# Examples for 9th grade - page 21

1. Oil rig Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
2. Two runners Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
3. Tiles From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
4. Trains for people It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 85 km, with regular train leave at 7:00 and arrive at 8:18, but train is late and has departure at 8:10 and arrive at 9:27.
5. Baker The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough?
6. Icerink Rectangular rink with dimensions of 68.7 m and 561 dm must be covered with a layer of ice 4.2 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 9.7% greater than the volume of water.
7. Aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
8. Rhombus base Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 12 cm and u2 = 10 cm. Prism height is twice base edge length.
9. ISO trapezium Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees.
10. Certificate There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2?
11. Triangle TBC TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
12. Truncated pyramid How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm?
13. Lines In how many points will intersect 14 different lines, where no two are parallel?
14. Iron sphere Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
15. Pine wood From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum
16. Apartments Apartment on the first floor was 10% more expensive than the same apartment on the second floor. The difference was 105 Kc annually. Calculate the annual rent of the apartment in the first floor and from apartment on the second floor.
17. Map - climb On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track?
18. Sphere - parts Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
19. Rectangle The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
20. Perpendicular Determine the slope of the line perpendicular to the line p: y = -x +4.

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