The y is directly proportional to x2 and y = m for a particular value of x. Find an expression for y in terms of m, when this value of x is doubled.
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Explanation
If y is directly proportional to x², it means that:
y ∝ x²
This can be written as an equation:
y = kx²
where k is the constant of proportionality.
Given Information:
We are given that y = m for a particular value of x. Let's call this value x₁.
So, we have:
m = kx₁²
Doubling the Value of x:
Now, we double the value of x. Let's call this new value x₂. So, x₂ = 2x₁.
We want to find the new value of y, let's call it y₂, when x = x₂.
Using the proportionality equation:
y₂ = kx₂²
Substitute x₂ = 2x₁:
y₂ = k(2x₁)²
y₂ = 4kx₁²
Substituting the value of kx₁² from the first equation:
We know that kx₁² = m. So, we can substitute this into the equation for y₂:
y₂ = 4m
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