# Examples for 9th grade - page 26

- Gauss

Help little C.F. Gauss sum all the integers from 1 to 340. - 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: - SAS triangle

The triangle has two sides long 7 and 19 and included angle 144°11'59″. Calculate area of this triangle. - Journey

The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla - Metal alloy

What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel? - Vertical prism

The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism - Forth and back

Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B? - 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? - Aircraft

The aircraft has in a fuel tank 100 hl of aviation fuel and flight consumes 4.3 liters of fuel. Identify the function, which expresses the dependence of the volume of fuel in tank on the track distance plane flew by. How many hectolites of fuel is still i - Work

First paver pave pavement for 33 hours. Second for 24 hours. Started first paver and after 5 hours, join the second. How long will they finish pavement? - Two runners

Two runners ran simultaneously towards each other from locations distant 21 km. The average speed of the first runner was 1/7 higher than the average speed of the second runner. How long should each ran a 21 km, if you know that they meet after 77 minute - Carpenter

From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off? - Rectangle

The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle. - Reciprocal

What is the reciprocal of the sum of the reciprocals of 7 and 2? - Horizontal Cylindrical Segment

How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank? - 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 - Interest

Calculate how much you earn for 7 years 14000 deposit if the interest rate is 1.8% and the interest period is a quarter. - 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? - Elections

In elections candidate 8 political parties. Calculate how many possible ways can the elections finish, if any two parties will not get the same number of votes.

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