# Grade - examples - page 92

1. Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
2. Water pool
What water level is in the pool shaped cuboid with bottom dimensions of 25 m and 10 meters, when is 3750hl water in the pool.
3. Stock
Enterprise sold 7/12 of their products to foreign markets and 2/5 of the remainder sold at home. How many % of the products is still in stock?
4. Tower model
Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
5. Wheel
What is the wheel diameter if on the 0.38 km track turns 128 times?
6. Book
To number pages of thick book was used 4201 digits. How many pages has this book?
7. Decimal to fraction
Write decimal number 8.638333333 as a fraction A/B in the basic form. Given decimal has infinite repeating figures.
8. Geometric progression 2
There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
9. Parachutists
Parachutists during freefall firstly held in groups of 4, then of 6, then 9, 12 and finally of 18 members. How many parachutists jump at least should be, if at each group must all be involved.
10. Legs
In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
11. Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q.
12. Parabola
Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
13. Scouts
Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type?
14. Euros
Michal, Peter, John and Lenka got together 2,400 euros. They share an amount in ratio 2:6:4:3. How many got each of them?
15. Farm
Agricultural cooperative (farm) produced 14144 liters of milk for 16 days. Which exceeded the plan by 1984 liters. How many liters of milk a day had planned to produce?
16. Center of gravity
The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system: A1 [14; -2; 5] m1 = 10.2 kg A2 [-2; -16; 7] m2 = 13.6 kg A3
17. QuizQ
An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side?
18. Profits
Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?
19. Cars speeds
Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
20. Tiler
On what surface m2 tiler must lay 30 square tiles, each of which has a side 25 cm?

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