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?

Here are the solutions to the problems:

1. Масштабын анықтаңыз (Determine the scale):

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

Step 1: Convert the real distance to centimeters to match the map distance units. $1 km = 100000 \text{ cm}$ $2500 km = 2500 \times 100000 cm = 250000000 \text{ cm}$

Step 2: Express the scale as a ratio of map distance to real distance. $\text{Scale} = \frac{Map distance}{Real distance} = \frac{10 cm}{250000000 cm}$

Step 3: 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 = $1:900$.

Step 1: 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. $\text{Real length} = Plan length \times \text{Scale factor}$ $\text{Real length} = 36 cm \times 900$ $\text{Real length} = 32400 \text{ cm}$

Step 2: Convert the real length from centimeters to meters. $1 m = 100 \text{ cm}$ $\text{Real length} = \frac{32400}{100} m = 324 \text{ m}$

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 = $1:4000000$.

Step 1: Convert the real length to centimeters. $1 km = 100000 \text{ cm}$ $4116 km = 4116 \times 100000 cm = 411600000 \text{ cm}$

Step 2: 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. $\text{Map length} = \frac{Real length}{Scale factor}$ $\text{Map length} = \frac{411600000 cm}{4000000}$

Step 3: Calculate the map length. $\text{Map length} = \frac{4116}{40} cm = 102.9 \text{ cm}$

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 = $1:200000$.

Step 1: Convert the real distance to millimeters. $1 km = 1000000 \text{ mm}$ $218 km = 218 \times 1000000 mm = 218000000 \text{ mm}$

Step 2: 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). $\text{Map distance} = \frac{Real distance}{Scale factor}$ $\text{Map distance} = \frac{218000000 mm}{200000}$

Step 3: Calculate the map distance. $\text{Map distance} = \frac{2180}{2} mm = 1090 \text{ mm}$

The correct option is A) 1090 mm.

5. Масштабтарды салыстыр: $70:5000 \square 7:500$ (Compare the scales: $70:5000 \square 7:500$)

Step 1: Simplify the first scale $70:5000$. $70:5000 = \frac{70}{5000}$ Divide both numerator and denominator by $10$: $\frac{70 \div 10}{5000 \div 10} = \frac{7}{500}$

Step 2: Compare the simplified first scale with the second scale. The first scale is $\frac{7}{500}$. The second scale is $\frac{7}{500}$.

Step 3: Determine the relationship between the two scales. Since $\frac{7}{500} = \frac{7}{500}$, the two scales are equal.

The correct option is C) =.

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