Maximum - high school - practice problems - page 3 of 4
Number of problems found: 65
- Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - 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? - Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm³. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Math logic
There are 20 children in the group. Every two children have a different name. Alena and John are among them. How many ways can we choose eight children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum o
- Circumference 4255
The rectangle has a circumference of 24 cm so that its area is maximum and its length is larger than its width. Find the dimensions of a rectangle. - Summands 4213
Divide the number 28 into two summands so that their product is maximal. - Manufacturer 4212
How many electronic scooters should the manufacturer sell to maximize their income if the income function is given by the equation TR (Q) = -4Q2 + 1280 Q + 350? - 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? - Z9–I–1
In all nine fields of given shape to be filled with natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in th
- Diameter 4111
How many balls with a diameter of 3.25 cm with a mixture in a circle with a diameter of 27 cm? - Daily temperature
The average daily temperature measurements for one week every day at the same hour was -2.8 °C. We measured all temperatures on different days are different. The highest daily maximum temperature was 2.4 °C, and the lowest was -6 °C. Determine the options - Probability 3296
The storm broke the telephone cable connecting places A and B at 2.5 km. What is the probability that this happened at a maximum length of 450 m from location A? - Owner of the company
The company's owner, with extensive administrative activity, wants to sell the obsolete three machines at the price of CZK 1000 per 1 machine with a six-month warranty period. If the machine breaks down during this period, the owner will return the employ - Traffic laws
Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped the car at 1.5 m from the wall. The dipped beam headlights are 60 cm high. At what height on th
- Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w - Max - cone
The workshop must produce the greatest cone from the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, and 6.2 cm. a) Calculate cone volume. b) Calculate the waste. - Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder. - Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divided by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles.
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