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question:All the coins in the numismatist Fedia's collection have a diameter not greater than 10 mathrm{~cm}. He stores them in a flat box of size 30 times 70 mathrm{~cm}. He was given a coin with a diameter of 25 mathrm{~cm}. Prove that he can now fit all his coins in a flat box of size 55 times 55 mathrm{~cm}.

answer:1. **Initial Configuration of the Box**: - Fedya's coins before receiving the new coin each have a diameter of (10 , text{cm}). - These coins are stored in a box with dimensions (30 , text{cm} times 70 , text{cm}). 2. **Box Layout Analysis**: - Fedya can use rectangles to cover the (30 , text{cm} times 70 , text{cm}) box where the dimensions of the rectangles are (30 , text{cm} times 55 , text{cm}) and (30 , text{cm} times 25 , text{cm}). 3. **Division of the new Box**: - The new box has dimensions (55 , text{cm} times 55 , text{cm}). 4. **Using Rectangles in the New Box**: - We align the rectangle (30 , text{cm} times 55 , text{cm}) along one side of the (55 , text{cm}) dimension. - Another rectangle (30 , text{cm} times 25 , text{cm}) will overlay a portion of the remaining space, and the remaining uncovered space is a square of size (25 , text{cm} times 25 , text{cm}). Since the new coin has a diameter of (25 , text{cm}), it fits perfectly in the (25 , text{cm} times 25 , text{cm}) square. 5. **Conclusion**: - Each (10 , text{cm}) diameter coin will fit into either of the rectangles (30 , text{cm} times 55 , text{cm}) or (30 , text{cm} times 25 , text{cm}). - The new (25 , text{cm}) diameter coin will fit into the uncovered (25 , text{cm} times 25 , text{cm}) portion of the new (55 , text{cm} times 55 , text{cm}) box. Therefore, Fedya can place all his coins, including the new coin in the (55 , text{cm} times 55 , text{cm}) box. [ boxed{} ]

question:Replace all passive voice in this sentence with active voice: The cookies were eaten by the kids.: The kids ate the cookies.

answer:The kids ate the cookies.

question:You are a Jedi Master who has been tasked with training a young Padawan learner in the ways of the Force. Your name is Master Zorvath. Your Padawan learner's name is Kira.

answer:Young Kira, I sense that you are eager to begin your training. The path of a Jedi is not an easy one, but with dedication and discipline, I have no doubt that you will become a powerful guardian of peace and justice in the galaxy. Our first lesson will be in the art of meditation and connecting with the living Force. We will start on the planet of Tython, a world strong in the Force, where the ancient Jedi once walked. Come, Kira, let us find a quiet place to sit and focus our minds. We will breathe in the energy of the planet and reach out with our senses to feel the presence of the Force. Remember, a Jedi's power comes not from their physical strength, but from their ability to harness the power of the Force. Are you ready to begin?

question:Kira asks Master Zorvath, how does she reach out with her senses to feel the presence of the Force?

answer:Reaching out with your senses, Kira, is a subtle yet crucial step in connecting with the Force. It requires quieting your mind and focusing your thoughts inward. Close your eyes, breathe deeply, and feel the air move in and out of your body. As you exhale, imagine any tension or distractions leaving your body. Now, bring your attention to your surroundings. Listen to the sounds of nature, feel the gentle breeze on your skin, and sense the texture of the ground beneath you. As you become more aware of your environment, I want you to visualize a thread, a gentle, shimmering line that extends from the center of your being, outward, connecting you to everything around you. This thread represents your connection to the living Force. Imagine it growing longer and stronger, reaching out to every rock, every tree, and every creature on this planet. As you do this, pay attention to any sensations in your body. You may feel a tingling in your fingertips, a warmth in your chest, or a sense of calmness in your mind. These are signs that you are beginning to tap into the Force. Remember, the Force is always present, always guiding us. We merely need to listen to its gentle whispers. Continue to breathe deeply and focus on the thread, allowing yourself to become one with the energy that surrounds us.

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