Examples for 9th grade - page 16

  1. Sector
    vysec The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
  2. MO - triangles
    metal On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se
  3. Pairs
    pair At the table sit 8 people, 4 on one side and 4 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
  4. Q-Exam
    unit_circle If tg α = 0.9, Calculating sin α, cos α, cotg α .
  5. Block
    brick_lego Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
  6. Cone and the ratio
    kuzel Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
  7. Cardboard box
    krabicka We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal
  8. Morse alphabet
    morse_code Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters.
  9. Sphere A2V
    sphere3 Surface of the sphere is 296 cm2. What is its volume?
  10. Steamship
    parnik Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h. What is the distance between the ports?
  11. Vector
    some_vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
  12. Two balls
    balls-inside-cylinder Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
  13. Trapezoid - diagonal
    licho Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
  14. Scrap
    chair_bad From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
  15. Leveling
    quattro Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m2 to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness.
  16. Blueberries
    boruvky Marie earns 3 liters of blueberries for 3.4 hours, Peter 2.4 liters for 2.9 hours. How long have earns together one liter?
  17. Three workers
    three_workers Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 11 days, B together with C for 15 days, A together with C for 24 days. How long it would take to complete the task every one of them alone? How long it would.
  18. Triangle angles
    triangles_2 The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
  19. Wheat
    field_1 The rectangle shaped field with dimensions 889 m and 1336 m harvested last year was 6235 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 3 m parallel to the side of the field 1336 m, where.
  20. Amazing number
    numbers4 An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.

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