Question

y∝1/√x If y=12 when X=9 find, x when y=4

Answer 1

Answer:

When y = 4, x = 81

Step-by-step explanation:

We have,

y ∝ (1/√x)

Now, to remove the Proportionality symbol, we are adding in a constant k.

So,

y = k(1/√x)

Squaring both sides we get,

(y)² = (k(1/√x))²

y² = k² × (1/√x)²

y² = k² × (1/x)

y² = k²/x

k² = xy²

Now,

we are given,

When y = 12, x = 9

So, putting in the values,

k² = (9)(12)²

k² = 9 × 144

k² = 1296

k = √1296

k = 36

Hence,

The constant 'k' will always have the value of 36, and is independent of the values of x or y.

So,

When y = 4,

k² = xy²

36² = x(4)²

1296 = 16x

x = 1296/16

x = 81

Hence,

When y = 4, x = 81

Hope it helped and believing you understood it........All the best