A builder needs to connect a partilly built house to a temporary power supply. on the plan, the coordinates of the house are (50,113) and the power supply is at ()147,82). what is the least amount of cable needed? why is it likely that the builder will use more cable than this?
Use your "distance between 2 points" formula, you are given the two points.
(I got 101.833 )
thanks reiny
To find the least amount of cable needed to connect the partially built house to the temporary power supply, we can calculate the distance between the coordinates of the house and the power supply using the distance formula, which is derived from the Pythagorean theorem.
The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given:
Coordinates of the house: (50, 113)
Coordinates of the power supply: (147, 82)
Using the distance formula, let's calculate the distance:
d = sqrt((147 - 50)^2 + (82 - 113)^2)
≈ sqrt(97^2 + (-31)^2)
≈ sqrt(9409 + 961)
≈ sqrt(10370)
≈ 101.84
Therefore, the least amount of cable needed to connect the partially built house to the temporary power supply is approximately 101.84 units.
Now let's address why it is likely that the builder will use more cable than this minimum amount. There are several reasons for this:
1. Safety and practicality: The builder may choose to use additional cable to ensure there is enough slack and flexibility in the wiring. Extra length of cable allows for adjustments, potential changes in construction plans, and easy access during the construction process.
2. Future expansion: Adding some extra cable beyond the minimum required allows for future expansion or modifications to the electrical system without the need for rewiring. This can save time and labor costs in the long run.
3. Accessibility and maneuverability: Depending on the layout and obstacles on the construction site, it may be more convenient to install additional cable to avoid potential obstructions, such as trees, rocks, or other structures. This provides more flexibility in routing the cable to reach the power supply.
4. Unforeseen circumstances: Construction sites can be unpredictable, and the builder may encounter unexpected challenges or changes during the construction process. Using more cable can account for any unforeseen circumstances that may require repositioning or rerouting of the power supply, ensuring that the builder has enough resources to handle any situation.
Overall, using more cable than the minimum ensures practicality, flexibility, and preparedness for any contingencies that may arise during the construction process.