Final answer:
To find the value of x when v is 16, knowing x varies inversely as v and x equals 6 when v is 8, multiply x and v to find the constant (48). Then, use this constant to determine that x equals 3 when v is 16.
Step-by-step explanation:
If x varies inversely as v, it means that the product of x and v is constant. Given that x = 6 when v = 8, we can find the constant by multiplying these two values: 6 × 8 = 48. This constant value must hold true for all values of x and v that are inversely proportionate to each other.
To find the value of x when v = 16, we set up the equation x × 16 = 48. Dividing both sides by 16 to solve for x gives x = 48 / 16 = 3. Therefore, x equals 3 when v equals 16. The correct answer is a. 3.