answer:Title: Tragic Deaths Mar Egypt's Revolution Anniversary Protests; Social Media Erupts with Outrage The anniversary of Egypt's revolution was marked by nationwide protests and upheaval, sadly resulting in the loss of 16 lives. Among those killed, one protester's story has spread like wildfire on social media, sparking heated debates and differing accounts of her death. Activists point to the police in search of answers, making this year's commemorations a grim reminder of the revolutionary struggle. The Egyptian revolution, which began in 2011, sparked a wave of change and hope across the Arab world, showcasing a display of unity and resilience among protesters urging for a more democratic and just society. The anniversary of this historic event, however, was plagued by violence and unrest in recent days, culminating in the tragic deaths of 16 people killed during nationwide protests. Even as the demonstrations turned tragic, the power of social media to disseminate information and encourage conversation was clearly demonstrated. Images of one protester killed on Saturday have captured the hearts and minds of social media users around the globe. Tragic photos and accounts of her death have flooded Twitter, Facebook, and other platforms, propelling her story into the international limelight. While more information about this victim and the other 15 individuals who lost their lives during the protests continues to be unearthed, the varying accounts of what transpired have elicited a range of responses. While some activists squarely place the blame on the police, others are still attempting to piece together the circumstances that led to these tragic deaths. As details emerge, the polarization around this issue reflects the larger divisions within Egyptian society, making the anniversary of the revolution a bittersweet recollection. With social media as a central stage for discourse and engagement, conversations about the past ten years since Egypt's revolution have become a focal point for citizens, activists, and intellectuals alike. As the dust settles, the country, and the world at large, must grapple with these tragic events and what they signify for the ongoing struggle for democracy, justice, and human rights in Egypt. With the truth remaining elusive and different accounts emerging, Egypt's revolution anniversary will forever be marred by the sorrow and loss experienced during these protests. Despite these recent tragedies, the spirit of the revolution lives on in the hearts of those who continue to fight for their dreams of a better future for Egypt and the world. As social media continues to play a crucial role in sharing the stories of ordinary people, the collective power of individuals to influence change remains a beacon of hope amid the darkness.

answer:To rewrite the solution into a detailed step-by-step format: **Part 1: Finding the functional relationship between sales volume y and price x** Given that at a price of 48 yuan, 200 sets can be sold per day. If the price increases by 2 yuan, 4 fewer sets are sold. This implies that for every 2 yuan increase in price, sales decrease by 4 sets. Therefore, the rate of change in sales volume with respect to price is -4 sets per 2 yuan, which simplifies to -2 sets per yuan. The change in sales volume (y) can be expressed as a function of the change in price (x - 48), where 48 yuan is the initial price point mentioned. Thus, we have: [y = 200 - frac{1}{2} times 4 times (x - 48)] Simplifying the equation: [y = 200 - 2(x - 48)] [y = 200 - 2x + 96] [y = -2x + 296] Therefore, the functional relationship between the sales volume y and the price x is: [y = -2x + 296] Encapsulating the final answer for part (1): [boxed{y = -2x + 296}] **Part 2: Maximizing the daily profit W from selling the sets** The profit W for selling each set is the difference between the selling price x and the cost price 34 yuan, multiplied by the sales volume y. From part (1), we know y = -2x + 296. Thus, the profit function W can be expressed as: [W = (x - 34)(-2x + 296)] Expanding and simplifying the expression: [W = -2x^2 + 296x - 34(-2x) + 34 times 296] [W = -2x^2 + 296x + 68x + 34 times 296] [W = -2x^2 + 364x + 34 times 296] [W = -2(x^2 - 182x) + 34 times 296] Completing the square for the quadratic expression: [W = -2[(x - 91)^2 - 91^2] + 34 times 296] [W = -2(x - 91)^2 + 2 times 91^2 + 34 times 296] [W = -2(x - 91)^2 + 6498] Since the coefficient of the quadratic term is negative (-2), the parabola opens downwards, indicating that the profit function W reaches its maximum when x = 91. Substituting x = 91 into the profit function: [W_{text{max}} = -2(91 - 91)^2 + 6498] [W_{text{max}} = 6498] Therefore, to maximize the daily profit from selling the sets, the selling price per set should be set at 91 yuan, and the maximum profit is 6498 yuan. Encapsulating the final answers for part (2): [boxed{text{Selling price per set} = 91 text{ yuan}}] [boxed{text{Maximum profit} = 6498 text{ yuan}}]

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answer:1. **Completing the square for x and y terms:** Start by rewriting the equation: [ 4x^2 - 24x - y^2 - 6y - 8 = 0. ] For x, factor out the 4 from the x terms: [ 4(x^2 - 6x) - y^2 - 6y - 8 = 0. ] Complete the square for the x terms: [ 4((x - 3)^2 - 9) - y^2 - 6y - 8 = 0. ] [ 4(x - 3)^2 - 36 - y^2 - 6y - 8 = 0. ] [ 4(x - 3)^2 - y^2 - 6y - 44 = 0. ] For y: [ y^2 + 6y = (y + 3)^2 - 9. ] Replacing in the hyperbola equation: [ 4(x - 3)^2 - (y + 3)^2 + 9 - 44 = 0. ] [ 4(x - 3)^2 - (y + 3)^2 - 35 = 0. ] 2. **Rewriting in standard form:** Add 35 to both sides: [ 4(x - 3)^2 - (y + 3)^2 = 35. ] Divide through by 35: [ frac{(x - 3)^2}{8.75} - frac{(y + 3)^2}{35} = 1. ] Here, a^2 = 8.75, so a = sqrt{8.75}. 3. **Finding the distance between the vertices:** The vertices are at pm a from the center along the x-axis. Thus, the distance between the vertices is: [ 2a = 2sqrt{8.75}. ] [boxed{2sqrt{8.75}}]