Equation + minimum - practice problems
Number of problems found: 23
- Summands 4213
Divide the number 28 into two summands so that their product is maximal. - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - Three numbers
Create from digits 1-9 three-digit numbers with their sum the smallest. What value is the sum of these numbers? (Use each digit only once) - Cherries
Cherries in the bowl can be divided equally among 20 or 15, or 10 children. How many are the minimum cherries in the bowl? - Equations 4781
Determine the smaller root of the root pair of the system of equations. 5a + 4b = 11 3a - 2b = 11 - 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. - Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C? - 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. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Seedcake
Seedcake costs 44 cents. How many minimum seedcakes must we buy that we can pay in cash, only whole euros? - Paper box
The hard rectangular paper has dimensions of 60 cm and 28 cm. We cut off the corners into equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box? - Classification 81133
One of the conditions for classification with grade 2 in geography is to obtain an average of at least 64 points from four tests. The minimum number of points a skater must receive from the fourth test to meet this condition is if she received 59, 67, or - Tableau pyramid
Your class will invent an original tableau pyramid from photos. What minimum dimensions will it have to have if you want to place 50 9x13 photos there? You want a classic pyramid, i.e., Each next row is one photo-less, but in the last row, two photos (the - 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 - Second hand store
The price of goods in the store for used goods is determined by agreement, while the sale price is deducted 15% commission - for the store owner. Matúš's parents decided to sell the TV to make their net profit at least 50 euros. What was the minimum selli - 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? - 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)? - 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. - TV competition
In the competition, ten contestants answer five questions, one question 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
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