# Units - examples - page 13

1. Isosceles trapezium
Trapezoid YSED (YS||ED) is isosceles. The size of the angle at vertex Y is 17 degrees. Calculate the size of the angle at vertex E.
2. Compound interest
Calculate time when deposit in the bank with interest 2.5% p.a. doubles.
3. Estate
Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy?
4. Angle between lines
Calculate the angle between these two lines: ? ?
5. Tetrapack
How high should be the milk box in the shape of a prism with base dimensions 8 cm and 8.8 cm if its volume is 1 liter?
6. n-gon
Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon?
7. Stairway
What angle rising stairway if step height in 17 cm and width 27 cm?
8. Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
9. Pension or fraud
Imagine that your entire working life working honestly and pay taxes and to Social Insurance (in Slovakia). You have a gross wage 730 Euros, you pay social insurance (you and your employer) monthly € 263 during 44 years and your retirement is 354 Eur.
10. Goat and circles
What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
11. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
12. Plan of the village
Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality.
13. Water
Into a full cylindrical tank high 3.6 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.9 m, 0.7 m. How many liters of water will come out?
14. Motion
From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
15. Peroxide
How much distilled water (in liters) must pharmacists pour into 300 ml of 23.6% solution of hydrogen peroxide to get 2.7% solution to gargle?
16. Sale
If the product twice price cut by 25%, what percentage was price cut in total?
17. Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
18. The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
19. Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
20. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.