Solve the equation for $a$.
[tex]g=\frac{5(-4 r-d)}{2 a}[/tex]
Answer (2)
Multiply both sides by 2 a : 2 a g = 5 ( − 4 r − d ) .
Divide both sides by 2 g : a = 2 g 5 ( − 4 r − d ) .
Simplify: a = 2 g − 20 r − 5 d .
The solution is: a = 2 g − 20 r − 5 d .
Explanation
Understanding the Problem We are given the equation g = 2 a 5 ( − 4 r − d ) and asked to solve for a . This involves isolating a on one side of the equation using algebraic manipulations.
Multiplying Both Sides First, we want to isolate a . To do this, we can multiply both sides of the equation by 2 a to get rid of the fraction: 2 a g = 5 ( − 4 r − d )
Dividing Both Sides Next, we want to isolate a by dividing both sides of the equation by 2 g :
a = 2 g 5 ( − 4 r − d )
Simplifying the Expression Finally, we can simplify the expression by distributing the 5 in the numerator: a = 2 g − 20 r − 5 d
Final Answer Therefore, the solution for a is: a = 2 g − 20 r − 5 d
Examples
In physics, this type of equation might relate gravitational force ( g ) to distance ( r ), density ( d ), and area ( a ). Solving for a allows you to determine the area needed to achieve a specific gravitational force given the other parameters. For example, if you know the gravitational force, distance, and density, you can calculate the required area using the solved equation. This is useful in designing experiments or understanding the relationships between physical quantities.
We solved the equation for a by isolating it through algebraic manipulations. The result is a = 2 g − 20 r − 5 d . This shows how a relates to the other variables in the equation.
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