Question

Spencer chooses to solve for this quantity by performing variable elimination in the order of − − z−x−c. Answer the following prompts to work your way through this procedure. What mathematical technique is Spencer using?

Answer 1

Spencer is employing the mathematical method of variable elimination to solve for an unknown quantity in an equation or set of equations by identifying knowns, choosing equations with the unknown, simplifying, and checking the result.

Step-by-step explanation:

Spencer is using the technique of variable elimination to solve for a quantity by systematically removing variables from an equation or a system of equations. This mathematical approach involves identifying the known variables and selecting the appropriate equation(s) that contain the desired unknown variable. In this case, Spencer has a sequence for eliminating variables: −z−x−c. To execute this, Spencer would:

1. Identify the known variables, such as v=0.500c and u'= -0.750c in the given example.
2. Identify the unknown variable that needs to be solved for, in this case u.
3. Choose the most appropriate equation that relates the knowns with the unknown.
4. Eliminate terms wherever possible to simplify the algebra.
5. Substitute the known values into the equation and solve for the unknown variable.
6. Finally, check the answer to ensure its reasonableness.