# Algebra - problems - page 16

1. Segments
Line segments 67 cm and 3.1 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
2. Tiles
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
3. Apartments
Apartment on the first floor was 10% more expensive than the same apartment on the second floor. The difference was 105 Kc annually. Calculate the annual rent of the apartment in the first floor and from apartment on the second floor.
4. Lines
In how many points will intersect 14 different lines, where no two are parallel?
5. Euclid3
Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.
6. Goat
Meadow is a circle with radius r = 34 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow?
7. Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
8. Certificate
There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2?
9. Chord
In a circle with radius r=70 cm is chord 10× longer than its distance from the center. What is the length of the chord?
10. Nice prism
Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
11. The car
The car has traveled the distance between A and B for four hour. If we increased the average by 17 km/h the car travel this distance an hour earlier. Determine the initial speed of the car and the distance between A and B.
12. Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.
13. Circle
Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
14. Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
15. Warehouses
To four warehouses is going cement in 20 kg bags. To first one third, to second quarter of the total. The third store got two thirds of the rest, and the last 110 tons came to fourth. How many cement is in all warehouses and how much got every one?
16. Angle of deviation
The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
17. Family
Martin has just as brothers as sisters. His sister Jana but has 2 times more brothers than sisters. a) How many children are in this family? b) How many boys and how many girls are in the family?
18. Acids
70% acid was make from same acid of two different concentrations. Amount weaker acid to the stronger acid is in ratio 2:1. What was the concentration of the weaker acid, if stronger had 91% concentration?
19. 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?
20. Column
Perpendicular pole high 8 m tall broke and its toe fell 2.7 m from the bottom of the pole. At what height above the ground pole broke?

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