y=k√x
dy/dx=k/2√x
The given equation is y = k√x, where k is a constant.
To understand this equation, we first need to know what a square root is. A square root is the value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, since 5×5 = 25.
The symbol √ represents the square root operation. So, √x means the square root of x.
Now, in the given equation, we have y = k√x. This means that y is proportional to the square root of x, where the constant of proportionality is k.
To understand this better, let’s take a few examples. Suppose k = 2. Then, if x = 4, we have y = 2√4 = 2×2 = 4. Similarly, if x = 9, we have y = 2√9 = 2×3 = 6. As we can see, when x increases by a factor of 2 (from 4 to 8), y also increases by a factor of 2 (from 4 to 8). Similarly, when x increases by a factor of 3 (from 9 to 27), y also increases by a factor of 3 (from 6 to 18).
Thus, we can conclude that the given equation represents a relationship between two variables, y and x, where y is proportional to the square root of x. The constant of proportionality, k, determines how steep the relationship is. A larger value of k means a steeper relationship, while a smaller value of k means a flatter relationship.
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