# Examples for 9th grade - page 12

Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
2. Speed of Slovakian trains
Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
3. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 49 cm.
4. Hole
In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?
5. Parquet floor
Three workers laid parquet floor for 2.9 hour. The first one would do this work alone 9 hours, the second in 7 hours. For how many hours would fulfill this work the third worker, if he worked alone?
6. Tinsmith
Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add \$x cm width of the plate?
Determine the radius of the circle, if its perimeter and area is the same number.
8. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
9. Discount
Product has been discounted twice by 19%. What is the total discount given?
10. Seedcake
Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 2 hours. How many hours will spend washing the windows this "women's team" if working togethe
12. Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?
13. Diofant equation
In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
14. Phone numbers
How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
15. Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
16. Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
17. Cubes
Cube, which consists of 27 small cubes with edge 4 dm has volume:
18. Freedom
In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number.
19. Map
On the tourist map at a scale of 1 : 50000 is distance between two points along a straight road 3.7 cm. How long travels this distance on a bike at 30 km/h? Time express in minutes.
20. Square diagonal
Calculate the length of diagonal of the square with side a = 23 cm.

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