# Examples for 8th grade - page 26

- 6-gon

Perimeter of regular hexagon is 41. Calculate its circumradius (radius of circumscribed circle). - River

From the observatory 15 m high and 39 m from the river bank, river width appears in the visual angle φ = 22°. Calculate width of the river. - Diofant equation

In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Electronics: Resistors in parallel

From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R_{1}= 8kΩ a R_{2}= 18kΩ - Donuts

In the dining room at one table sit Thomas, Filip and Martin. Together they eat 36 donuts. How many donuts eaten everyone, when Filip ate twice as much as Thomas and Martin even half over Filip? - Pumps A and B

Pump A fill the tank for 12 minutes, pump B for 24 minutes. How long will take to fill the tank if he is only three minutes works A and then both pumps A and B? - Rope slack

Between two streets 20 m away give the lamp, which is in the middle and hanging 60 cm bellow the taut rope. Can be done with 20.5 meters rope? - Cuboid aquarium

Cuboid 25 times 30 cm. How long is third side if cuboid contains 30 liters of water? - 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. - Price reduction

Price of camera is 800 USD on sale its price reduced to 423 USD. Calculate the percentage reduction in the price of the camera. - Students

In the front row sitting three students and in every other row 11 students more than the previous row. Determine how many students are in the room when the room is 9 lines, and determine how many students are in the seventh row. - Backpack

Large backpack cost CZK 1352, little is 35% cheaper. How much we paid for 5 large and 2 small backpacks? - Children

Margaret and Zdena weighs the same and Petra 3 kg more. Together weigh 156 kg. How much does they weigh? - Pupils

Four pupils is going via dark hall. Start at one side and have to get to the other side for 17 minutes. They have only one lamp for the trip. The corridor is narrow, they can therefore go up two pupils at a time and go at the slower speed. Each pupil went. - Distance runner

Distance runner already climbed three fifths of the total route. Thus passed 90 km. How many km he have to stop? How long is his route? - Father and son

Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son? - Children

Less than 20 children is played various games on the yard. They can create a pairs, triso and quartets. How many children were in the yard when Annie came to them? - Rope

One half of rope use Mam for packaging, half of the rest got son, half of the rest he took father and two fifths of what remained, got daughter. Remained 52 cm of rope. How long was rope at the beginning? - Family

Mom is 42 years old and her daughters 13 and 19. After how many years will mother as old as her daughter together? - Ladder

Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder?

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