Asosiy tarkibga o'tish

4.9-bo'lim : Ko'proq optimallashtirish

  1. Biz o'rtasi to'rtburchak, oynaning yuqori va pastki qismi yarim doira bo'lgan oyna qurmoqchimiz. Agar bizda 50 metr ramka materiali bo'lsa, derazaning o'lchamlari qanday bo'lishi mumkin, bu eng yorug'likni beradi?
    A sketch of the window described in the problem. It is a rectangle with a semicircle on the top and another semicircle on the bottom, and dashed lines mark where the top and bottom of the rectangle meet the flat sides of the two semicircles.
    Yechim
  2. Radiusi 1 bo‘lgan aylana ichiga chizilishi mumkin bo‘lgan eng katta to‘rtburchakning maydonini aniqlang.
    A sketch of a rectangle inscribed in a circle. All four corners of the rectangle touch the circle and the rectangle is wider than it is tall.
    Yechim
  3. \(x = 3 - 2{y^2}\) da \(\left( { - 4,0} \right)\) ga eng yaqin nuqta(lar)ni toping. Yechim
  4. 80 sm uzunlikdagi sim ikki qismga bo'linadi. Bir bo'lak teng qirrali uchburchakka egiladi, ikkinchisi esa bir tomoni boshqa tomonining uzunligidan 4 barobar ko'p bo'lgan to'rtburchaklar shaklida egiladi. Ikkala raqam bilan o'ralgan maydonni maksimal darajada oshirish uchun simni qayerda kesish kerakligini aniqlang. Yechim
  5. \(\left( {2,5} \right)\) nuqtadan o'tadigan chiziq \(x\) o'qi va \(y\) o'qi bilan to'g'ri burchakli uchburchak hosil qiladi.st kvadrant. Ushbu uchburchakning maydonini minimallashtiradigan chiziq tenglamasini aniqlang.
    A sketch of the triangle described in the problem. A line falls from the upper left to the lower right, passing through the point \(\left( {2,5} \right)\), which is marked on the line. The line together with the x-axis and the y-axis forms a right triangle in the first quadrant and the inside of the triangle is shaded and labeled “Minimize This Area”.
    Yechim
  6. Quvur bo'lagi 18 fut kenglikdagi koridor bo'ylab olib ketilmoqda. Yo'lakning oxirida to'g'ri burchakli burilish mavjud va koridor 12 metr kengligida torayadi. Koridorda burilish bo'ylab ko'tarilishi mumkin bo'lgan eng uzun quvur (har doim gorizontal holatda) nima?
    A sketch of the hallway described in the problem, seen from above. The wide hallway is 18 feet across and runs vertically, the narrow hallway is 12 feet across and runs horizontally, and they meet at a right-angled turn. The pipe is drawn as a straight line lying diagonally across the inside corner of the turn, touching the outer wall of each hallway and resting against the inner corner.
    Yechim
  7. 10 metr balandlikdagi ikkita ustun bir-biridan 30 metr masofada joylashgan. Har bir qutbning yuqori qismiga uzunlikdagi sim bog'langan va u ikki qutb o'rtasida bir joyda erga qo'yilgan. Minimal sim miqdori ishlatilishi uchun simni qaerga qo'yish kerak?
    A sketch of the two poles and the wire. Both poles are 10 meters tall and the ground between them is marked as 30 meters. The wire runs from the top of the left pole down to a stake on the ground between the poles and then back up to the top of the right pole, forming a “V” shape.
    Yechim