Question

1.скорость самолёта 900км/ч, скорость автомобиля 108км/ч. Выразите эти скорости в м/с и допишите пропорцию 900:108​ 2. Продолжите цепочку пропорций:72/360=24/120=...=...=...=...

Answer 1

1.

$900 \frac{км}{ч} = \frac{900 \: км}{ч} = \frac{900 \: \times 1000 \: м}{3600 \: с} = \frac{250 \: м}{с} = 250 \frac{ м}{с}$

$108 \frac{км}{ч} = \frac{108 \: км}{ч} = \frac{108 \: \times 1000 \: м}{3600 \: с} = \frac{30 \: м}{с} = 30 \frac{ м}{с}$

$\frac{900 \frac{км}{ч}}{108 \frac{км}{ч}} = \frac{250 \frac{ м}{с} }{30 \frac{ м}{с} } = \frac{25 \frac{ м}{с} }{3 \frac{м }{с} } = \frac{25}{3}$

2.

$\frac{72}{360} = \frac{24}{120} = \frac{8}{40} = \frac{4}{20} = \frac{2}{10} = \frac{1}{5}$

$\frac{72}{360} = \frac{1}{5} = \frac{1 \times 72}{5 \times 72}$

$\frac{24}{120} = \frac{1}{5} = \frac{1 \times 24}{5 \times 24}$

Answer 2

Converting speeds from km/h to m/s

To convert speeds from kilometers per hour (km/h) to meters per second (m/s), you can use the following conversion factor:

1 km/h = 0.2778 m/s

Let's apply this conversion to the given speeds:

1. The speed of the airplane is 900 km/h. To convert it to m/s, we multiply it by the conversion factor:

900 km/h * 0.2778 m/s = 250 m/s

Therefore, the speed of the airplane is 250 m/s.

2. The speed of the car is 108 km/h. Using the same conversion factor, we can calculate its speed in m/s:

108 km/h * 0.2778 m/s = 30 m/s

Thus, the speed of the car is 30 m/s.

Proportions

A proportion is an equation that states that two ratios are equal. Let's continue the given chain of proportions:

1. 72/360 = 24/120

To solve this proportion, we can cross-multiply:

72 * 120 = 360 * 24

Simplifying both sides of the equation:

8640 = 8640

Therefore, the equation is true, and the proportion is valid.

2. 24/120 = x/600

To find the value of x, we can cross-multiply:

24 * 600 = 120 * x

Simplifying both sides of the equation:

14400 = 120x

Dividing both sides by 120:

x = 120

Therefore, the missing value in the proportion is 120.

3. x/600 = 120/600

To find the value of x, we can cross-multiply:

x * 600 = 120 * 600

Simplifying both sides of the equation:

600x = 72000

Dividing both sides by 600:

x = 120

Thus, the missing value in the proportion is also 120.

4. x/600 = 120/600

This proportion is the same as the previous one, so the missing value is also 120.

Therefore, the chain of proportions can be continued as follows:

72/360 = 24/120 = 120/600 = 120/600 = 120/600 = 120/600

The missing value in each proportion is 120.