = 8 / Z
That's an example of an inverse variation!
Example 2: If y varies inversely as x , and the constant of variation is k = , what is y when x = 10 ?
xy =
10y =
y = × = × =
k is constant. Thus, given any two points ( x 1, y 1 ) and ( x 2, y 2 ) which satisfy the inverse variation, x 1 y 1 = k and x 2 y 2 = k . Consequently, x 1 y 1 = x 2 y 2 for any two points that satisfy the inverse variation.
Example 3: If y varies inversely as x , and y = 10 when x = 6 , then what is y when x = 15 ?
x 1 y 1 = x 2 y 2
6(10) = 15y
60 = 15y
y = 4
Thus, when x = 6 , y = 4 .
Hope I helped!
What else can I help you with?
What is inverse variation in algebra?
x=yr
Can you can use rational functions to study the relationships of inverse variation?
yes
What is the difference between direct variation and inverse variation?
Direct variation is the ratio of two variable is constant. Inverse variation is when the product of two variable is constant. For example, direct variation is y = kx and indirect variation would be y = k/x .
In the inverse variation function what happens to the output when the functions input is doubled?
the output is halved
In the inverse variation function what happens to the output when the function's input value is divided by 5?
The output is multiplied by 5.
How do you write equations for each inverse variation?
it would be, X*Y=K (X multiplied by Y equals K) You get inverse equations when there is no specific number you are multiplying by. it can also be Y=K/X, hope this helps :)
What is the inverse variation?
The inverse variation is the indirect relationship between two variables. The form of the inverse variation is xy = k where k is any real constant.
How do you do a direct variation with an inverse variation problem?
If a variable X is in inverse variation with a variable Y, then it is in direct variation with the variable (1/Y).
What has the author Kozhanov A I written?
Kozhanov. A. I. has written: 'Composite type equations and inverse problems' -- subject(s): Differential equations, Inverse problems (Differential equations)
Find the constant variation k for the inverse variation then write an equation for the inverse variation y 2.5 when x 9?
The equation is xy = 22.5
How are direct variation and joint variation related?
Both are variations of certain kinds of equations. X=kY is a direct variation since X varies directly as Y and k is the constant of variation. X=k/Y is an inverse variation where X varies inversly as Y and k is the constant of variation. Both of these variations are also functions.
Does the graph of an inverse variation pass through the origin?
Inverse variation does not pass through the origin, however direct variation always passes through the origin.
What is the difference direct variation and inverse variation?
Direct variation is the ratio of two variable is constant. Inverse variation is when the product of two variable is constant. For example, direct variation is y = kx and indirect variation would be y = k/x .
Is y equals 24 divided by x a direct variation?
No, this is an inverse variation.
Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.?
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} ).
How do you use additive inverse in the real world?
The additive inverse is used to solve equations; equations, in turn, are used to model many real-world situations.
What is an example of inverse variation?
for variables x and y and constanat k -
