Mathematics: If y is directly proportional to x square and y equal 1/8 when x = 1/2 what is the positive value of x when y it was 9/2? a) 3/4b) 3/2c) 9/4d) 3

If y is directly proportional to x square and y

21hendlill

01.02.2022

Step-by-step explanation:

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

y = kx² ← k is the constant of proportion

To find k use the condition y = $\frac{1}{8}$ when x = $\frac{1}{2}$ , then

$\frac{1}{8}$ = k( $\frac{1}{2}$ )² = $\frac{1}{4}$ k ( multiply both sides by 8 )

1 = 2k ( divide both sides by 2 )

k = $\frac{1}{2}$

y = $\frac{1}{2}$ x² ← equation of proportion

When y = $\frac{9}{2}$ , then

$\frac{9}{2}$ = $\frac{1}{2}$ x² ( multiply both sides by 2 )

9 = x² ( take the square root of both sides )

x = ± $\sqrt{9}$ = ± 3

with positive value x = 3 → d

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