Examples for secondary school students - page 230 of 237
Number of problems found: 4730
- Cone
The circular cone has height h = 15 dm and base radius r = 2 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume. - Log
If log4 x+ log8 x = log_b x, what is b? - Web server
Calculate how many average minutes the web server is unavailable a year if the availability is 99%. - Crystal
The crystal grows every month at 1.2 permille of its mass. How many months does it take to develop from weight 177 g to 384 g? - Pool
Water flows into a pool through two inlets and fills it in 5 hours. If the first inlet alone takes 5 hours longer than the second inlet alone, how long does each inlet take to fill the pool on its own? - Equation
How many real roots have equation x³=x? - R triangle
Calculate the area of a right triangle whose longer leg is 7 dm shorter than the hypotenuse and 10 dm longer than the shorter leg. - 7 heroes
6 riders are galloping on 6 horses in single file. In how many ways can they be arranged in order? - Wiring
A conduit has a cross-section of 54 mm². Is it possible to fit 6 conductors each with a cross-section of 6.7 mm² inside it? - River
Calculate the average gradient in per mille of river Hudson, given that along a 952 km section the water flows from 1231 m above sea level down to 131 m above sea level. - Factors
Can the expression 4x ² -47.6x +39.6 be factored into rational factors? - Fraction
For what x expression (x²-64)/(10x² -80x) equals zero? - Compare II
Which of the numbers 710 and 107 is greater? - Angle between lines
Calculate the angle between the following two lines: p: -4x +7y +7 =0 q: -x +4y +7=0 - Mast
A mast casts a shadow of length 16 on a slope that rises from the base of the mast in the direction of the shadow at an angle of 9.7°. Determine the height of the mast if the sun is at an angle of 40°48'° above the horizon. - Cube corners
From the cube of edge 24 cm, we cut off all vertices so that each cutting plane intersects the edges 2 cm from the nearest vertice. How many edges will this body have? - Sea
How far can you see from the top of a ship's mast that is 9 metres above sea level? (The Earth's radius is 6370 km km.) - Center
Calculate the coordinates of the centroid T[x, y] of triangle ABC; A[-19,3] B[-20,25] C[22,10]. - Cyclist
A cyclist rides 7 km uphill in 46.9 minutes and the same distance downhill in 15.4 minutes, applying the same force to the pedals throughout. How long would it take to cycle the same 7 km on flat ground? - Powers
Express the expression (1000) ^ (21) * (10) ^ (101) * (10) ^ (145) as the n-th power of the base 10.
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