Examples for secondary school students - page 98 of 230
Number of problems found: 4593
- Coordinates of a centroind
Let A = [3, 2, 0], B = [1, -2, 4], and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians). - Consumption 17823
The roof is a regular hexagonal pyramid shell with a wall height of v = 5 m and a base edge of a = 4 m. Calculate the consumption of sheet metal to cover the roof, assuming 15% losses. - Fourth-week 17783
They earned CZK 113,400 in the shop in four weeks. The first and fourth-week sales were the same, the second week 10% higher than the first week and the third week 5% lower than the first week. How much did they earn each week? - One-fifth 17753
The store stacked two hundred boxes of washing powder in three piles. There were 13 more boxes in the first pile than in the second pile, one-fifth more in the second pile than in the third pile. How many boxes were in which pile? - Removed 17713
The miner removed 135 carts of coal in 5 days so that the next day he removed three carts of coal more. How many carts did he drive on the first day? - Receives 17653
Honza, Lucas, and David are to split CZK 5,400 so that Lucas receives CZK 400 more than Honza and David CZK 400 less than Honza. How much will each of them receive? - Probability 17503
If we choose four numbers from 1 - 20, what is the probability that 6 or 10 will be among them? - Observation 17433
The aircraft flying just above point A can be seen from observation B, 2,400 meters away from point A, at an altitude of 52°30'. How high does the plane fly? - Corona virus
Calculate an estimate of the GDP (Gross Domestic Product) percentage that declined due to the quarantine related to the corona COVID-19 virus that lasted for two months. During this time, economic activity is down by 80%. - Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³. - Big Earth
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km. - Oscillation 17313
The period of the natural oscillation of the railway car is 1.25s. The length of the rails is 25 m. At what speed does the vibration, caused by the impact of the wheels on the joints between the rails, reach a maximum? Give the result in m/s. - Self-oscillation period
The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s. - Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zones? Tropics border individual zones at 23°27' and polar circles at 66°33'. - Researchers
Researchers asked 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the famili - (four-seater) 17053
Karel wants to take some 15 classmates out of school after graduation. How many passengers does he have to choose if he has to fill the car (four-seater)? - Probability 17023
In the draw pole, five numbers out of 35 are drawn. The third prize is paid for three guessed numbers. What is the probability of winning the third prize if we submit a ticket with one of five numbers? - Probability 17013
What is the probability that a randomly written two-digit number from number 20 to number 99 will be divisible by 11, the power of number 3, or a prime number? - VOCABULARY 16893
Load. Car. ... .8.30 45km/h delivery. ... . ..9.00 75km/h At what time and distance did the van catch up with the truck? WORD PROBLEM ON MOVEMENT. - Tetrahedral pyramid 8
Let all the side edges of the tetrahedral pyramid ABCDV be equally long and its base let us be a rectangle. Find its volume if you know the deviations A=40° B=70° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h=
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