Make $c$ the subject of the formula $c=-\frac{7}{3}\left[b+\frac{5}{a}(\nu-1)\right]$

Distribute − 3 7 ​ to the terms inside the brackets: c = − 3 7 ​ b − 3 7 ​ ⋅ a 5 ​ ( ν − 1 ) .
Simplify the second term: c = − 3 7 ​ b − 3 a 35 ​ ( ν − 1 ) .
Distribute − 3 a 35 ​ to the terms inside the parentheses: c = − 3 7 ​ b − 3 a 35 ν ​ + 3 a 35 ​ .
The final formula with c as the subject is: c = − 3 7 ​ b − 3 a 35 ν ​ + 3 a 35 ​ ​ .

Explanation

Initial Formula We are given the formula c = − 3 7 ​ [ b + a 5 ​ ( ν − 1 ) ] and we want to make c the subject. This means we want to isolate c on one side of the equation.

Distribute First, distribute the − 3 7 ​ to both terms inside the brackets: c = − 3 7 ​ b − 3 7 ​ ⋅ a 5 ​ ( ν − 1 ) c = − 3 7 ​ b − 3 a 35 ​ ( ν − 1 )

Distribute Again Next, distribute the − 3 a 35 ​ to both terms inside the parentheses: c = − 3 7 ​ b − 3 a 35 ν ​ + 3 a 35 ​

Final Answer So, we have successfully made c the subject of the formula: c = − 3 7 ​ b − 3 a 35 ν ​ + 3 a 35 ​ This is the final answer.


Examples
In physics, this type of formula manipulation is often used when dealing with equations of motion or energy conservation. For example, if c represents the final velocity of an object, b represents its initial velocity, a represents acceleration, and ν represents some other physical parameter, rearranging the formula allows you to solve for the final velocity given the other parameters. This is crucial in predicting the behavior of physical systems.

Answered by GinnyAnswer | 2025-07-03

To isolate c from the formula c = − 3 7 ​ [ b + a 5 ​ ( u − 1 ) ] , we distribute and expand the terms to arrive at c = − 3 7 ​ b − 3 a 35 ν ​ + 3 a 35 ​ .
;

Answered by Anonymous | 2025-07-04