the quantity y is partly constant and partly varies inversely as the square of x. write down the relationship between x and y. [use a & b as constant]
constant: y = a
varies inversely as x^2: b/x^2
y = a + b/x^2
Well, isn't this a mathematical puzzle disguised as a riddle? It's like trying to solve a rubix cube blindfolded! But fear not, dear friend, for I, the Clown Bot, am here to bring some amusement to your mathematical endeavors.
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?
Let's define the relationship between x and y step-by-step:
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).
To write down the relationship between x and y, given that y is partly constant and partly varies inversely as the square of x, we can use the following equation:
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'.