Question

Решите уравнение x^3 -10x + 2= (корень из 2-х)^2пристани А и В расположены на реке скорость течения которой на этом участке равна 3 км.ч .Собственная скорость (скорость катера в неподвижной воде ) равна 15 км.ч Найдите среднюю скорость катера во время движения от пристани А до пристани В и обратно , если известно что в пути у катера не было остановок

Answer 1

1.Уравнение равносильно x^3 -10x  + 2=|2-x|

При этом х<=2,т.к. подкоренное выражение д.б. положительным или нулем.

Решаем на промежутке х<=2:

x^3 -10x  + 2=2-x

x^3-9x=0
x(x-3)(x+3)=0

x=0:x=-3. {x=3 не подходит, т.к. х должен быть <=2).

 

2.Туда : скорость катера + скорость течения=15+3=18
Обратно: скорость катера - скорость течения=15-3=12

Средняя = (18+12)/2=15.

 

 

Answer 2

Problem Analysis

To solve the equation x^3 - 10x + 2 = (sqrt(2-x))^2, we need to find the values of x that satisfy the equation.

To find the average speed of the boat during its round trip from point A to point B, we need to consider the speed of the boat in still water and the speed of the current.

Let's break down the problem into two parts: 1. Solving the equation x^3 - 10x + 2 = (sqrt(2-x))^2 to find the values of x. 2. Calculating the average speed of the boat during its round trip from point A to point B.

Solving the Equation

To solve the equation x^3 - 10x + 2 = (sqrt(2-x))^2, we can start by simplifying the equation and then solving for x.

1. Simplify the equation: - x^3 - 10x + 2 = 2 - x - x^3 - 10x + x = 0 - x^3 - 9x = 0

2. Factor out x: - x(x^2 - 9) = 0

3. Set each factor equal to zero and solve for x: - x = 0 (one solution) - x^2 - 9 = 0 - x^2 = 9 - x = ±3 (two solutions)

Therefore, the equation x^3 - 10x + 2 = (sqrt(2-x))^2 has three solutions: x = 0, x = 3, and x = -3.

Calculating Average Speed

To calculate the average speed of the boat during its round trip from point A to point B, we need to consider the speed of the boat in still water and the speed of the current.

Let's assume the speed of the boat in still water is v km/h, and the speed of the current is c km/h.

1. Speed from point A to point B: - The boat is moving in the direction of the current, so the effective speed is the sum of the boat's speed in still water and the speed of the current: v + c km/h.

2. Speed from point B to point A: - The boat is moving against the current, so the effective speed is the difference between the boat's speed in still water and the speed of the current: v - c km/h.

3. Average speed: - The average speed is the total distance traveled divided by the total time taken. - Since the distance from point A to point B is the same as the distance from point B to point A, the total distance traveled is twice the distance from point A to point B. - The total time taken is the sum of the time taken from point A to point B and the time taken from point B to point A. - Therefore, the average speed is given by: (2 * distance) / (time_A_to_B + time_B_to_A).

Since the problem does not provide the distance or the time taken, we cannot calculate the exact average speed. However, we can provide a general formula for the average speed based on the given information.

General Formula for Average Speed

Let's denote the distance from point A to point B as d km.

1. Time taken from point A to point B: - The time taken is given by: time_A_to_B = d / (v + c).

2. Time taken from point B to point A: - The time taken is given by: time_B_to_A = d / (v - c).

3. Average speed: - The average speed is given by: (2 * d) / (time_A_to_B + time_B_to_A).

Therefore, the general formula for the average speed of the boat during its round trip from point A to point B, based on the given information, is: (2 * d) / (d / (v + c) + d / (v - c)).

Please note that this formula assumes that the boat maintains a constant speed throughout the journey and does not make any stops.

I hope this helps! Let me know if you have any further questions.