find the variation constant and an equation of variation where y varies directly as x and y = 54 when x =x6
" y varies directly as x" ---> y =kx, where k is a constant.
if x= ?? , is that a typo? , then y = 54
plug in those two values into y = kx,
solve for k and put that back into the equation.
(if you mean x = x^6, then
54 = kx^6
k = 54/x^6
then y = (54/x^6) (x) = 54/x^5 )
To find the variation constant and equation of variation when y varies directly as x, we can use the formula:
y = kx
where k represents the variation constant.
Given that y = 54 when x = 6, we can substitute these values into the equation:
54 = k * 6
To find the value of k, we can solve for it:
k = 54 / 6 = 9
Hence, the variation constant is 9.
Now we can substitute the value of k into the equation:
y = 9x
Therefore, the equation of variation is y = 9x when y varies directly as x.
To find the variation constant and the equation of variation where y varies directly as x, we can use the formula for direct variation:
y = kx
In this equation, y represents the dependent variable, x represents the independent variable, and k is the variation constant.
Given that y = 54 when x = x6, we can substitute these values into the equation:
54 = k * x6
To find the value of k, we need to solve for it. Divide both sides of the equation by x6:
54/x6 = k
Simplifying the right side, we get:
k = 54/x6
So, the variation constant is equal to 54 divided by x6.
The equation of variation is then:
y = (54/x6) * x
Alternatively, we can simplify it to:
y = (54/x6) x
This represents the direct variation relationship between y and x, with the variation constant being 54/x6.