# Algebra - problems - page 15

1. Quadrant II
Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
2. Geometric mean
Calculate the geometric mean of numbers a=15.2 and b=25.6. Determine the mean by construction where a and b are the length of the lines.
3. Rectangle
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
4. Two runners
Two runners ran simultaneously towards each other from locations distant 34.6 km. The average speed of the first runner was 1/5 higher than the average speed of the second runner. How long should each ran a 34.6 km, if you know that they meet after 67 mi
5. Tiles
From how many tiles 20 cm by 30 cm we can build a square of maximum dimensions, if we have maximum 881 tiles.
6. Baker
The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough?
7. 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?
8. Lines
In how many points will intersect 14 different lines, where no two are parallel?
9. Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
10. 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.
11. 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.
12. 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.
13. Goat
Meadow is a circle with radius r = 19 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?
14. 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.
15. Perpendicular
Determine the slope of the line perpendicular to the line p: y = -x +4.
16. Chord
In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord?
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. Deposit
If you deposit 959 euros the beginning of each year, how much money we have at 2.1% (compound) interest after 19 years?
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. Line
Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.

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