Solution to problem 13.2.6 from the collection of Kepe O.E.

Problem 13.2.6 from the collection of Kepe O.?. is formulated as follows: “By what percentage will the area of ​​a circle increase if its radius is increased by 10%?”

The solution to this problem can be done as follows.

Let the initial radius of the circle be r, then its area is S = πr^2. If you increase the radius by 10%, then the new radius will be r1 = 1.1r. The area of ​​the new circle will be S1 = πr1^2 = π(1.1r)^2 = 1.21πr^2.

Thus, the area of ​​the circle increases by (S1 - S)/S * 100% = (1.21πr^2 - πr^2)/(πr^2) * 100% = 21%.

Answer: The area of ​​the circle will increase by 21%.

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Problem 13.2.6 from the collection of Kepe O.?. refers to the section "Dynamics of a system of material points". To solve it, you need knowledge of Newton's laws and the ability to work with vectors.

The problem statement gives the initial conditions for the motion of two material points whose masses are known, and also the forces acting on these points. It is necessary to determine the trajectories of movement of points and their speeds at given times.

Solving the problem involves the use of formulas connecting forces, masses and accelerations of material points, as well as the use of vector analysis methods to calculate trajectories and velocities.

As a result, the solution to problem 13.2.6 from the collection of Kepe O.?. will allow you to learn how to apply Newton's laws and vector analysis to solve problems on the dynamics of a system of material points.

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