Reason + square (second power, quadratic) - practice problems
Number of problems found: 126
- Tetrahedron 83144
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - Inaccessible 82710
Determine the distance between two inaccessible places K, L, if the angles KAL=62°10", LAB=41°23", KBL=66°34", and LBA were measured from points A, B, which are 870 m apart = 34°52". Thank you. - Circle - analytics geometry
Write the equation of the circle that passes through the points Q[3.5] R[2.6] and has its center on the line 2x+3y-4=0. - Multiplied 82243
Zuzka divided 52 by 2 8 times and multiplied by 2 6 times. What number did she get? - Diameter 81760
Winding drum length 180mm, initial diameter 60mm. Using a 6mm rope with a length of 50m, what will be the diameter of the wound drum with the rope? - Dimensions 81670
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si - Quadrilateral calc
The square ABCD is given. The midpoint of AB is E, the midpoint of BC is F, CD is G, and the midpoint of DA is H. Join AF, BG, CH, and DE. Inside the square (approximately in the middle), the intersections of these line segments form a quadrilateral. Calc - Equilateral 81142
The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body. - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Quadrilateral 81097
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ - SKMO
Petra had written natural numbers from 1 to 9. She added two of these numbers, deleted them, and wrote the resulting sum instead of the summaries. She thus had eight numbers written down, which she managed to divide into two groups with the same product. - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Chessboard 80533
How many ways can one white and one black square be selected on an 8x8 chessboard if the selected squares cannot lie in the same row or column? - Distances 79974
The picture shows three villages, A, B, and C, and their mutual air distances. The new straight railway line is to be built so that all the villages are the same distance from the line and that this distance is the smallest possible. How far will they be - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Gardener 75344
A gardener lays tiles around a square flower bed. It needs 12 tiles around the 2x2 bed. How many tiles will he need around the size of the bed? a) 9x9 b) nxn? How big was the bed for which the gardener consumed c) 112 d) 4n tiles? - In an
In an ABCD square, n interior points are chosen on each side. Find the number of all triangles whose vertices X, Y, and Z lie at these points and on different sides of the square. - Calculate 73024
Calculate the permille descent of the railway line in the section of 7.2 km by 21.6 m. - Observatory 71934
The aircraft flying towards the observatory was aimed at a distance of 5300 m at an elevation angle of 28º and after 9 seconds at a distance of 2400 m at an elevation angle of 50º. Calculate the distance the plane has flown in this time interval, its spee - Rectangles 70304
How many rectangles with side lengths expressed in natural numbers have an area of 96 cm²?
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