Maths practice for 14 year olds - page 369 of 379
Number of problems found: 7575
- Proof PT
Can you easily prove Pythagoras' theorem using Euclidean theorems? If so, do it. - Newton's task
Grass grows in the meadow equally fast and evenly. It is known that 35 cows graze meadow for 27 days and 39 cows by 24 days. How many cows graze the meadow for 6 days? - Divisors
Find all divisors of number 432. How many are there? - Movement
Two cyclists (each on a different road) started from the crossing of two perpendicular roads. One runs at an average speed of 16 km/h, and the second 25 km/h. Determine the distance between them after 20 minutes of cycling. - Wire D
Wire length 1 m is bent to form a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Steps
How many steps do you save if you go square estate for diagonal (crosswise) rather than circumvent the two sides of its perimeter with 458 steps? - Estate
Semicircle estate must be a fence. The straight section has a 32 meters long fence. How many meters of the fence should we buy?
- Square 2
Points D[10,-8] and B[1,-10] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Gimli Glider
Aircraft Boeing 767 lose both engines at 35000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 2100 feet and maintain constant speed 201 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - Triangle TBC
TBC is an isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB? - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Forces
In point, G acts three orthogonal forces: F1 = 16 N, F2 = 7 N, and F3 = 6 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3. - Diagonal
Determine the dimensions of the cuboid if it is diagonally long 60 dm and has an angle with one edge 35° and with another edge 77°. - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and an area of 415 cm². Calculate the volume of a cone.
- Axial section
The axial section of the cone is an equilateral triangle with an area 208 km². Calculate the volume of the cone. - Rotation
The right triangle with legs 11 cm and 18 cm rotates around the longer leg. Calculate the volume and surface area of the formed cone. - Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 5a +5b = 7c - Right isosceles
Calculate the area of the isosceles right triangle whose perimeter is 26 cm. - Euclid1
The right triangle ABC has hypotenuse c = 20 cm. How large sections cut height hc=9 cm on the hypotenuse c?
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