# Examples for secondary school students - page 23

- Square pyramid

Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees. - Tourist Jirka

Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey? - Bomber

Bomber flies 10 km at 600 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s^{2}. - Trapezoid - hard example

Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter. - Grandson and granddad

Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years. - Reciprocal

What is the reciprocal of the sum of the reciprocals of 4 and 9? - Quadratic equation

Solve quadratic equation: 2x^{2}-58x+396=0 - Two cars

From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what. - Future of libraries

You know that thanks to the Internet, electronic communications and developing online resources on the Internet annually declining number of traditional readership by 17%. These deal is irreversible evolutionary shift from old books from libraries to immed - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - Square

If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm^{2}. Determine the side length of the original square. - Building

The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building? - Surface of the cylinder

Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height. - Circle sector

Circular sector with a central angle 80 ° has area 1257 cm^{2}. Calculate its radius r. - Population

The town has 65,000 inhabitants. 40 years ago there were 157,000. How many people will live in town in 10 years if the average rate in population is as in previous years? - Field with vegetables

Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated? - Cars plates

How many different licence plates can country have, given that they use 3 letters followed by 3 digits? - Internal angles

The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete - Water

On the lawn which has area 914 m^{2}rained 3 mm of water. How many liters of water rained? - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance?

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