# Examples for secondary school students - page 30

1. 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?
2. Vinegar
What percentage vinegar we get if we mix 1 if dm³ eight percent vinegar with 1.5 dm³ six percent vinegar?
3. 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)
4. 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?
5. Simple interest 4
Find the simple interest if 5243 USD at 4.3% for 261 days. Assume a 361-day year.
6. Parallelogram
Parallelogram has sides lengths in the ratio 3: 4 and perimeter 2.8 meters. Determine the lengths of the sides.
7. 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).
8. 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).
9. Bevel
I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
10. 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?
12. Slope
What is the slope of the line defined by the equation -2x +3y = -1 ?
13. 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.
14. Secret number
Determine the secret number n, which reversed decrease by 16.4 if the number increase by 16.4.
15. 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?
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. 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.
18. Decibel
A circuit has an input power of 58 mW. Its output power is 6 mW. What is the loss in decibels?
19. 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
20. Isosceles IV
In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.

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