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📰 Solution: First, calculate the area of the triangle using Heron's formula. The semi-perimeter $ s = \frac{13 + 14 + 15}{2} = 21 $. The area is $ \sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = \sqrt{7056} = 84 \, \text{km}^2 $. The altitudes correspond to each side: $ h_a = \frac{2 \times 84}{13} \approx 12.92 $, $ h_b = \frac{2 \times 84}{14} = 12 $, $ h_c = \frac{2 \times 84}{15} = 11.2 $. The shortest altitude is $ \boxed{11.2} $ km. 📰 Question: A hydrologist models a groundwater reservoir as a hemisphere with radius $ 3x $ and compares it to a cylindrical aquifer with radius $ x $ and height $ 3x $. What is the ratio of the hemisphere's volume to the cylinder's volume? 📰 Solution: The volume of a hemisphere is $ \frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi 27x^3 = 18\pi x^3 $. The cylinder's volume is $ \pi x^2 \cdot 3x = 3\pi x^3 $. The ratio is $ \frac{18\pi x^3}{3\pi x^3} = \boxed{6} $. 📰 Lost Luggage 9287503 📰 Parlering 882753 📰 How To Repairs Microsoft Word Instantlyyou Wont Want To Contact Support Again 5379564 📰 Stephen In The Bible 8013827 📰 The Shocking Truth About Chinese Breakfast That Doctors Wont Tell You 8896239 📰 Keyboard Polling Rate 7352526 📰 Due Cucina Italian Restaurant Redmond 9398681 📰 Paradise Cove 3464774 📰 Free Brain Training Games You Can Play Nowno Download No Cost Just Instant Mental Games 4984117 📰 Sherman Commander 6630476 📰 Note That 45240 Is Clearly Divisible By 4 Last Two Digits 40 Are Divisible By 4 And The Sum Of Digits Is 45240 15 Which Is Divisible By 3 Thus 45240 Is Divisible By 12 So The Remainder Is 0 4382997 📰 Laundry Hamper With Wheels 6734539 📰 Cette Gabriele Corcos Something She Never Wanted The World To See 6886366 📰 Lorenzo Oneal 4161312 📰 Here Come The Brides 9460109