Analysis of the option of the exam Larina
Full analysis of tasks 1-15. If you have any questions about the solution, ask in the comments, I will try to answer everyone
13 17:43
14 21:16
15 32:26
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4 Before the start of a football match, the referee tosses a coin to determine which team will start the game with the ball. The Cosmos team plays three matches with different teams. Find the probability that in these matches the Cosmos team will start the game with the ball all three times.
10
When a source and receiver of sound signals moving in a certain medium in a straight line towards each other approach each other, the frequency of the sound signal recorded by the receiver does not coincide with the frequency of the original signal f0 = 150 Hz and is determined by the following expression (Hz), where c is the speed of signal propagation in the medium (in m/s), and u = 10 m/s and v = 15 m/s are the speeds of the receiver and source relative to the medium, respectively. At what maximum speed c (in m/s) of signal propagation in the medium will the signal frequency f in the receiver be no less than 160 Hz?
11
The distance between cities A and B is 150 km. A car left city A for city B, and 30 minutes later a motorcyclist left behind it at a speed of 90 km/h, caught up with the car in city C and turned back. When he returned to A, the car arrived in B. Find the distance from A to C. Give your answer in kilometers.
14 In an acute-angled triangle ABC, heights AK, BM and CN are drawn. On the side AB, a point P is chosen so that the circle described about the triangle РКМ touches the side AB
a) Prove that the angle КАМ is equal to the angle МВС
b) Find РN if PA = 30, РВ = 10