This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
13. Given that (a)/(b) = (1)/(p) - (1)/(C), make C the subject. Step 1: Isolate the term containing C. We have the equation: (a)/(b) = (1)/(p) - (1)/(C) To make C the subject, first move the term (1)/(C) to the left side and (a)/(b) to the right side: (1)/(C) = (1)/(p) - (a)/(b) Step 2: Combine the terms on the right side by finding a common denominator. The common denominator for p and b is pb. (1)/(C) = (b)/(pb) - (ap)/(pb) (1)/(C) = (b - ap)/(pb) Step 3: Invert both sides of the equation to solve for C. C = (pb)/(b - ap) Discrepancy with Options: The derived answer is C = (pb)/(b - ap). However, all the provided options (A, B, C, D) contain a variable 'q' which is not present in the original equation. This indicates a potential typo in either the question or the options. Given the requirement to select an option, and assuming there is a typo where 'q' in the options should be 'p', let's re-evaluate. Even with this assumption, none of the options directly match C = (pb)/(b - ap). If we assume the question intended to be (a)/(b) = (1)/(C) - (1)/(p) and 'q' in the options is a typo for 'p', then: (1)/(C) = (a)/(b) + (1)/(p) (1)/(C) = (ap+b)/(bp) C = (bp)/(ap+b) Comparing this with the options (assuming q=p): A. C = (bp)/(ap+bp) = (bp)/(p(a+b)) = (b)/(a+b) (Not a match) Due to the clear inconsistency with the variable 'q' in the options, a definitive answer cannot be provided from the given choices based on the question as written. However, if forced to choose the closest form, and assuming a typo in the question where it should have been (a)/(b) = (1)/(p) - (1)/(q) and the options are for q, then q = (pb)/(b-ap). None of the options match this. Given the constraints, I must select an option. This implies there is an intended correct answer among the options. Without further clarification on the typo, it's impossible to be certain. I will state the derived answer and highlight the discrepancy. The mathematically derived answer from the given equation is C = (pb)/(b - ap). Since this does not match any of the options due to the presence of 'q' in the options, I cannot confidently select an option. 3 done, 2 left today. You're making progress.