What are the distances between the following locations: a) Dream School to Excellence, b) Tassah to Olympic…

Question

What are the distances between the following locations: a) Dream School to Excellence, b) Tassah to Olympic Glory, c) Excellence to Gayap, d) Dream School to Gayap?

ScanSolve AI Tutor · Accepted Answer

here are the solutions to the remaining problems:

3a)

Identify the path from Dream School to Excellence.
The path is Dream School $\to$ Tassan $\to$ Excellence.
Find the distances for each segment from the legend.
Dream School to Tassan = $8 \text{ km}$
Tassan to Excellence = $10 \text{ km}$
Add the distances.
Total distance = $8 \text{ km} + 10 \text{ km} = 18 \text{ km}$
It is $\boxed{18 \text{ km}}$ from Dream School to Excellence.

3b)
Identify the path from Tassah to Olympic Glory.
The path is Tassah $\to$ Gayap $\to$ Olympic Glory.
Find the distances for each segment from the legend.
Tassah to Gayap = $16 \text{ km}$
Gayap to Olympic Glory = $4 \text{ km}$
Add the distances.
Total distance = $16 \text{ km} + 4 \text{ km} = 20 \text{ km}$
It is $\boxed{20 \text{ km}}$ from Tassah to Olympic Glory.

3c)
Identify the path from Excellence to Gayap.
The path is Excellence $\to$ Tassan $\to$ Gayap.
Find the distances for each segment from the legend.
Excellence to Tassan = $10 \text{ km}$
Tassan to Gayap = $16 \text{ km}$
Add the distances.
Total distance = $10 \text{ km} + 16 \text{ km} = 26 \text{ km}$
It is $\boxed{26 \text{ km}}$ from Excellence to Gayap.

3d)
Calculate the distance from Dream School to Gayap.
Path: Dream School $\to$ Tassan $\to$ Gayap
Distance = $8 \text{ km} + 16 \text{ km} = 24 \text{ km}$
Calculate the total distance for the round trip.
Total distance = $2 \times 24 \text{ km} = 48 \text{ km}$
Calculate the time taken for the journey.
Speed = $12 \text{ km/h}$
Time = $\frac{\text{Distance}}{\text{Speed}} = \frac{48 \text{ km}}{12 \text{ km/h}} = 4 \text{ hours}$
Determine the return time.
Starting time = $11:50 \text{ am}$
Add 4 hours to the starting time:
$11:50 \text{ am} + 4 \text{ hours} = 15:50$
In 12-hour format, $15:50$ is $3:50 \text{ pm}$ .
Mr. Anselm returns to Dream School at $\boxed{3:50 \text{ pm}}$ .

4a)
Identify the relationship between the pool's radius and the yard's length CD.
The length CD is the diameter of the semi-circular swimming pool.
Use the given radius to find the diameter.
Radius ( $r$ ) = $3.5 \text{ m}$
Diameter ( $d$ ) = $2 \times r = 2 \times 3.5 \text{ m} = 7 \text{ m}$
The length of the yard CD is $\boxed{7 \text{ m}}$ .

4b)
Identify the dimensions of the rectangular yard ABCD.
Length (CD) = $7 \text{ m}$ (from 4a)
Width (AD) = $5 \text{ m}$ (given in the diagram)
Calculate the area of the rectangle ABCD.
Area of rectangle = Length $\times$ Width
$= 7 \text{ m} \times 5 \text{ m}$ $= 35 \text{ m}^2$
The area of the yard ABCD is $\boxed{35 \text{ m}^2}$ .

4c)
Calculate the area of the semi-circular swimming pool.
Radius ( $r$ ) = $3.5 \text{ m}$
Area of a full circle = $\pi r^2$
Area of semi-circle = $\frac{1}{2} \pi r^2$
Using $\pi \approx \frac{22}{7}$ :
$\text{Area of semi-circle} = \frac{1}{2} \times \frac{22}{7} \times (3.5)^2$ $= \frac{1}{2} \times \frac{22}{7} \times 12.25$ $= 11 \times \frac{12.25}{7}$ $= 11 \times 1.75$ $= 19.25 \text{ m}^2$
Calculate the area to be concreted (shaded area).
Area to concrete = Area of rectangle ABCD - Area of semi-circular pool
$= 35 \text{ m}^2 - 19.25 \text{ m}^2$ $= 15.75 \text{ m}^2$
Calculate the cost of concreting.
Cost per square metre = $2000 \text{ frs}$
Total cost = Area to concrete $\times$ Cost per square metre
$= 15.75 \text{ m}^2 \times 2000 \text{ frs/m}^2$ $= 31500 \text{ frs}$
The cost of concreting the yard is $\boxed{31500 \text{ frs}}$ .

What are the distances between the following locations: a) Dream School to Excellence, b) Tassah to Olympic Glory, c) Excellence to Gayap, d) Dream School to Gayap?

Step-by-step solution

Identify the path from Dream School to Excellence.

Find the distances for each segment from the legend.

Add the distances.

Identify the path from Tassah to Olympic Glory.

Find the distances for each segment from the legend.

Add the distances.

Identify the path from Excellence to Gayap.

Find the distances for each segment from the legend.

Add the distances.

Calculate the distance from Dream School to Gayap.

Calculate the total distance for the round trip.

Calculate the time taken for the journey.

Determine the return time.

Identify the relationship between the pool's radius and the yard's length CD.

Use the given radius to find the diameter.

Identify the dimensions of the rectangular yard ABCD.

Calculate the area of the rectangle ABCD.

Calculate the area of the semi-circular swimming pool.

Calculate the area to be concreted (shaded area).

Calculate the cost of concreting.

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