Minimum - practice problems - page 3 of 6
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 107
- Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - Shopping malls
The chain of department stores plans to invest up to 24,000 euros in television advertising. Ads will place all commercials on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers. Durin - Summands
We want to split the number 110 into three summands so that the first and the second summand are in ratio 4:5, and the third with the first are in ratio 7:3. Calculate the smallest summands. - Regulations 20113
According to school regulations, a student receives an excellent grade if he achieves at least 26 points in a test with a total of 30 points. What is the minimum number of points a student must obtain in a test with a total of 50 points if the same passin - Benches 18013
There are 12 benches in the park. Four people can sit on the bench. At least two people sit on each of them. How many and most people sit on benches? - Rotaty motion
What minimum speed and frequency do we need to rotate with the water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling? - TV competition
Ten contestants in the competition answer five questions, one per round. Anyone who answers correctly will receive as many points as the number of competitors who answered incorrectly in that round. After the contest, one of the contestants said: We got 1 - The percent 2
The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5%, respectively. Suppose you have 3200 to invest and want to put twice as much in the growth fund as in the money market to maximize your return. How should you inve - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - 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? - The observatory
The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal need to be covered to cover it, and must we add 15 percent to the minimum amount due to joints and waste? - Hens and pigs
Hens and pigs have 46 feet in total. At least how much can heads have? - Diameter 7648
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? - Exercisers
How many exercisers are in the gym (minimum number) if there is one left after ordering into three, four, and five steps? - Kocourkov 7007
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? - Test scores
Jo's test scores on the first four 100-point exams are as follows: 96,90,76, and 88. If all exams are worth the same percentage, what is the minimum test score necessary on his last exam to earn an A grade in the class (90% or better)? - Minimum surface
Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm, respectively, can be packed.
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