Find the variation constant and an equation of variation where y varies directly as x and y=50 when x=10
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y = k x
50 = k * 10
k = 5
y = 5 x
In this case, since y varies directly with x, the equation of variation can be written as y = kx, where k is the variation constant.
To find the value of k, we can rearrange the equation and substitute the given values of y and x:
y = kx
50 = k * 10
Now solve for k:
k = 50 / 10
k = 5
So the variation constant (k) is 5.
Substituting this value back into the equation of variation, we have:
y = 5x
Therefore, the equation of variation where y varies directly as x is y = 5x.
To find the variation constant and equation of variation where y varies directly as x, we can use the formula:
y = kx,
where k is the variation constant.
Given that y = 50 when x = 10, we can substitute these values into the formula:
50 = k(10).
To solve for k, we divide both sides of the equation by 10:
50/10 = k.
Simplifying the equation gives us:
5 = k.
Therefore, the variation constant, k, is equal to 5.
To find the equation of variation, we substitute the value of k into the formula:
y = kx.
Therefore, the equation of variation is:
y = 5x.