# Examples for secondary school students

#### Number of problems found: 2059

• Height of the arc - formula Calculate the height of the arc if the length of the arc is 77 and chord length 40. Does exist a formula to solve this?
• Repair company The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired?
• Euclidean distance Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
• Rotation of the Earth Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
• Skid friction Find the smallest coefficient of skid friction between the car tires and the road so that the car can drive at a 200 m radius at 108 km/h and does not skid.
• Circle annulus There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
• Diamond diagonals Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
• Bernoulli distribution The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest 3 decimals).
• Components In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
• Neighborhood I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
• V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
• Hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
• Car At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)
• Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
• Center In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
• Sss triangle Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
• Sun rays If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current heig
• Kerosine and petrol if 4 litres of petrol containing 15% kerosine are added to another 7 litres of petrol containing 10% kerosine, what percentage of the petrol is kerosine?
• Deficiencies During the hygienic inspection in 2000 mass caterers, deficiencies were found in 300 establishments. What is the probability that deficiencies in a maximum of 3 devices will be found during the inspection of 10 devices?
• Angles in triangle The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?

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