y is directly proportional to x².
It is know that y=5 for a particular value of x.
Find the value of y when x is halved.
y = kx^2
if you replace x with x/2, then the new y is
k(x/2)^2 = 1/4 kx^2
so the y value is divided by 4
think of the way area scales when the linear dimensions are changed.
To find the value of y when x is halved, we need to understand the concept of direct proportionality first.
In a direct proportion, when one variable (in this case, x) is multiplied by a constant factor (in this case, 1/2, because we want to find the value of y when x is halved), the other variable (y) is also multiplied by the same constant factor.
Given that y is directly proportional to x², we can write the relationship as y = kx², where k is the constant of proportionality.
We also know that for a particular value of x, y = 5. Using this information, we can substitute these values into the equation and solve for k.
5 = kx²
Now, we need to find the value of k. Let's rearrange the equation to solve for k:
k = 5 / x²
Since we know the value of y when x is halved, we need to substitute x with (1/2)x:
k = 5 / ((1/2)x)²
Next, we simplify the equation:
k = 5 / (1/4)x²
k = 20 / x²
Now, we have the value of k. Let's substitute it back into the original equation:
y = (20 / x²) x²
y = 20
So, when x is halved, the value of y will be 20.