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📐 Matematika — DTM savollari va yechimlari

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Planimetriya

  1. #960Muntazam oltiburchakning ichki burchagini toping.
  2. #966To'g'ri to'rtburchakning tomonlari 5 va 12 ga teng. Uning diagonalini toping.
  3. #1425To'g'ri burchakli uchburchakning katetlari 9 va 12 ga teng. Unga tashqi chizilgan aylana radiusini toping.
  4. #1902Uchburchakning tomonlari 5, 7 va 8 ga teng. 7 ga teng tomon qarshisidagi burchakni toping.

Progressiyalar

  1. #1561 dan 100 gacha bo'lgan 3 ga bo'linadigan barcha natural sonlar yig'indisini toping.
  2. #933Arifmetik progressiyada a₂ + a₈ = 26. a₅ ni toping.
  3. #10053; 6; 12; … geometrik progressiyaning 6-hadini toping.
  4. #1755Cheksiz kamayuvchi geometrik progressiyaning yig'indisi 24 ga, maxraji 1/4 ga teng. Uning birinchi hadini toping.

Stereometriya

  1. #1041Silindrning o'q kesimi yuzi 36 ga teng bo'lgan kvadratdan iborat. Silindr hajmini toping.
  2. #1251Silindrning asos radiusi 4 ga, balandligi 6 ga teng. Silindrning yon sirti yuzini toping.
  3. #1815Konusning asos radiusi 3 ga, balandligi 7 ga teng. Konus hajmini toping.
  4. #1884Kubga shar ichki chizilgan. Kub hajmining shar hajmiga nisbatini toping.

Tenglamalar

  1. #351Tenglamani yeching: 3x − 7 = 11
  2. #768x + y = 7 va x − y = 3 sistemaning yechimi (x; y) bo'lsa, x · y ni toping.
  3. #1131Tenglamani yeching: 3/(x − 2) = 5/(x + 2)
  4. #1140Ikki sonning yig'indisi 56 ga, ayirmasi 14 ga teng. Katta sonni toping.
  5. #1200Tenglamani yeching: |x + 1| = 2x − 4
  6. #1299x² + y² = 13 va xy = 6 bo'lib, x > 0, y > 0 bo'lsa, x + y ni toping.
  7. #1461Tenglamani yeching: 5x + 8 = 2x − 7
  8. #1551Tenglamani yeching: √(x + 6) + √(x + 1) = 5
  9. #20762x + 3y = 13 va 3x − y = 3 sistemaning yechimi (x; y) bo'lsa, x + y ni toping.

Tengsizliklar

  1. #372(x + 3)/(x − 2) < 2 tengsizlikning [0; 10] kesmadagi butun yechimlari nechta?
  2. #1332Tengsizlikni yeching: (x − 5)/(x + 2) ≤ 0
  3. #14495(x − 2) > 2x + 3 tengsizlikning eng kichik butun yechimini toping.
  4. #1587(x² − 4)(x − 7) ≤ 0 tengsizlikning natural yechimlari nechta?
  5. #2019Tengsizlikni yeching: x² − 6x + 9 > 0

Trigonometriya

  1. #606y = 3 sin x − 4 cos x funksiyaning eng katta qiymatini toping.
  2. #795sin x = 1/2 tenglamaning [0; 2π] kesmadagi ildizlari nechta?
  3. #1224cos α = 0,6 va α — birinchi chorak burchagi. sin α ni toping.
  4. #1323cos x = −1/2 tenglamaning [0; π] kesmadagi ildizini toping.