Scott, Arif, and Diane run a small delivery company. For thier business, they use licensed two-way radios with a 20 km range. Scott is at their office which they have marked as the origin on their map of the town. Arif is dropping off a package at (-8, 16) while Diane is making a pick up at )4,20)
a) Find an equation that desrcibes the boundry of this area
If "the area" is a triangle, it would take three equations to define the boundary. I don't see what the 20 km range of the radios has to do with that boundary.
If what they want is the equation of the boundary of radio reception, it is the circle
x^2 + y^2 = 20^2 = 400
Diane is outside the boundary and Arif is inside it.
does anybody knows how to solve for x+2y is
To find the equation that describes the boundary of the delivery area, we can use the distance formula. The distance formula between any two points (x1, y1) and (x2, y2) is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Since the two-way radios have a range of 20 km, the distance between the office (origin) and any point on the boundary of the delivery area should be 20 km.
Let's start by finding the equation for Arif's drop-off location (-8, 16).
Using the distance formula, the equation can be written as:
sqrt((x2 - x1)^2 + (y2 - y1)^2) = 20
Replacing (x1, y1) with the coordinates of the office (0, 0) and (x2, y2) with the coordinates of Arif's drop-off location (-8, 16), we have:
sqrt((-8 - 0)^2 + (16 - 0)^2) = 20
Simplifying:
sqrt(64 + 256) = 20
sqrt(320) = 20
Squaring both sides to eliminate the square root:
320 = 20^2
320 = 400
This equation is not true, which means that (-8, 16) is outside the delivery area. Let's proceed to find the equation for Diane's pick-up location.
Using the same process as above, we can write the equation as:
sqrt((x2 - x1)^2 + (y2 - y1)^2) = 20
Replacing (x1, y1) with the coordinates of the office (0, 0) and (x2, y2) with the coordinates of Diane's pick-up location (4, 20), we have:
sqrt((4 - 0)^2 + (20 - 0)^2) = 20
Simplifying:
sqrt(16 + 400) = 20
sqrt(416) = 20
Squaring both sides to eliminate the square root:
416 = 20^2
416 = 400
This equation is also not true, indicating that (4, 20) is outside the delivery area.
Since the coordinates provided for Arif's and Diane's locations do not satisfy the equation, we cannot determine the equation that describes the boundary of this area with the given information.
To find the equation that describes the boundary of this area, we first need to consider the 20 km range of the two-way radios.
Since Scott is at the office (origin), we know his coordinates are (0, 0). Arif is dropping off a package at (-8, 16), and Diane is making a pick-up at (4, 20). We need to find the maximum distance they can be from Scott's location within the 20 km range.
Let's calculate the distance between Scott and Arif:
√((-8 - 0)^2 + (16 - 0)^2) = √(64 + 256) = √320 ≈ 17.89 km
Now, let's calculate the distance between Scott and Diane:
√((4 - 0)^2 + (20 - 0)^2) = √(16 + 400) = √416 ≈ 20.4 km
Since the radio range is 20 km, both Arif and Diane are at the edge of its reach from Scott's location. This means that the boundary of the area would be a circle with Scott's location at the center and a radius of 20 km.
In the form of an equation, the boundary of the area can be described as:
(x - 0)^2 + (y - 0)^2 = 20^2
x^2 + y^2 = 400
Therefore, the equation describing the boundary of this area is x^2 + y^2 = 400.