The most difficult problems

  1. Kostka
    sphere_in_cube Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
  2. Bent scale
    vaha_1 Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the weight on the scale was bent. How much did they really weigh?
  3. A swiming
    water2 A swiming pool holds 30000lt of water. How many gallons does it hold? 1 gallon= 4.55lt
  4. Compute 4
    14-12-12 Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long.
  5. The freezer
    freezing 1. The temperature inside a freezer is minus 23 degree Celsius. The temperature falls by a further 12 degree degree Celsius. What is the new temperature? 2. What is the difference between temperatures of 12 degree Celsius and 210 degree Celsius?
  6. Decide 2
    vectors2 Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line
  7. Prescription
    acylpyrin Jannin knows that Mr. Robinson needs 14 tablets for a week's supply of an anti-inflammatory drug Mr. Robinson is going to vacation and needs a four week supply. How many tablets does Johnny need to fill his prescription?
  8. Chord BC
    tetiva2 A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?
  9. Vector perpendicular
    3dperpendicular Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1)
  10. Vector equation
    collinear2 Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent
  11. Five-gon
    5gon_diagonal Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
  12. Fall sum or same
    dices2 Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice.
  13. Annulus
    annulus_inscribed_circles Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
  14. Coordinates of a centroind
    triangle_234 Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
  15. A library
    bookshelf A library has 12,500 fiction books and 19,000 non fiction books. Currently 2/5 of the fiction books are checked out. Currently 2/5 of the non fiction books are checked out. Of the books checked out, only 1/10 are due back this week. How many books are due
  16. What percentage
    astronaut What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
  17. Tropics and polar zones
    circles_on_Earth What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'
  18. Tetrahedral pyramid 8
    pyramid_4s Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p
  19. Runners
    runners If John has a running speed of 3.5miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 am and Lucy starts running at 10:30 am, at what time will they meet? (as soon as possible)
  20. Adding
    eq1 Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.

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