# Examples for secondary school students - page 40

1. Moivre 2 Find the cube roots of 125(cos 288° + i sin 288°).
2. Crates 2 In 6 crates is 45 kg of apples In  5 crates is equally In 1 in crate is 3 kg more How many kilograms in each crate?
3. Computer The computer was purchased 10000,-. Each year, the price of a computer depreciates always the same percentage of the previous year. After four years, the value of the computer is reduced to 1300,- How many percent was depreciated price of the computer each
4. Reciprocal Calculate reciprocal of z=0.8-1.8i:
5. Double-track On double-track express met with a freight train. Express travel at speed 72 km/h, a freight train at speed 36 km/h. After what time period will be from 9 km apart?
6. Jar From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
7. High wall I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
8. Powers Express the expression ? as the n-th power of the base 10.
9. Regular triangular prism Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m.
10. Fraction For what x expression ? equals zero?
11. Alfa beta gama The triangle's an interior angle beta is 10 degrees greater than the angle alpha and gamma angle is three times larger than the beta. Determine the size of the interior angles.
12. Series Your task is express the sum of the following arithmetic series for n = 14: S(n) = 11 + 13 + 15 + 17 + ... + 2n+9 + 2n+11
13. The tent The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
14. Roof Tiles are stacked in rows on the trapezoidal shaped roof. At the ridge is 15 tiles and each subsequent row has one more tile than in the previous row. How many tiled is covered roof if lowermost row has 37 tiles?
15. Calculation of CN Calculate: ?
16. Line Write an equation of a line parallel to To 9x + 3y = 8 That Passes Through The Point (-1, -4). Write in form ax+by=c.
17. V - slope The slope of the line whose equation is -3x -9 = 0 is
18. Family Family has 4 children. Ondra is 3 years older than Matthew and Karlos 5 years older than the youngest Jane. We know that they are together 30 years and 3 years ago they were together 19 years. Determine how old the children are.
19. Office Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400?
20. Chords How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones?

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