# Examples for 8th grade - page 51

- Against each other

From two points A, B distant 45 km at the same time started two cars against each other at speeds 81 km/h and 67 km/h. How long does cars meet and what distance passes each of them? - Map - climb

On the map of High Tatras in scale 1:25000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 156 mm. Altitude of this stations are 944 m and 1755 m. What is average angle of climb of this cable car track? - Lid

What is the weight of concrete cover (lid) to round shape well with a diameter 1.3 m, if the thickness of the cover is 15 cm? 1 m^{3}of concrete weighs 2190 kg. - Wire D

Wire length 5 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 35 cm. - Wheat

The rectangle shaped field with dimensions 979 m and 540 m harvested last year was 2775 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 6 m parallel to the side of the field 540 m, where no - Triangle

Calculate heights of the triangle ABC if sides of the triangle are a=48, b=81 and c=98. - Window

Peter demolish box hole in the wall for window frame 48×48 cm. When they came masters fitted frame and window will be found that glass is 13.7 cm from the hole in each direction. Calculate how much percent less light enters the window than hole? - Slope of track

Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long. - Engineer Kažimír

The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri - Rhombus and diagonals

The a rhombus area is 150 cm^{2}and the ratio of the diagonals is 3:4. Calculate the length of its height. - Content area and percents

Determine what percentage is smaller cube surface, when the surface area of the wall decreases by 25%. - Shots

Determine the percentage rate of keeper interventions if from 32 shots doesn't caught four shots. - Runner

Peter ran a speed of 12.4 km / h. After 45 minutes running he had a hiatus. The track is 31 km long. How many kilometers he still to run if he still running at the same speed? - Coins

Denis and Zdeno together have 97 coins. If Denis had 4 coins less than he has now, the number of the coins would be in the ratio 14: 17. Determine the number of coins owned by Denis and Zdeno. - The deposit

Deposit has been placed for one year at an annual rate of 4.5%. After the added interst amount rose to € 2,612.5. Determine initial deposit. - Schools

Three schools are attended by 678 pupils. To the first attend 21 students more and to the third 108 fewer students than to second school. How many students attend the schools? - Mr. John

Mr. John wants to buy winter apples Spartan. There are two ways to buy: 1) buy apples at the marketplace, where 1 kg costs 15 CZK. 2) Bring the car to the agricultural farm, where the apples are sold after 9 CZK per kilogram. However, he must pay CZK 150. - Salary increase

Ms. Merry salary increased by 15% and that was 83e. What should pay before the increase? - Outer contact of circles

Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S_{1}S_{2}S_{3}.

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