Both u and v vary directly with each other. When u is 10, vis 15, which of the following is not a possible pair of corresponding values of u and v?
a. 2 and 3
b. 8 and 12
c. 15 and 20
d. 25 and 37.5
To determine if a given pair of values is possible for u and v, we need to check if they satisfy the direct variation relationship.
The direct variation relationship between u and v can be expressed as u = kv, where k is the constant of variation.
Given that when u is 10, v is 15, we can write:
10 = k * 15
k = 10/15
k = 2/3
Therefore, the equation that relates u and v is u = (2/3)v.
Now we can check which of the given pairs of values of u and v satisfy this equation:
a. 2 and 3: 2 = (2/3) * 3 -> 2 = 2, True
b. 8 and 12: 8 = (2/3) * 12 -> 8 = 8, True
c. 15 and 20: 15 = (2/3) * 20 -> 15 = 40/3, Not True
d. 25 and 37.5: 25 = (2/3) * 37.5 -> 25 = 25, True
Therefore, the pair of values 15 and 20 is not a possible pair of corresponding values of u and v. The correct answer is c. 15 and 20.