Examples for secondary school students - page 26 of 237
Number of problems found: 4730
- Water tube pressure
Water flows in a horizontal tube at a speed of 2.24 m/s and has a pressure of 0.1 MPa. How fast does the water flow in the narrowed part of the tube if its pressure is 0.09 MPa? - Car braking force
What constant braking force is required to stop a car weighing 1 ton in 10 seconds traveling at 50 km/h? - Coordinates - ellipse
Write the equation of the ellipse that passes through the points, and its axes are identical to the coordinate axes when A = [2, 3] and B = [−1, −4]. - Robinson on the island
Robinson Crusoe came to the island with 4 grains of corn. How many years did it take him to grow enough grain for bread if he got 10 grains from one grain on average and he needed at least 1 kg of bole for 1 bread, and 1 grain weighs about 0.2 g? (assume - Three vertices
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A. - Club animal count
Twenty-nine children attend the club. Eleven said that they have a dog, 14 children have a cat, and 12 children have a hamster. Two children have all three animals. Seven children do not have any animals at home. How many children have at least two of the - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the space diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Tram - safe downhill
What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15. - Number product factors
The product of two whole numbers, one of which is 19 greater than the other, equals the number 416. Find both factors. - Alcohol concentration mixing
In the hospital laboratory, two containers contained different concentrations of alcohol. After mixing 10 liters of alcohol from the first container with 14 liters from the second container, 75% of the alcohol was formed. If 40 liters from the first conta - Quadratic equation - Viets
In the equation 3x²+bx+c=0, one root is x1 = -3/2. Determine the number c so that the number 4 is the root of the equation. Hint - use Viet's formulas. - Lever force distance
Calculate at what distance from the axis of rotation a force of 60 N acts on one side of a double-return lever; if a force of 180 N acts on the other side at a distance of 1 meter from the axis of rotation, the lever is in equilibrium. - Permutation element count
From how many elements can we make 5040 permutations without repetition? - Arithmetic sequence
Determine the sum of the first 12 terms of an AP (arithmetic sequence) if a4 is equal to 7 and a8 is equal to minus 1. - Theater seat rows
The theater has 20 rows of seats on the ground floor. There are 16 seats in the first row, and each subsequent row has two more seats than the previous one. Find the number of seats on the ground floor of the theater. - Hydraulic patient lifting
A dentist lifted a patient in a chair by 10 cm using a hydraulic device. The mass of the patient with the chair is 100 kg. a) What force did the dentist have to apply to the small piston, if the ratio of the areas of the large and small pistons is S2/S1=2 - Parabola focus equation
Determine the equation of the parabola that has the point F = [3,2] as its focus and the line x+y+1=0 as its shift line. - Watch alarm price
The alarm clock, women's watch, and men's watch cost a total of 1370 CZK. How much does each item cost if a women's watch is six times more expensive than an alarm clock and a men's watch is 200 Sk more expensive than a women's watch? - Shirt price purchase
A customer was buying three shirts. First, he chose a white one, then a sports one, which was 32 Sk more expensive than a white one, and finally, a short-sleeved shirt, which was 27 Sk cheaper than a white shirt. How many crowns did the individual shirts - Triangle interior angles
Calculate the interior angles of the triangle. The angle alpha is 16° greater than beta, and the angle gamma is 17° less than alpha.
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