\( y-x=2 \) and \( x^{2}+y^{2}=20 \) The formula used to determine \( C R \) (compression ratio) when combustion and swept volumes are given is: Where: \( C R=\frac{C V+S V}{S V} \) \[ \begin{aligned} C R & =\text { compression ratio } \\ C V & =\text { combustion volume }\left(\mathrm{cm}^{3}\right)\end{aligned} \] Make \( C V \) swept volume \( \left(\mathrm{cm}^{3}\right) \) \( \begin{array}{l}\text { Me subject of the formula. } \\ \text { Hence, calculate the numerical value of } C V \text { if } S V=48 \mathrm{~cm}^{3} \text { and the } \\ \text { compression ratio is equal to } 9,5: 1 .\end{array} \)

To make \( C V \) the subject of the formula, we start with the equation for the compression ratio: \[ C R = \frac{C V + S V}{S V} \] Multiplying both sides by \( S V \) gives us: \[ C R \cdot S V = C V + S V \] Now, isolate \( C V \): \[ C V = C R \cdot S V - S V \] You can factor out \( S V \): \[ C V = S V (C R - 1) \] Now, substituting in the values \( S V = 48 \, \text{cm}^3 \) and \( C R = 9.5 \): \[ C V = 48 \, (9.5 - 1) = 48 \cdot 8.5 = 408 \, \text{cm}^3 \] So, the value of \( C V \) is \( 408 \, \text{cm}^3 \). For a bit of fun, did you know that compression ratios are a significant factor in an engine's efficiency? Higher ratios usually lead to better fuel economy, but they can also lead to knocking if the fuel quality isn't up to par. It's a delicate balance, much like picking the right ingredients for a perfect cake! Happy calculating! In the realm of real-world applications, the compression ratio can be vital for performance in racing engines, where maximizing power output while maintaining reliability is key. Different racing categories might have specific limitations on compression ratios to ensure a level playing field, akin to the careful rules of a board game where strategy and fairness go hand in hand. Whether you're a car enthusiast or just diving into physics, ratios help reflect a design's capabilities!