Minimum - practice problems
The minimum is the smallest value in a set of numbers or the lowest point on a function within a specified domain. In calculus, local minima occur where a function changes from decreasing to increasing, found by setting the derivative to zero and applying the second derivative test. Global minima represent the absolute lowest value across the entire domain. Minimum problems are essential in optimization, seeking to find the least amount of resources, time, or cost needed. Real-world applications include minimizing material usage, reducing travel distance, and finding optimal production levels. Identifying minima requires understanding of functions, critical points, and inequality constraints.Directions: Solve each problem carefully. Show all your work.
Number of problems found: 119
- A person 3
A person distributes his pens among four friends A, B, C, and D in the ratio 1/3 : 1/4 : 1/5 : 1/6. What is the minimum number of pens the person should have? - A variable
A variable rectangle has a constant area of 35 cm². Find the side lengths when the perimeter is at its minimum. - Minimum interior angle
What is the minimum interior angle possible for a regular polygon? - The size 3
The size of a wooden block is 15 cm × 12 cm × 20 cm. How many such blocks will be required to construct a solid wooden cube of minimum size? - Amy needs
Amy needs to serve 100 people with hashed browns. The hashed browns are sold in packs of 8 boxes, and each box in the pack serves 4 people. How many packs should she buy, minimum? How many people will she be able to serve with this purchase? - Tent - spherical cap
I have a tent in the shape of a spherical cap. Assume we want the volume to be 4 cubic meters, to sleep two or three people. Assume that the material making up the dome of the ten is twice as expensive per square as the material touching the ground. What - Min-max
What is the maximum and minimum of the data set: 6, 2, 3, 3, 2, 2? - A plumber 3
A plumber can buy plastic pipes in 6-foot and 12-foot lengths. The current job requires eight 4-foot lengths, five 5-foot lengths, and three 7-foot lengths. The plumber wants to figure out how many of each of the two stock lengths should be bought to mini - Dogde Caliber
The petrol kilometers M (unit: kilometers per liter) of the Dodge Caliber car is modeled by the function: M(s) = - 1/28 s² + 3 s- 31 What is the car's best petrol kilometers, and what speed is attained? - Prove 2
Prove that the minimum number of straight single cuts/strokes needs to divide a given right-angled triangle or an obtuse-angled triangle into a collection of all acute-angled triangles is seven(7). - How many 147
What is the minimum number of consecutive natural numbers from 1 to n that must be added so that their sum exceeds 1,000,000? - Children - dividing
What is the minimum number of nuts needed to be able to divide them equally among 10, 12, and 18 children? - TEV physical education
Students lined up in rows of three in a physical education class, and then in rows of four, and each time there was exactly one student left over. What is the minimum number of students that could be in the gym? - Balls 6
Jane has balls in her bag that can be divided equally among 4, 5, or 6 children. What is the minimum number of balls Jane could have in her bag? - Lollipop price minimum
Mom bought 6 lollipops for €17. If the cashier rounded up the purchase price to whole euros, what was the least one lollipop could cost? - Cube cuboid minimum Let us have a cube whose edge length is expressed in centimeters and is a natural number. What is the smallest number of such identical cubes that can be made into a cuboid with dimensions of 24 cm, 32 cm, and 60 cm? How long will the edge of these cubes
- Closest point
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Container water addition
There are 45 liters of water in a 50-liter container. How many liters of water will it contain if we add another 10 liters of water to it? - Inventory of bottles
Determine the standard stock of mineral water bottles needed for smooth operation if the restaurant requires 18,000 half-litre bottles per year. The delivery cycle is 14 days. The minimum safety stock is set at 5 days' supply. How many litres of mineral w - Grouped data range
In grouped data classes such as 10-15, 16-20, 21-25, 26-30 with the respective frequencies of each class as 3, 5, 4, 3, then the range (range of variation) is: a. 15 b. 6 c. 20 d. 5
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