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July 2022
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30 баллов решите 3,4
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Regent1828
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3). Периметр прямоугольника: Р = 2(a + b).
Тогда: a + b = P/2 = 68:2 = 34 => b = 34 - a
a² + b² = 26²
a² + (34 - a)² = 676
a² + 1156 - 68a + a² - 676 = 0
2a² - 68a + 480 = 0
a² - 34a + 240 = 0 D = b²-4ac = 1156 - 960 = 196 = 14²
a₁ = (-b+√D)/2a = (34+14)/2 = 24 b₁ = 34 - 24 = 10
a₂ = (-b -√D)/2a = (34-14)/2 = 10 b₂ = 34 - 10 = 24
Проверим: a² + b² = c²
24² + 10² = 26²
576 + 100 = 676
676 = 676
Ответ: {24; 10}, {10; 24}
4). при х = -4 f(x) = -4/x = -4/(-4) = 1
при х = 0 f(x) = -x + 3 = 3
при х = 4 f(x) = -x + 3 = -4 + 3 = -1
график f(x) выделен красным цветом
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Verified answer
3). Периметр прямоугольника: Р = 2(a + b).Тогда: a + b = P/2 = 68:2 = 34 => b = 34 - a
a² + b² = 26²
a² + (34 - a)² = 676
a² + 1156 - 68a + a² - 676 = 0
2a² - 68a + 480 = 0
a² - 34a + 240 = 0 D = b²-4ac = 1156 - 960 = 196 = 14²
a₁ = (-b+√D)/2a = (34+14)/2 = 24 b₁ = 34 - 24 = 10
a₂ = (-b -√D)/2a = (34-14)/2 = 10 b₂ = 34 - 10 = 24
Проверим: a² + b² = c²
24² + 10² = 26²
576 + 100 = 676
676 = 676
Ответ: {24; 10}, {10; 24}
4). при х = -4 f(x) = -4/x = -4/(-4) = 1
при х = 0 f(x) = -x + 3 = 3
при х = 4 f(x) = -x + 3 = -4 + 3 = -1
график f(x) выделен красным цветом