answer:1. The Hestfolk - Bonus 1: +10% farming output (Green Thumb) - Bonus 2: +5% trade income (Tradesman) - Bonus 3: +10% fortification defense (Defender) - Male names: Alton, Bertram, Clarence, Desmond, Edmund, Floyd, George, Harold, Jonathan, Kenneth, Leonard, Marcus, Newton, Orion, Percy, Quentin, Raymond, Sylvester, Thaddeus, Ulrich - Female names: Adeline, Beryl, Claudette, Della, Editha, Felicity, Gwendolyn, Hortense, Isadora, Josephine, Laverne, Marjorie, Nerida, Ophelia, Philippa, Quinby, Rosalind, Sylvia, Trudie, Urania - Surnames: Appleby, Bellamy, Cartwright, Dunsmuir, Elwood, Farnsworth, Galloway, Hawthorne, Jefferies, Kingsley, Lancaster, Montague, Neville, Oakley, Pembroke, Quincey, Rawson, Salisbury, Tilney, Waverly - Noble Clothes: The Hestfolk nobles love bright and bold colors, often incorporating intricate embroidery and lace into their outfits. They favor tall hats and finely made boots. - Commoner's Clothes: The Hestfolk commoners prefer practicality over fashion, with sturdy shirts and trousers, and warm coats for the colder months. - Architecture: Hestfolk buildings are typically made of stone or brick, with sloping roofs. Houses often have small gardens which residents use to grow their own food. 2. The Bayfolk - Bonus 1: +10% naval combat (Sea Dogs) - Bonus 2: +5% production income (Artisans) - Bonus 3: +5% trade income (Merchants) - Male names: Andrew, Benedict, Calvin, David, Ethan, Francis, Gabriel, Henry, Isidore, James, Kenneth, Luke, Matthew, Nathaniel, Oliver, Philip, Quinton, Rufus, Simon, Theodore - Female names: Amanda, Beatrice, Cassandra, Diana, Eleanor, Florence, Grace, Helena, Isabelle, Jane, Katherine, Lillian, Margaret, Naomi, Olivia, Penelope, Rosalind, Sabrina, Teresa, Violet - Surnames: Banks, Carstairs, Drake, Ellington, Fairfax, Grey, Hastings, Irving, Jowett, Kipling, Landon, Montrose, North, Oakes, Pendergast, Radcliffe, Somerset, Trelawney, Utley, Victoria - Noble Clothes: The Bayfolk nobles favor stylish jackets and breeches made of waterproof material in shades of blue and green. They wear knee-high boots and caps. - Commoner's Clothes: Bayfolk commoners wear practical, durable clothing. They favor woolen trousers, shirts, and thick, woolen coats. - Architecture: Bayfolk architecture often features wide porches, wooden siding, and small balconies. Most buildings are near the water and are built on stilts to protect against flooding during high tide. 3. The Thornfolk - Bonus 1: +15% archery damage (Marksman) - Bonus 2: +10% siege damage (Siege Specialist) - Bonus 3: +5% production income (Craftsmen) - Male names: Bartholomew, Clement, Darcy, Eustace, Ferdinand, Geoffrey, Horatio, Isaiah, Julian, Lysander, Magnus, Nathaniel, Orlando, Peregrine, Roderick, Sebastian, Theodoric, Upton, Vicente, Warren - Female names: Abigail, Bethany, Celestia, Daphne, Elisabeth, Felicity, Genevieve, Henrietta, Imogen, Josephine, Kendra, Lyra, Molly, Ophelia, Phoebe, Rosalind, Sabina, Thalia, Ursula, Violet - Surnames: Blackwood, Carver, Delacroix, Easton, Fairchild, Guildford, Harrison, Ingram, Jarvis, Kendal, Lumley, Marmont, Neville, Otway, Pennington, Quinby, Redmond, Stanhope, Thorne, Winstanley - Noble Clothes: Thornfolk nobles prefer simple, well-tailored clothing, with a preference for darker, muted colors. They wear knee-high boots and carry short bows for hunting. - Commoner's Clothes: Thornfolk commoners favor sturdy leather boots, thick woolen trousers, and cloaks in neutral colors. - Architecture: Thornfolk buildings often have high, pointed roofs, and thick walls. Many have crenellated battlements and towers. 