Question

Yis inversely proportional to the square of x. If Y= 3 when x = 2, find Y, when xis 1.

For full credit:
1. Write a proportion.
2. Solve for y.
3. Show work.

Answer 1

3/4 or 0.75

Explanation:

1. Based on the given information, we can write the proportion as follows:

Y₁ / (x₁)² = Y₂ / (x₂)²

where Y₁ and x₁ represent the initial values of Y and x, respectively, and Y₂ and x₂ represent the values we want to find.

2. Let's solve the proportion for Y₂:

Y₁ / (x₁)² = Y₂ / (x₂)²

Substituting the given values:

3 / (2)² = Y₂ / (1)²

Simplifying the equation:

3 / 4 = Y₂ / 1

Cross-multiplying:

3 = 4Y₂

3/4 = Y₂

3. Therefore, Y₂ is equal to 3/4 or 0.75.