# Examples for 9th grade - page 27

- Angles ratio

In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is: - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei - Tributaries

The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries? - Tetrahedron

Calculate height and volume of a regular tetrahedron whose edge has a length 11 cm. - Gauss

Help little C.F. Gauss sum all the integers from 1 to 340. - Bomber

Bomber flies 5 km at 1400 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.} - 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? - Cube - wall

V kocke ABCDEFGH je ?. Aký je povrch kocky? - Quadratic equation

Solve quadratic equation: x^{2}+16x-225=0 - Car

The driver of a car is to get to 378 km distant city. From atlas found that 99 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 117 km/h. Calculate how many hours it will ta - Two diggers

There are two diggers. One digger digs a pit 83 hours second gidding 1.4 times faster. a) how long took to dig a pit second digger b) how long took dig together - Diamond ABCD

In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - 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.} - Racing track

On the racing track circling three cars. The first passes one circuit for 8 seconds, the second for 16 seconds and a third for 15 seconds. a) Calculate number of seconds since the start to catch all three cars together for the first time again across the. - Sphere cuts

At what distance from the center intersects sphere with radius R = 60 plane, if the cut area and area of the main sphere circle is in ratio 3/6. - 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. - Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm^{2.} - Racer

The first racer run at a speed 12 m/s and is 470 meters before the finish and ahead 22 meters before second competitor. At what speed must run the second racer to catch first racer at the finish line? - 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. - Ice cream in cone

In the ice cream cone with a diameter of 3.6 cm is 0.9 dl of ice cream. Calculate the depth of the cone.

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