# Examples for 9th grade - page 29

1. Reciprocal What is the reciprocal of the sum of the reciprocals of 4 and 9?
2. Mountain railway Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
3. Car The driver of a car is to get to 608 km distant city. From atlas found that 162 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 116 km/h. Calculate how many hours it will t
4. Two diggers There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster. a) how long took to dig a pit second digger b) how long took dig together
5. Tourist Jirka Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
6. Sphere cuts At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
7. Bomber Bomber flies 10 km at 600 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s2.
8. Trapezoid Area of trapezoid is 135 cm2. Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation...
9. Grandson and granddad Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years.
10. 30-60-90 The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
11. Quadratic equation Solve quadratic equation: 2x2-58x+396=0
12. Iron fence One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m3.
13. Two cars From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what.
14. Racer The first racer run at a speed 20 m/s and is 750 meters before the finish and ahead 79 meters before second competitor. At what speed must run the second racer to catch first racer at the finish line?
15. Pyramid Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
16. Chicken I threw three chicken for a handful of grains and I noticed that it eat in a ratio of 8:7:6 and two of them grabbed 156 grains. How many grains have fought that chicken?
17. Square If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
18. Building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
19. Cube and water How many liters of water can fit into a cube with an edge length of 0.11 m?
20. Flowerbed 2 Around the square flower bed in a park is sidewalk 2 m wide. The area of ​​this sidewalk is 243 m2. What is the area of the flowerbed?

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