Minimum - examples
- 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 co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
In all nine fields of given shape to be filled 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 the cir
In a class are 26 children. During the holidays 16 children were in the camps and 14 children on holiday with their parents. Determine the minimum and maximum number of children that may have been in the camp and on holiday with their parents at the same
- Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
- Sphere and cone
Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
- Fixed expenses 2013
Since 2013, the Slovak government plans to tax more small one person businesses. Instead of fixed expences 40% will be fixed expences 40% of gross income up to 420 Eur. Calculate what percentage of fixed expences will in 2013 pays from gross income 2236 E
Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
Write the smallest and largest 1-digit number.
In the class was 12 students. Nine students wearing trousers and turtleneck eight. How many students worn trousers with a turtleneck?
- 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)
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
In the box were total of 200 cookies. These products have sugar and chocolate topping. Chocolate topping is used on 157 cookies. Sugar topping is used on 100 cakes. How many of these cookies has two frosting?
The florist got 72 white and 90 red roses. How many bouquets can bind from all these roses when each bouquets should have the same number of white and red roses?
- Timber log
The ship goes from point x to y. Downstream it takes 4 hours, upstream 6 hours. How long does it take from a point x to y a log?
- Paper box
Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?
- Skoda cars
There were 16 passenger cars in the parking. It was the 10 blue and 10 Skoda cars. How many are blue Skoda cars in the parking?
- Minimum of sum
Find a positive number that the sum of the number and its inverted value was minimal.
- Endless lego set
The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They