Examples for secondary school students - page 53 of 213
Number of problems found: 4253
- Created trio
What is the probability that in the created trio, which consists of 19 boys and 12 girls, they will be: a) the boys themselves b) the girls themselves c) 2 boys and one girl? - The bomber
An aircraft flying at an altitude of 1260 m. From what distance in front of the target must a parachute load be dropped from an airplane? The load slopes at a speed of 5.6 m/s and moves in the direction of movement at 12 m/s. What is the direct distance o - Acceleration 43741
The tram starts with a constant acceleration of 0.3 m/s2. How long will it take to cover the tenth meter of its track? - Acceleration 43731
The car starts with constant acceleration, and at a distance of 567 m, it has a speed of 12.6 m/s. How long will it take from the start? - Mechanical 43721
A body weighing 2 kg falls from a height of 45 m in a free fall. What will be its potential energy and total mechanical energy after 2 s from the beginning of the movement? - Fruits
We want to plant five fruit trees in the garden, of which three are apple trees and two pears. How many different ways can we organize them? - Probability 43581
What is the probability that the sum of 12 will fall on a roll of two dice? A. 1/6 B. 1/36 C. 1/18 D. 36 - Rotation 43561
The boy is sitting on a two-arm swing, and his seat is 300 cm away from the center of rotation. Its weight is 48 kg. The girl is sitting at the other end of the swing, and her mass is 36 kg. How far from the center of rotation must the girl sit for them t - Photos
Three friends, Mirka, Lucka, and Hanka, collect photos. If Mirka had three more photos, she would have as many as Hanka. If Lucka had five photos less than she has, she would be like Hanka. How many photographs does each have if they have 431 together? - A rectangle 4
A rectangle has an area of 300 and a perimeter of 80. What is the ratio of length and width? - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - The roof
The tower's roof has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste. - 1200 screws
1200 screws are to be divided into three groups so that in the 1st group, there are 300 screws more than in the 2nd group, and in the 2nd group, 150 screws less than in the 3rd group. How many screws will be in each group? - Tarzan
Tarzan, weighing m = 90 kg, tries to cross the river by swinging with a vine hanging from a tree leaning over the river. Liana has a length l = 12 m. The speed of the Tarzan in the lowest swing position is v = 8 m/s. Tarzan doesn't know that the liana wil - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - Altitude angles
Cities A, B, and C lie in one elevation plane. C is 50 km east of B, and B is north of A. C is deviated by 50° from A. The plane flies around places A, B, and C at the same altitude. When the aircraft is flying around B, its altitude angle to A is 12°. Fi - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal. - 8 wooden
Eight wooden poles are used for pillars, and the length of the pillars is from an arithmetic progression. If the second pole is 2 meters and the sixth pole is in order 5 meters, find the difference between the sixth and seventh poles. - Aircraft bearing
Two aircraft will depart from the airport simultaneously. The first flight flies with a course of 30°, and the second with a course of 86°. Both fly at 330 km/h. How far apart will they be in 45 minutes of flight?
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