4. The Harvesters - Bonus 1: +10% farming output (Harvest Blessing) - Bonus 2: +5% production income (Craftsmen) - Bonus 3: +10% fortification defense (Defender) - Male names: Abram, Benjamin, Caleb, Daniel, Elijah, Gideon, Hiram, Isaac, Jacob, Jesse, Joshua, Martin, Micah, Noah, Obadiah, Samuel, Silas, Tobias, Zachary, Zebediah - Female names: Abigail, Bathsheba, Dinah, Esther, Hannah, Jemima, Keziah, Leah, Magdalena, Naomi, Rebecca, Ruth, Sarai, Tabitha, Tamar, Tirzah, Zeruiah - Surnames: Barnard, Chandler, Davenport, Emery, Farnham, Goodwin, Hackett, Johnson, Kimball, Lambert, Merrill, Norwood, Osgood, Putnam, Sawyer, Thurber, Upham, Vincent, Weston, Young - Noble Clothes: The Harvesters nobles wear flowing robes in shades of green and gold, with jewelry made from the fruits of their harvest. They favor simple leather sandals. - Commoner's Clothes: Harvesters commoners wear durable but elegant clothing, with loose-fitting trousers and tunics, and simple leather shoes. - Architecture: Harvesters buildings are often made of wood from the surrounding forests, with thatched roofs. Many farmhouses have small gardens, decorated with colorful flowers. 5. The Wanderers - Bonus 1: +10% movement speed (Wayfarer) - Bonus 2: +10% caravan income (Caravan Master) - Bonus 3: +5% trade income (Merchant Prince) - Male names: Abel, Cyrus, Donovan, Everett, Felix, Giles, Leo, Miles, Orion, Phineas, Soren, Tiberius, Vesper, Wilder, Xander - Female names: Aurora, Calliope, Daphne, Elodie, Freya, Guinevere, Imogen, Juniper, Liriel, Maelle, Niamh, Orla, Phoebe, Sable, Thalia, Zinnia - Surnames: Ash, Birch, Cedar, Cypress, Elder, Fox, Hawthorn, Ivy, Juniper, Linden, Maple, Oak, Pine, Rowan, Sequoia, Spruce, Thorn, Willow, Yew, Zephyr - Noble Clothes: The Wanderers nobles dress in brightly colored, flowing robes, with ornate jewelry and headdresses made from crystals and beads. - Commoner's Clothes: Wanderers commoners wear practical clothing, but with a flair for color and pattern, often incorporating bright scarves and shawls. - Architecture: Wanderer buildings are often temporary, consisting of tents or yurts for easy disassembly and relocation. Larger settlements may have more permanent structures made of stone or brick. 6. The Lightsmiths - Bonus 1: +10% mining output (Miner) - Bonus 2: +5% production income (Craftsmen) - Bonus 3: +10% fortification defense (Defender) - Male names: Alistair, Bran, Cedric, Draven, Eamon, Finnian, Garrick, Hadrian, Iain, Jareth, Kael, Lysander, Magnus, Nicolai, Oisin, Percival, Qasim, Rurik, Soren, Taran - Female names: Alessa, Briar, Calantha, Darya, Eira, Faline, Gaia, Hestia, Isolde, Junia, Kaida, Lirien, Marigold, Nyx, Ophelia, Phaedra, Rhiannon, Sable, Thalia, Zinnia - Surnames: Ashcroft, Blackwood, Crowhurst, Darkwood, Emberwood, Firestone, Goldsmith, Irons, Lightfoot, Silvermane, Snow, Starlight, Steel, Sunflower, Thunderhoof, Windrider, Wolfson, Woodland, Wyrmwood, Zephyr - Noble Clothes: The Lightsmiths nobles prefer flowing, ornate robes in shades of gold and bronze, with intricate detailing in silver and gemstones. They wear tall boots. - Commoner's Clothes: Lightsmiths commoners wear durable and simple clothes in warm colors, with practical boots. - Architecture: Lightsmiths buildings are often adorned with intricate ironwork, and decorated with shimmering crystals. They favor durable materials like stone and metal in construction.

