# Grade - examples - page 40

1. Area codes How many 6 digit area codes are possible if the first number can't be zero?
2. Carpet The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag
3. Diagonals Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus.
4. Isosceles triangle Calculate the perimeter of isosceles triangle with arm length 26 cm and base length of 21 cm.
5. Circles Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles?
6. Center In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
7. 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?
8. BMI index Calculate BMI (body mass index, an index indicating obesity, overweight, normal weight, underweight) man weighing m = 71 kg and height h = 170 cm. Index is calculated according to equation (formula): ? With BMI index is possible to compare people of diff
9. Three drivers Three driversdriving the same direction found that they have same amounth of gasoline. The first is enough to go 6 km, 4 km second and third 3km. Gasoline they divided so all three just drove to the nearest petrol station. How many km away was a petrol sta
10. Four pupils Four pupils divided \$ 1485 so that the second received 50% less than the first, the third 1/2 less than a fourth and fourth \$ 154 less than the first. How much money had each of them?
11. Angles in a triangle The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle?
12. Rope One half of rope use Mam for packaging, half of the rest got son, half of the rest he took father and two fifths of what remained, got daughter. Remained 143 cm of rope. How long was rope at the beginning?
13. Hexagon 5 The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon.
14. Park In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
15. Cotangent If the angle α is acute, and cotg α = 1/3. Determine the value of sin α, cos α, tg α.
16. School trip The class has 19 students. What different ways students can be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms. (Each room has its unique number)
17. OPT What is the perimeter of a right triangle with the legs 14 cm and 21 cm long?
18. Machines In the workshop are three machines. The first is treated 250 parts for 4.7 hours, the second is treated 300 parts for 1.9 hours and the third is treated 230 parts for 4.6 hours. How long will take to make 3100 parts if worked all three machines at the.
19. Semicircle In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
20. Center Calculate the coordinates of the circle center: ?

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