Question

Каждую секунду в бассейн поступает 0,5 м3 воды.Сколько кубометров воды станет в бассейне через х сек.,если сейчас в нем 120 м3 воды?Задайте формулой зависимость объема воды в бассейне от времени его наполнения.Является ли эта зависимость линейной функцией?

Answer 1

Решение на фото, надеюсь видно.

Answer 2

Calculation of Water Volume in the Pool

To calculate the volume of water in the pool after a certain number of seconds, we need to consider the rate at which water is entering the pool and the initial volume of water in the pool.

Given: - Rate of water entering the pool: 0.5 m^3/s - Initial volume of water in the pool: 120 m^3

Let's denote the time in seconds as 't' and the volume of water in the pool as 'V(t)'.

The formula to calculate the volume of water in the pool at any given time is:

V(t) = V(0) + (rate of water in * t)

Where: - V(t) is the volume of water in the pool at time 't' - V(0) is the initial volume of water in the pool - rate of water in is the rate at which water is entering the pool - t is the time in seconds

Using this formula, we can calculate the volume of water in the pool after 'x' seconds.

Let's substitute the given values into the formula:

V(x) = 120 + (0.5 * x)

So, the volume of water in the pool after 'x' seconds can be calculated using the formula V(x) = 120 + (0.5 * x).

Linearity of the Function

To determine if the relationship between the volume of water in the pool and the time it takes to fill the pool is a linear function, we need to check if the rate of change of the volume with respect to time is constant.

In the given scenario, the rate of water entering the pool is constant at 0.5 m^3/s. This means that for every second that passes, an additional 0.5 m^3 of water enters the pool. Since the rate of change is constant, the relationship between the volume of water and time is indeed a linear function.

Therefore, the relationship between the volume of water in the pool and the time it takes to fill the pool is a linear function.

Please note that the search results provided did not contain specific information related to the calculation and linearity of the function. The provided explanation is based on mathematical principles and reasoning.