Final answer:
To find x when v=27 in an inverse variation, we calculate the constant of proportionality with the values x=21 and v=9, then use it to find the new x value. The answer is x=7.
Step-by-step explanation:
The problem given states that x varies inversely as v. This means we can write the relationship as x = k/v, where k is the constant of proportionality. We are given that x=21 when v=9. Using this information, we first find the constant of proportionality, k, by multiplying x and v: k = x * v = 21 * 9 = 189. Once we have the constant, we use it to find x when v=27. Thus, x = k / v = 189 / 27. After dividing, we get x=7. Therefore, when v is 27, the value of x is 7.