Question

Express y in terms of x

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

Given y is inversely proportional to x² then the equation relating them is

y = $\frac{k\\}{x^2}$ ← k is the constant of variation

To find k use any ordered pair from the table.

Using (1, 4 ) , then

4 = $\frac{k}{1^2}$ = $\frac{k}{1}$ ( multiply both sides by 1

4 = k

y = $\frac{4}{x^2}$ ← equation of variation

(b)

When y = 25 , then

25 = $\frac{4}{x^2}$ ( multiply both sides by x² )

25x² = 4 ( divide both sides by 25 )

x² = $\frac{4}{25}$ ( take the square root of both sides )

x = ± $\sqrt{\frac{4}{25} }$ = ± $\frac{2}{5}$

Since x > 0 then x = $\frac{2}{5}$