# Examples for secondary school students - page 30

1. Pool 2 The first supply by the pool fill for five hours and the second fill for six hours, drain should be drained for 15 hours. For how many hours the pool is full, when we open both inlet now and outlet open two hours later?
2. Similarity Rectangle ABCD has dimensions of 7 cm and 6 cm. Rectangle PQRS has dimensions 14 cm and 12 cm. Determine coefficient of the similarity k of the rectangles, if they aren't similar enter zero as the coefficient of similarity.
3. Sheep Shepherd tending the sheep. Tourists asked him how much they have. The shepherd said, "there are fewer than 500. If I them lined up in 4-row 3 remain. If in 5-row 4 remain. If in 6-row 5 remain. But I can form 7-row." How many sheep have herdsman?
4. Church roof The roof of the church tower has the shape of a regular tetrahedral pyramid with base edge length 5.4 meters and a height 5 m. It was found that needs to be corrected 27% covering of the roof area. What amount of material will be required?
5. Vinegar What percentage vinegar we get if we mix 1 if dm³ eight percent vinegar with 1.5 dm³ six percent vinegar?
6. Bomber The aircraft flies at an altitude of 4100 m above the ground at speed 777 km/h. At what horizontal distance from the point B should be release any body from the aircraft body to fall into point B? (g = 9.81 m/s2)
7. Flowerbed Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
8. Parallelogram Parallelogram has sides lengths in the ratio 3: 4 and perimeter 2.8 meters. Determine the lengths of the sides.
9. Simple interest 4 Find the simple interest if 5243 USD at 4.3% for 261 days. Assume a 361-day year.
10. Ball Ball was fired at an angle of 35° at initial velocity 437 m/s. Determine the length of the litter. (g = 9.81 m/s2).
11. Digits A, B, C For the various digits A, B, C is true: the square root of the BC is equal to the A and sum B+C is equal to A. Calculate A + 2B + 3C. (BC is a two-digit number, not a product).
12. Bevel I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
13. Comparing powers How many times is number 56 larger than number 46? After 548 hours decreases the activity of a radioactive substance to 1/9 of the initial value. What is the half-life of the substance?
15. Slope What is the slope of the line defined by the equation -2x +3y = -1 ?
16. Sphere vs cube How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
17. BW-BS balls Adam has a full box of balls that are large or small, black or white. Ratio of large and small balls is 5:3. Within the large balls the ratio of the black to white is 1:2 and between small balls the ratio of the black to white is 1:8 What is the ratio of.
18. Secret number Determine the secret number n, which reversed decrease by 16.4 if the number increase by 16.4.
19. Two boxes-cubes Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
20. Nuts, girl and boys Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed.

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