answer:1. The Hestfolk: A peaceful and agrarian society, the Hestfolk are known for their expertise in farming and trading. They live on sprawling estates dotted with small gardens and fruit orchards. Their noble clothing is colorful and flashy, while the commoners prefer practicality above all else. 2. The Bayfolk: A seafaring people, the Bayfolk are skilled in navigation, fishing, and shipbuilding. They live in small coastal towns and villages, with wooden houses built on stilts to protect against the tides. Their nobles wear waterproof clothing in shades of blue and green, while the commoners prefer woolen clothing. 3. The Thornfolk: A fierce and warlike culture, the Thornfolk are skilled archers and warriors. They inhabit the dense forests and rugged mountains of their homeland, building fortresses to protect themselves against invading armies. Their noble clothing is simple and muted, while commoners wear durable leather and wool clothing. 4. The Harvesters: A society centered on agriculture and nature, the Harvesters are known for their green thumbs and bountiful harvests. They live in small but tightly knit communities, where everyone works together to ensure a good harvest. Their clothing is practical yet elegant, with nobles favoring flowing green and gold robes. 5. The Wanderers: A nomadic culture that traverses borders and terrain, the Wanderers are skilled in trading, cartography, and discovery. They live in temporary settlements, where their brightly colored clothing and appreciative of aesthetics reflects a love for life and adventure. 6. The Lightsmiths: A highly skilled civilization of miners and smiths, the Lightsmiths are expert metallurgists and gem cutters, creating luminescent jewelry, and beautiful weapons. They favor building sturdy stone structures and prefer noble clothing embellished with gold and precious stones to show off their wealth and skill.

answer:First, let's find an expression for the polar moment of inertia (IP). The polar moment of inertia of a hollow tube can be found using the following formula: IP = (π/2) * (R_outer^4 - R_inner^4) where R_outer is the outer radius of the tube and R_inner is the inner radius of the tube. Since the tube has a very thin wall with thickness t, we can say that R_outer = R_inner + t. Now, for a thin-walled tube, t << R_inner, so we can write: IP ≈ π * R_inner^3 * 2t Now, let's find the allowable torque (Tallow). To do this, we use the formula: Tallow = 𝜏allow * IP / R_inner where 𝜏allow is the allowable shear stress. We have already found an expression for the polar moment of inertia IP, and R_inner is the inner radius of the tube. Now substitute the expression for IP into the above formula: Tallow = 𝜏allow * (π * R_inner^3 * 2t) / R_inner Simplify the formula: Tallow = 2 * π * 𝜏allow * R_inner^2 * t Now, if we let the ratio of the thickness to the inner radius be negligible, that is (t/R_inner) ≈ 0, we have: Tallow ≈ 2 * π * 𝜏allow * R_inner^2 * t So, the allowable torque Tallow for a thin-walled tube subject to torsion can be given by the following expression: Tallow = 2 * π * 𝜏allow * R_inner^2 * t

answer:We already derived an expression for the allowable torque (Tallow): Tallow = 2 * π * 𝜏allow * R_inner^2 * t Now we need to find an expression for the weight (W) of the tube. The weight can be described as mass (m) times acceleration due to gravity (g): W = m * g The mass (m) of the tube can be represented as: m = ρ * V where ρ is the density of the material and V is the volume of the tube. The volume of the tube can be found as the difference between the volumes of the outer and inner cylinders: V = π * L * (R_outer^2 - R_inner^2) where L is the length of the tube. Since the tube has a thin wall and t << R_inner, we can write: V ≈ 2 * π * R_inner * L * t Now, we can substitute this back into the expression for mass: m = ρ * [2 * π * R_inner * L * t] Now, let's substitute the mass expression back into the weight equation: W = ρ * [2 * π * R_inner * L * t] * g Now, we can find the strength-to-weight ratio, T/W, by dividing Tallow by W: T/W = Tallow / W T/W = (2 * π * 𝜏allow * R_inner^2 * t) / (ρ * [2 * π * R_inner * L * t] * g) Notice that several terms cancel out: T/W = 𝜏allow / (ρ * L * g) Since the strength-to-weight ratio is requested as an approximate expression and t/R is negligible, the above equation represents the strength-to-weight ratio of the thin-walled tube: T/W ≈ 𝜏allow / (ρ * L * g)