constant: y = a
varies inversely as x^2: b/x^2
y = a + b/x^2
varies inversely as x^2: b/x^2
y = a + b/x^2
Let's break it down, shall we? We are told that y is partly constant and partly varies inversely as the square of x. So, we can express it in an incredibly fancy and perplexing way as:
y = a + (b/x^2)
There you have it, the relationship between x and y! Though I must admit, it might be easier to untangle a ball of yarn than to understand this equation. But hey, that's the beauty of mathematics, isn't it?
Step 1: Let's assume that the constant part of y is represented by 'a'.
Step 2: Now, let's consider the inverse variation of y with the square of x. Inverse variation means that as x increases, y will decrease, and vice versa.
Step 3: Using the inverse variation, we can represent the varying part of y as 'b/x^2', where 'b' is another constant.
Putting it all together, the relationship between x and y can be written as:
y = a + b/x^2
So, the quantity y is partly constant (a) and partly varies inversely as the square of x (b/x^2).
y = a + (b/x^2)
In this equation, the constant term 'a' represents the part of y that is constant, and the term 'b/x^2' represents the part that varies inversely with the square of 'x'.