x is partly constant and partly varies as y when y=5, x=7,and y=7,x=8.find the law of variation and also x, when y=11
x = a+ky
7 = a+5k
8 = a+7k
x = 9/2 + y/2
x(11) = 10
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To find the law of variation and the value of x when y=11, we need to analyze the given data points.
We are given that x is partly constant and partly varies as y. This suggests that x can be expressed as a sum of a constant term and a term that depends on the value of y.
Let's start by finding the constant term. When y=5, we are given that x=7. This means that when y is 5 units, the constant term contributes a value of 7 to x.
Now, let's find the varying term. We are told that when y=7, x=8. This implies that the varying term contributes a value of 1 when y increases by 2 units (from 5 to 7).
To determine the varying term per unit change in y, we divide the change in x (1) by the change in y (2). This gives us 1/2 or 0.5.
Therefore, the relationship between x and y is described by the equation:
x = constant term + (0.5 * y)
We already found the constant term to be 7. Plugging in this value, the equation becomes:
x = 7 + (0.5 * y)
To find the value of x when y=11, substitute y=11 into the equation:
x = 7 + (0.5 * 11)
x = 7 + 5.5
x = 12.5
Therefore, when y=11, x=12.5.
The law of variation is x = 7 + (0.5 * y), and when y=11, x=12.5.