Question

y is inversely proportional to the square root of x We know that y = 0.7875 when x = 64 What is y when x = 196? Give your answer as a decimal.

Answer 1

y = 0.45 when x = 196.

Explanation:

The general equation for inverse variation is given by:

y = k / x, where:

• y is inversely proportional to x,
• and k is the constant of proportionality.

Since y is inversely proportional to the square root of x, the equation for this problem is given by:

y = k / √x

----------------------------------------------------------------------------------------------------------Finding the constant of proportionality (k):

Since we know that y = 0.7875 when x = 64, we can substitute 0.7875 for y and 64 for x in y = k / √x to find k, the constant of proportionality:

0.7875 = k / √64

(0.7875 = k / 8) * 8

6.3 = k

Thus, the constant of proportionality (k) is 6.3

Therefore, the equation we'll use to find y when x = 196 is given by:

y = 6.3 / √x

Finding y when x = 196:

Now, we can find y when x = 196 by substituting 196 for x in y = 6.3 / √x:

y = 6.3 / √196

y = 6.3 / 14

y = 0.45

Therefore, y = 0.45 when x = 196.