Examples for secondary school students - page 91 of 237
Number of problems found: 4730
- Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1. - Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - Roots and coefficient
In the equation 2x² + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b. - Prism surface calculation
Calculate the surface area of a triangular prism with a height of 7 dm. Measures the edges of the triangular base 45 cm, 5 dm, 550 mm. - Flower boxes
How many m² of 10 mm thick boards are needed to make 12 flower boxes? The boxes' dimensions are 180, 150, and 1500 mm. - Cone calculation complete
There is a rotating cone: r = 6.8 cm s = 14.4 cm. Find the area of the cone surface S2, the height h, and the volume V. - Quarantine cupcakes
Mr. Honse was baking quarantine cupcakes. Mrs. Carr made twice as many as Mr. Honse. Ms. Sanchez made 12 cupcakes, more than Mr. Honse. Suppose they put all their cupcakes together (which they can't because. of quarantine!), they would have 108 cupcakes. - In mass
In the mass production of a product, the average dimension is 250 mm, whereas the dimensions of individual products due to inaccuracies in the production fluctuate around this mean value. The dimension of the products has a normal distribution with standa - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How long is its longest side? - 2 cyclists and car
One cyclist rides at a constant speed over a 100-meter-long bridge. When he is 40 meters behind, he meets an oncoming cyclist riding at the same speed. The car travels along the bridge in the same direction as the first cyclist at a speed of 70 km/h. He m - Lottery - eurocents
Tereza bets in the lottery and finally wins. She went to the booth to have the prize paid out. An elderly gentleman beside him wants to buy a newspaper but is missing five cents. Tereza is in a generous mood after the win, so she gives the man five cents - The funnel
The funnel has the shape of an equilateral cone. If you pour 3 liters of water into the funnel, calculate the area wetted with water. - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Powerplant chimney
From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a 5° 50 ′ depth angle. How tall is the chimney? - Distance time calculation
The truck drove at an average speed of 20 km/h and left Prague toward Liberec. At the same time, a bus left with him, traveling at an average speed of 30 km/h, and it arrived in Liberec 2 hours earlier than the truck. What is the distance between Prague a - Triangle side calculation
Calculate the lengths of the remaining sides of right triangle ABC, given angle alpha = 45° and perimeter o = 125. - Trapezoid area calculation
The LICH isosceles trapezoid has 5.2 cm long arms and its bases are 7.6 cm and 3.6 cm long. Find the area of the LICH trapezoid. - Candles
Before Christmas, Eve bought two cylindrical candles—red and green. Red was 1 cm longer than green. She lit a red candle on Christmas Day at 5:30 PM and a green candle at 7:00 PM, leaving them on fire until they burned. At 9:30 PM, both candles were the s - Gutter material calculation
The length of the gutter is 2 m, and the diameter of the gutter is 0.4 m. It is necessary to add 7% of the material to the joints. Find the consumption of sheet metal for the gutter construction. - Intersections 3
Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0
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