A builder needs to connect a partially built house to a temporary power supply. On the plan, the coordinates of the house are (50,114) 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?
pls help me.And explain how you did it.
thanks
if they are coordinates, can't you use the distance formula? the least amount would be:
square root of ( (x2-x1)^2 + (y2-y1)^2 ) = 102.142
he will probably need more cable because in real life there may possibly be obstacles preventing a straight line of cable
Well, to find the least amount of cable needed, we can use a bit of good old Pythagorean theorem! The length of the cable will be the straight-line distance between the house and the power supply.
So, let's break it down:
First, we need to find the horizontal distance between the two points. We subtract the x-coordinates of the power supply and the house: 147 - 50 = 97.
Next, we find the vertical distance by subtracting the y-coordinates of the power supply and the house: 82 - 114 = -32.
Hold on, what's with that negative sign? Well, when we subtracted the y-coordinates, we got a negative value because the power supply is below the house. But no worries, we'll just take the absolute value: |-32| = 32.
Now, we have the horizontal distance (97) and the vertical distance (32). To find the cable length, we use Pythagorean theorem: c² = a² + b², where c represents the hypotenuse.
Plugging in the values, we get: c² = 97² + 32² = 9409 + 1024 = 10433.
To calculate c, we take the square root of 10433 (approximately 102.13). So the least amount of cable needed is around 102.13 units.
Now, why is it likely that the builder will use more cable than this? Well, construction usually involves some contingency planning. Builders might account for potential obstacles, changes in plans, or optimal cable routing that may require additional length. It's always better to have a little extra than to risk running short!
To calculate the least amount of cable needed to connect the partially built house to the temporary power supply, we can use the distance formula.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
For this case, the coordinates of the house are (x1, y1) = (50, 114) and the coordinates of the power supply are (x2, y2) = (147, 82).
Using the distance formula, we can calculate the distance between the two coordinates:
d = √((147 - 50)^2 + (82 - 114)^2)
= √(97^2 + (-32)^2)
= √(9409 + 1024)
= √10433
≈ 102.1 units (rounded to one decimal place)
So, the least amount of cable needed to connect the house to the power supply is approximately 102.1 units.
However, it is likely that the builder will use more cable than this for a few reasons:
1. Safety: To ensure there is enough slack and to account for any unforeseen circumstances or future changes to the layout, the builder may choose to have additional cable length.
2. Routing: The builder may need to route the cable around obstacles such as trees, landscaping, or existing structures, which may require extra cable length.
3. Code Compliance: Depending on local building codes or regulations, there may be minimum cable-length requirements set by authorities to meet safety standards. The builder may need to adhere to these requirements, resulting in additional cable usage.
Therefore, it is advisable for the builder to consider factors like safety, routing, and code compliance when determining the amount of cable to be used, which could result in more cable than the minimum required distance calculated.
To find the least amount of cable needed to connect the partially built house to the temporary power supply, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and can be used to determine the length of the hypotenuse of a right triangle, given the coordinates of its endpoints.
The distance formula is as follows:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates, we can plug them into this formula:
d = √((147 - 50)^2 + (82 - 114)^2)
= √((97)^2 + (-32)^2)
= √(9409 + 1024)
= √(10433)
≈ 102.12
Therefore, the least amount of cable needed to connect the partially built house to the temporary power supply is approximately 102.12 units.
Now, let's address why it is likely that the builder will use more cable than this. There are a few reasons for this:
1. Practicality and Safety: It is important to have some extra cable to allow for flexibility during installation. The builder may encounter unforeseen obstacles or need to reroute the cable due to other factors on the construction site. It is always a good practice to have some extra length available to ensure a safe and reliable connection.
2. Future-proofing: The builder might anticipate the need for additional outlets or extensions in the future. By using more cable initially, they can avoid the hassle and cost of adding more cable later on.
3. Regulations and Codes: There may be specific regulations or building codes that require a certain amount of extra cable to be used for safety or compliance reasons. These rules vary by region, so the builder will need to follow the guidelines specific to their location.
It is important to note that while the distance calculated using the distance formula represents the minimum amount of cable needed between the two points, the actual amount used by the builder may be greater due to the factors mentioned above.