# Examples for 9th grade - page 11

- Axial section

Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base. - Team

The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player? - Diofant 2

Is equation ? solvable on the set of integers Z? - Road

Between cities A and B is route 7 km long of fall average 4‰. Calculate the height difference of cities A and B. - 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 - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18]. - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 49 cm. - 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? - 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? - 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? - 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/m^{3}. Result round to one decimal place. - Radius

Determine the radius of the circle, if its perimeter and area is the same number. - Discount

Product has been discounted twice by 19%. What is the total discount given? - Seedcake

Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros? - Madams

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 - 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) - Euclid1

Right triangle has hypotenuse c = 27 cm. How large sections cuts height h_{c}=3 cm on the hypotenuse c? - 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. - 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° - Phone numbers

How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?

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