# Algebra - problems - page 62

1. VCP equation Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
2. Church roof 2 The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
3. Factory In the factory workers work in three shifts. In the first inning operates half of all employees in the second inning and a third in the third inning 200 employees. How many employees work at the factory?
4. Tickets On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
5. Three numbers What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
6. Infirmary Two thirds of children from the infirmary went on a trip seventh went to bathe and 40 children remained in the gym. How many children were treated in the infirmary?
7. Novak Novak needed to dig up three of the same pit in the garden. The first pit dug father alone for 15 hours. His second dig son helped him and it did that in six hours. The third pit dug son himself. How long it took him?
8. Primes 2 For what primes p,q,r is true: p2-(q+r)2=647
9. Tailor From the rest of the cloth tailor could cut off either 3 m in men's suits without vest or 3.6 m with vest. What shortest possible length could the rest of the cloth have? How many suits a) without a vest b) with vest could make the tailor from the re
10. Bags The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
11. Two-digit number I am a two-digit number less than 20. When I divided by three, then you get the rest 1 and when you divide me by four you get also rest 1. What number am I?
12. Cuboid enlargement By how many percent increases the volume of cuboid if its every dimension increases by 30%?
13. Working together One painter paint the nursery in 10 days, the second in 8 days. How many days will the nursery be painted if they work together?
14. Cuboid surface Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.
15. Unknown number 6 Determine the unknown number, which is by 1.5 greater than its fourth.
16. Divisible by 5 How many three-digit odd numbers divisible by 5, which are in place ten's number 3? A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter. Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38 The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume. Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?