# Equation - high school - examples

1. Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit
2. Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
3. Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
4. Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
5. Company and employees
There are 370 employees in the company - women are 15% less than men. How many men work in the company?
6. The size
The size of a Trapezium are 3/4×cm, ×cm 2(×+1)cm and 3(×+2)cm long respectively if it's perimeter is 60cm, calculate the length of each side.
7. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
8. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
9. Bonus
Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?
10. Logic
A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together?
11. Beer
After three 10° beers consumed in a short time there are 5.6 g of alcohol in 6 kg adult human blood. How much is it per mille?
12. Clock
How many times a day hands on a clock overlap?
13. Server
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
14. River
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
15. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
16. Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
17. Observer
The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
18. Two cars
Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?
19. Circles
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
20. Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18

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