# The second stage of the project -Water: mathematical problems.

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The second stage of the project -Water: mathematical problems

Exercise 1. RECYKLING means leading used up materials to the state which enable their later reuse. How many letter in the word recykling is/are middle symmercial? Answer: C In this word are two letters middle symmercial.

Exercise 2. One tonne wastepaper let save 17 trees which cutting down would be crucial for making new paprer. How many kilograms of wastepaper save one tree? Answer: C To save one tree we need about 59kg of wastepaper.

Exercise 3. The oldest in Poland - Chrobry oak has the height of 130 cm and its circumference is 9, 92 m. What is the diameter of oak trunk on that height? Answer: D On that height diameter of oak is about 3,16 m.

Exercise 4. What is the height of 'Bartek oak', one of the oldest natural monuments in Poland? Give the result with 1 m precision. A=34,7mx= (a√3)/2 α=60 degressx=(34,7√3)/2 x =?x=30m Answer: 'Bartek oak‘ has 30m height. x

Exercise 5. At the same time from a harbour sailed away a passenger steamer and cutter. Both ships were sailing in the same direction, the first one with speed of 24 km per hour, the second one with speed 15 km per hour. After 3 hours steamer grounded. After some time streamer continued travelling and 7 hours later caught cutter. How many hours the steamer was grounded ? x – number of hours steamer grounded 15*(10+x) km – way traveled by couter 24*10 km – way traveled by steamer Way traveled by steamer and couter is this same, so: 15*(10+x)=24*10 150+15x=240 15x=240-159 15x=90/:15 x=6 Answer: Steamer was grounded 6 hours.

Exercise 6. Two barrels contain together 240 litres of water. If we pour from the first barrel amount of water to double the content of the second, and next from the second barrel pour amount of water to double the content of the first, then in both barrels will be the same amount of water. How many litres of water were in barrels at the beginning? X - starting number litres of water in first barrel Y - starting number litres of water in second barrel If we pour some water from the first barrel to second barrel to double the content of the second barrel, then te number litres of water in the first barrel will be x-y, and 2y in second barrel. This shows that: {x+y=240 {x=240-y {2y-(x-y)=2(x-y) {-720+3y+5y=0 {x+y=240 {x=240-y {2y-z+y=2x-2y {8y=720/:8 {x+y=240 {x=240-y {-3x+5y=0 {y=90 {x=240-y {x=150 {-3(240-y)+5y=0 {y=90 Answer: In first barrel was 150l. of water and 90l in the second.

Exercise 7. In maths competition took part 100 scientists. 90 of them were speaking English, 75 of them Polish, 70 of them Italian and 66 of them Spanish. Was among them a scientist who was speaking all four languages? Each participant in the Congress we give cards with the letters A, P, W, or H, indicating which language speaks. We distributed a total of 90 +70 +75 +66 = 301 pages. If each of mathematicians ruled no more than three languages, then all pages would be no more than 100 * 3 = 300, which is inconsistent with the fact that cards are 301. Thus, at least one of the participants speaks four languages.