Two variables, vand w,are inversely proportional such that when v= 7, w= 14. What is the value of wwhen v= 2?
F. 1
To find the value of variable w when v=2, we can use the concept of inverse proportionality.
In an inversely proportional relationship, as one variable increases, the other variable decreases, and vice versa. Mathematically, we can express this relationship as v ∝ 1/w, where ∝ denotes proportionality.
We are given that v=7 when w=14. From this information, we can write the inverse proportionality equation as:
7 ∝ 1/14
To find the value of w when v=2, we can set up a ratio using the given proportionality equation:
7/1 = 1/14
We want to find w when v=2, which can be written as 2/1. So, we can set up a proportion:
7/1 = 1/14 = 2/1
Cross-multiplying, we get:
7 * 2 = 1 * 1/14 * w
14 = 1/14 * w
To solve for w, we can multiply both sides of the equation by 14:
14 * 14 = w
w = 196
Therefore, the value of w when v=2 is 196.