Make $k$ the subject of $d=\frac{k+m}{2}$
Answer (1)
Multiply both sides of the equation by 2: 2 d = k + m .
Subtract m from both sides: 2 d − m = k .
Therefore, make k the subject of the formula.
The final answer is k = 2 d − m .
Explanation
Understanding the Problem We are given the equation d = 2 k + m and we want to isolate k on one side of the equation. This means we want to rewrite the equation in the form k = some expression involving d and m .
Multiplying by 2 To isolate k , we first multiply both sides of the equation by 2 to get rid of the fraction: 2 × d = 2 × 2 k + m 2 d = k + m
Subtracting m Next, we subtract m from both sides of the equation to isolate k :
2 d − m = k + m − m 2 d − m = k Thus, we have k = 2 d − m .
Final Answer Therefore, k is the subject of the formula and the equation is k = 2 d − m .
Examples
In physics, if you know the average distance d an object travels and the additional distance m due to some external factor, you can find the initial distance k using the formula k = 2 d − m . For example, if the average distance d is 10 meters and the additional distance m is 2 meters, then the initial distance k is 2 ( 10 ) − 2 = 18 meters. This concept applies to various scenarios where you need to isolate a variable to understand its relationship with other quantities.
