It is given that y is directly proportional x ^ n Write down the value of n when
(i) y * m ^ 2 is the area of a square of length x m,.
Tell the value of k
If y is directly proportional to x^n, we can write:
y = kx^n
where k is the constant of proportionality.
(i) If y * m^2 is the area of a square of length x m, we can write:
y * m^2 = x^2
Substituting y = kx^n, we get:
kx^n * m^2 = x^2
Simplifying, we get:
k = x^(2-n) / m^2
Since the area of a square is given by side^2, we can write:
y * m^2 = x^2
y = x^2 / m^2
Substituting k, we get:
y = kx^n
x^2 / m^2 = kx^n
Simplifying, we get:
n = 2
Therefore, the value of n is 2. The value of k can be found using the equation:
k = x^(2-n) / m^2
Substituting n = 2, we get:
k = x^0 / m^2
k = 1 / m^2