# Examples for 8th grade - page 64

- Three workers

Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 25 days, B together with C for 16 days, A together with C for 10 days. How long it would take to complete the task every one of them alone? How long it would. - VAT

In the country XYZ car Daewoo Leganza costs 3779 Euros including VAT; 3325.52 Eur without VAT. a) Determine the rate of VAT. b) How much is Euro VAT paid on the purchase? c) How many % of the total price of the goods is VAT? VAT = value added tax. - Icerink

Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water. - Diagonal

Diagonal of the rectangle has length 14 cm. Angle between diagonal and londer sife of rectangle is 37°. Calculate area of the rectangle. - Silo

Outer perimeter of silo is 24 m. Concrete wall is 18 cm thick. What is diameter and area of inside floor of silo? - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ) - Steamship

Between the two ports on the river is going steamship. The journey there and back takes 14:49. Downstream steamship traveling at 21 km/h, upstream 9 km/h. What is the distance between the ports? - Triangle

For how many integer values of x can 8, 11 and x be the lengths of the sides of triangle? - Triangle ABC

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19 - 2x cone

Circular cone height 60 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - Cubes

Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm^{2.}Determine the length of the edges of this cubes. - Box

Calculate the angle between box base 5 x 7 and body diagonal length 14. - Concrete pipe

Concrete pipe is cylindrical with an inner diameter 130 cm and outer 142 cm. Calculate the surface of the concrete pipe, if it is 6 m long. - Magnification of the square

If we increase the square side, increase the content of the 42 %. About what percentage was increased his sides? - Similarity n-gon

11-gones ABCDEFGHIJK and A'B'C'D'E'F'G'H'I'J'K' are similar. The area of 11-gon ABCDEFGHIJK is S_{1}=254 cm^{2}and the diagonal length HG is 20 cm. Calculate area of the 11-gon A'B'C'D'E'F'G'H'I'J'K' if H'G' = 36 cm. - Glass mosaic

How many dm^{2}glass is nessesary to produc 50 slides of a regular 6-gon, whose side has length 7 cm? Assume that cutting glass waste is 14%. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 53.7°. Consider a globe with a radius of 6378 km. - Czech crown salary

The monthly salary of the employee is CZK 10,800. In the course of the year the bulk salary increased by CZK 500. Calculate which month (1 ... 12) was increased if its annual income was 133,600 CZK. - Three numbers

The sum of the three numbers is 287. These numbers are in a ratio of 3: 7: 1/4 Define these numbers

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