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question:Let F_{1} and F_{2} be the left and right foci of the ellipse frac{x^{2}}{25} + frac{y^{2}}{16} = 1, respectively, and let P be a point on the ellipse. Let M be the midpoint of F_{1}P, and |OM| = 3. Then, the distance from point P to the left focus of the ellipse is A: 4 B: 3 C: 2 D: 5

answer:From the given information, we know that OM is the median line of triangle PF_{1}F_{2}. Since |OM| = 3, it follows that |PF_{2}| = 6. Additionally, since |PF_{1}| + |PF_{2}| = 2a = 10, it follows that |PF_{1}| = 4. Therefore, the correct choice is boxed{A}. From the given information, we know that OM is the median line of triangle PF_{1}F_{2}. By using |OM| = 3, we can deduce that |PF_{2}| = 6. Then, by applying the definition of an ellipse, we can find the value of |PF_{1}|. This problem tests the definition of an ellipse and the application of its simple properties. Identifying OM as the median line of triangle PF_{1}F_{2} is key to solving the problem, making it a medium-difficulty question.

question:Design a waterpark for an arid city like Phoenix.

answer:Imagine a waterpark that not only provides a thrilling escape from the desert heat but also incorporates sustainable design elements and nods to the region's unique natural beauty. Oasis Springs would be a 25-acre waterpark in Phoenix, designed to transport visitors to a lush, verdant world that defies the arid landscape. As guests enter the park, they're greeted by a sprawling, majestic canyon – a large, winding structure made from natural stone and reclaimed wood, evoking the majestic rock formations found in Arizona's wilderness. This canyon serves as the park's main thoroughfare, providing shade and shelter from the sun as visitors make their way to various attractions. The park is divided into distinct ecosystems, each with its unique attractions, landscaping, and architectural features. The Sonoran Splash area, for instance, is inspired by the region's iconic saguaro cacti, with towering water slides and a lazy river that winds its way through a forest of giant cacti. The Desert Oasis area, meanwhile, is designed to resemble a serene, natural oasis, complete with palm trees, tranquil water features, and a large wave pool that generates gentle, rolling waves perfect for lounging or swimming. Visitors can also explore the Arroyo Adventure area, featuring a series of winding waterways, rapids, and interactive water play elements that mimic the natural flow of an arroyo. One of the park's showpieces is the Monsoon Falls complex, which simulates the intense, thrilling experience of an Arizona monsoon storm. Visitors can enjoy a heart-pounding plummet down a steep water slide, followed by a splashy landing in a large pool. The surrounding area features cleverly designed stormwater elements, including splash pads and interactive water features that create a fun, immersive atmosphere. Throughout the park, innovative water-saving technologies and sustainable design elements are incorporated to minimize the facility's water footprint. These features include advanced water filtration systems, rainwater harvesting, and drought-resistant landscaping. At night, Oasis Springs transforms into an enchanting, twinkling wonderland, with carefully designed lighting that highlights the park's naturalistic architecture and creates an unforgettable ambiance. As visitors depart, they're left with memories of a unique, transportive experience that's equal parts thrilling adventure and serene retreat – a true oasis in the desert.

question:How does the water filtration system work?

answer:The water filtration system at Oasis Springs is a state-of-the-art, multi-stage process designed to minimize water waste and reduce the park's overall water footprint. Here's a peek into how it works: The system begins with a series of high-efficiency, submerged membrane bioreactors that treat and filter the park's wastewater, including water from the wave pool, water slides, and other attractions. These bioreactors utilize beneficial microorganisms to break down organic pollutants and remove suspended solids, resulting in a high-quality effluent that's nearly 99% free of contaminants. The filtered water is then passed through a series of advanced oxidation processes, including ultraviolet (UV) and ozone treatment, to further remove any remaining impurities and disinfect the water. This step not only ensures the water is safe for reuse but also helps to eliminate any lingering bacteria, viruses, or other microorganisms that might be present. Next, the treated water is stored in a large, underground cistern for later reuse in various applications throughout the park. This might include irrigating the park's landscaping, replenishing the wave pool or water slides, or even flushing toilets and urinals in the park's restrooms. One of the most innovative aspects of Oasis Springs' water filtration system is its incorporation of a proprietary, AI-powered water management platform. This system continuously monitors and analyzes the park's water usage patterns, detecting even the slightest anomalies or inefficiencies in the filtration process. By leveraging machine learning algorithms and real-time data analysis, the platform can optimize water treatment protocols, predict maintenance needs, and minimize waste – ultimately reducing the park's overall water consumption by up to 70%. To take it a step further, Oasis Springs has also implemented a comprehensive rainwater harvesting system, which collects and stores rainwater from the park's rooftops and parking lots for non-potable uses, such as flushing toilets and irrigating landscaping. This not only reduces the park's reliance on municipal water supplies but also helps to decrease stormwater runoff and alleviate pressure on local drainage systems. By integrating these cutting-edge technologies and sustainable design principles, Oasis Springs has created a water filtration system that not only minimizes its environmental footprint but also serves as a model for water-conscious innovation in the entertainment and hospitality industries.

question:How do you collect rainwater in a place that rarely experiences rain?

answer:While it's true that Phoenix, Arizona receives relatively little rainfall, Oasis Springs' rainwater harvesting system is designed to maximize collection potential during those infrequent but intense desert storms. The system begins with a network of sleek, curved collection canopies that cover the park's parking lots and walkways. These canopies are designed to not only provide shade for visitors but also serve as a large, impermeable surface for collecting rainwater. The canopies are sloped to direct rainwater towards a series of hidden gutters and downspouts, which funnel the water into a large, underground cistern. To augment the collection potential, the park's rooftops and building facades are also equipped with a specialized, waterproof membrane that allows rainwater to flow freely into the collection system. Even the park's landscaped areas are designed with rainwater collection in mind, featuring shallow, meandering channels that direct rainwater towards the cistern. While the rainfall in Phoenix might be infrequent, the storms that do occur can be intense, producing a significant amount of rainfall in a short period. By designing the collection system to capture as much of this rainfall as possible, Oasis Springs can still harvest a substantial amount of water – even if it's not as frequent as in more temperate climates. To give you an idea of the potential, a single, intense thunderstorm in Phoenix can produce up to 1-2 inches of rainfall in a matter of hours. With a collection area of over 100,000 square feet, Oasis Springs' rainwater harvesting system can potentially collect up to 200,000 gallons of water from a single storm event. Of course, the collected rainwater is then treated and filtered using advanced technologies, including UV and ozone treatment, to ensure it's safe for non-potable uses throughout the park. By combining innovative design, clever engineering, and a deep understanding of the local climate, Oasis Springs' rainwater harvesting system is able to make the most of the limited rainfall in Phoenix, reducing the park's reliance on municipal water supplies and showcasing the potential for sustainable water management in even the driest of environments.

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