# Examples for 9th grade - page 29

- 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. - 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? - 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? - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2}. Determine the side length of the original square. - 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. - 30-60-90

The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg? - 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? - Divisors

Find all divisors of number 493. How many are them? - Flowerbed 2

Around the square flower bed in a park is sidewalk 2 m wide. The area of this sidewalk is 243 m^{2}. What is the area of the flowerbed? - Circle sector

Circular sector with a central angle 80 ° has area 1257 cm^{2}. Calculate its radius r. - RT and ratio

Right triangle whose cathetus are in a ratio 7:14 has hypotenuse 78 m long. How long are cathetus? - Cube and water

How many liters of water can fit into a cube with an edge length of 0.11 m? - Cone and cube

About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r? - Field with vegetables

Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated? - Cars plates

How many different licence plates can country have, given that they use 3 letters followed by 3 digits? - Interest

Calculate how much you earn for 10 years 43000 deposit if the interest rate is 1.3% and the interest period is a quarter. - Water

On the lawn which has area 914 m^{2}rained 3 mm of water. How many liters of water rained? - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance? - Trapezoid ABCD

Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.

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