# Examples for 9th grade - page 29

- Reciprocal

What is the reciprocal of the sum of the reciprocals of 4 and 9? - 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. - 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 - 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 - 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? - 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. - 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/s^{2}. - Trapezoid

Area of trapezoid is 135 cm^{2}. Sides a, c and height h are in a ratio 6:4:3. How long are a,c and h? Make calculation... - 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. - 30-60-90

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

Solve quadratic equation: 2x^{2}-58x+396=0 - 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/m^{3}. - 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. - 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? - 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. - 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? - 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. - 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? - Cube and water

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

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