Егер картада 10 см кескінмен бейнеленген арақашықтықтың жер бетіндегі арақашықтығы 2500 км болса, масштабты…

Question

Егер картада 10 см кескінмен бейнеленген арақашықтықтың жер бетіндегі арақашықтығы 2500 км болса, масштабты анықтаңыз: 2. Жоспардағы үйдің ұзындығы 36 см-ге тең. Егер жоспардың масштабы 1:900 болса, үйдің жердегі ұзындығы неге тең?

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Here are the solutions to the problems:

1. Масштабын анықтаңыз (Determine the scale):

Given: Map distance = $10 \text{ cm}$ , Real distance = $2500 \text{ km}$ .

Convert the real distance to centimeters to match the map distance units.
$1 \text{ km} = 100000 \text{ cm}$ $2500 \text{ km} = 2500 \times 100000 \text{ cm} = 250000000 \text{ cm}$
Express the scale as a ratio of map distance to real distance.
$\text{Scale} = \frac{\text{Map distance}}{\text{Real distance}} = \frac{10 \text{ cm}}{250000000 \text{ cm}}$
Simplify the ratio to the form $1:N$.
$\text{Scale} = \frac{10}{250000000} = \frac{1}{25000000}$
The scale is $1:25000000$ .

The correct option is A) 1:25 000 000.

2. Үйдің жердегі ұзындығы неге тең? (What is the real-world length of the house?)
- Given: Plan length = $36 \text{ cm}$ , Scale = $1:900$ .
Use the scale to find the real length.
The scale $1:900$ means $1 \text{ cm}$ on the plan represents $900 \text{ cm}$ in reality.
$\text{Real length} = \text{Plan length} \times \text{Scale factor}$ $\text{Real length} = 36 \text{ cm} \times 900$ $\text{Real length} = 32400 \text{ cm}$
Convert the real length from centimeters to meters.
$1 \text{ m} = 100 \text{ cm}$ $\text{Real length} = \frac{32400}{100} \text{ m} = 324 \text{ m}$
The correct option is B) 324 m.

3. Картада осы магистральды бейнелейтін кесіндінің ұзындығы қандай? (What is the length of the segment representing this line on a map?)
- Given: Real length = $4116 \text{ km}$ , Scale = $1:4000000$ .
Convert the real length to centimeters.
$1 \text{ km} = 100000 \text{ cm}$ $4116 \text{ km} = 4116 \times 100000 \text{ cm} = 411600000 \text{ cm}$
Use the scale to find the map length.
The scale $1:4000000$ means $1 \text{ cm}$ on the map represents $4000000 \text{ cm}$ in reality.
$\text{Map length} = \frac{\text{Real length}}{\text{Scale factor}}$ $\text{Map length} = \frac{411600000 \text{ cm}}{4000000}$
Calculate the map length.
$\text{Map length} = \frac{4116}{40} \text{ cm} = 102.9 \text{ cm}$
The correct option is D) 102.9 cm.

4. Картада осы екі қаланың арақашықтығын (миллиметрмен) табыңыз. (Find the distance between these two cities on a map (in millimeters).)
- Given: Real distance = $218 \text{ km}$ , Scale = $1:200000$ .
Convert the real distance to millimeters.
$1 \text{ km} = 1000000 \text{ mm}$ $218 \text{ km} = 218 \times 1000000 \text{ mm} = 218000000 \text{ mm}$
Use the scale to find the map distance.
The scale $1:200000$ means $1 \text{ mm}$ on the map represents $200000 \text{ mm}$ in reality (or $1 \text{ unit}$ on map represents $200000 \text{ units}$ in reality).
$\text{Map distance} = \frac{\text{Real distance}}{\text{Scale factor}}$ $\text{Map distance} = \frac{218000000 \text{ mm}}{200000}$
Calculate the map distance.
$\text{Map distance} = \frac{2180}{2} \text{ mm} = 1090 \text{ mm}$
The correct option is A) 1090 mm.

5. Масштабтарды салыстыр: $70:5000 \text{ } \square \text{ } 7:500$ (Compare the scales: $70:5000 \text{ } \square \text{ } 7:500$ )
Simplify the first scale $70:5000$.
$70:5000 = \frac{70}{5000}$
Divide both numerator and denominator by 10:
$\frac{70 \div 10}{5000 \div 10} = \frac{7}{500}$
Compare the simplified first scale with the second scale.
The first scale is $\frac{7}{500}$ .
The second scale is $\frac{7}{500}$ .
Determine the relationship between the two scales.
Since $\frac{7}{500} = \frac{7}{500}$ , the two scales are equal.

The correct option is C) =.

Answer

Step-by-step solution

Convert the real distance to centimeters to match the map distance units.

Express the scale as a ratio of map distance to real distance.

Simplify the ratio to the form $1:N$.

Use the scale to find the real length.

Convert the real length from centimeters to meters.

Convert the real length to centimeters.

Use the scale to find the map length.

Calculate the map length.

Convert the real distance to millimeters.

Use the scale to find the map distance.

Calculate the map distance.

Simplify the first scale $70:5000$.

Compare the simplified first scale with the second scale.

Determine the relationship between the two scales.

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