# Examples for secondary school students - page 31

- 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? - 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. - 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. - Decibel

A circuit has an input power of 58 mW. Its output power is 6 mW. What is the loss in decibels? - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - 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? - Golden ratio

Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line. - Nuts

How many we must have at least nuts if we can equally divide it to 10 children, 11 children or 19 children and any nut left? - Wind drift

The plane flies at 860 km/h, passing distance 3000 kilometers with the wind and once again against the wind for 6 h 59 min. What is the wind speed? - Meridian

What is the distance (length) the Earth's meridian 23° when the radius of the Earth is 6370 km? - Three-digit

How many three-digit natural numbers is greater than 321 if no digit in number repeated? - Aircrafts

Above the town hall tower flew the plane with constant speed 592 km/h and 15 minutes later the second plane at speed of 675 km/h. How long and how far from the town hall will be aircrafts caught up? - Bottles of juice

How many 2-liter bottles of juice need to buy if you want to transfer juice to 50 pitchers rotary cone shape with a diameter of 24 cm and base side length of 1.5 dm. - Prism

The volume of tetrahedral prism is 2.43 m^{3}. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism. - Sequence 2

Write the first 5 members of an arithmetic sequence a_{11}=-14, d=-1 - Diagonal 20

Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be? - Combinatorics

The city has 7 fountains. Works only 6. How many options are there that can squirt ? - Angle in RT

Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions. - Rectangle vs square

One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle. - RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.

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