Maximum - practice problems - page 6 of 10
Number of problems found: 187
- Rocket start
A body launched vertically upward returns to its starting point after 6 seconds. What maximum height did it reach? - The pool - optimization
A block-shaped pool with a volume of 200 m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Ten boys
Ten boys chose to go to the supermarket. Six boys bought gum, and nine boys bought a lollipop. How many boys bought gum and a lollipop? - Cup Diameter Ball Displacement
The mug has the shape of a cylinder with a height of 60.7 mm. There is two dl of water in it. If we dip a ball with a diameter of 40 cm into the water, the water will not overflow. What is the minimum diameter of the cup? - Allan
Allan keeps tropical fish. His aquarium is 4 feet long, 1 foot wide, and 2 feet tall. Each fish needs at least 0.5 ft³ of water. What is the maximum number of fish he can keep in the aquarium? Please show your solution. Please - Mice of Each Color
The hat has 14 grays, eight white, and six mice. What is the smallest number of mice we have to pull out of our hats to ensure we have at least one mouse of each color? - A tenth of a second
A frequent competition, even for amateurs, is long-distance running. The running time was measured with a stopwatch with a precision of one tenth of a second. Two other competitors were diligently overtaking each other in the last metres before the finish - Confectionery
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - A car
A car weighing 1.05 tonnes, travelling at the maximum speed limit in a village (50 km/h), crashes into a solid concrete barrier. Calculate the height from which the car would have to fall onto a concrete surface to produce the same impact force as in the - Trees in alley
There are four trees in the alley between which the distances are 35 m, 15 m, and 95 m. Trees must be laid in the spaces so that the distance is equal and maximum. How many trees will they put in, and what will be the distance between them? - Left handed
It is known that 25% of the population is left-handed. What is the probability that there is a maximum of three left-handers at a seminar with 30 participants? - Runner acceleration speed
The runner ran the track 100 m in 10.2 seconds. He ran the first 20 m with a uniformly accelerated movement. Then he ran evenly. What was its acceleration on the 20 m section, and what was its maximum speed? - An equilateral
An equilateral triangle with a side of 10 m represents a wooden platform standing on a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat? - Car crash
A car crash occurred on the road with a maximum permitted speed of 60 km/h. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, assu - Train Route Times Comparison
The train will run from Kockov to Drakov in 2 hours and 40 minutes, from Oslice to Kocourkov in 180 minutes, and from Kocourkov to Mokrov in 2 hours and 30 minutes. Which route will the train travel in the shortest and which in the longest time? - Classmates
Roman is ranked 12th highest and eleventh lowest pupil. How many classmates does Roman have? - Snake Shelves Construction
The boys at school were tasked with drawing a snake according to the assignment, each snake consists of several shelves. Michal had to build a snake from 5 three-shelf parts, Adam from 4 four-shelf parts, and Andrew from 7 two-shelf parts. Did the snake h - Non-linear effects
Since 2017, the percentage rate of flat-rate expenses has been increased from 40% to 60% of the total income. The monthly limit (420 euros) has been cancelled and the annual limit of the sum of flat-rate expenses is increased from 5 040 euros to 20 000 eu - Summer Camp and Vacation
There are 22 pupils in the class. During the holidays, nine students will go camping. Fifteen pupils will go on holiday together with their parents. How many students will go to summer camp and a family vacation? - Rectangle Carpet Dimensions Perimeter
The electrified carpet was rectangular, 16 square meters in area, and no two points on it were more than 7 meters apart. What different circuits can carpets that meet these conditions have?
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