people located less than 10 km from the hospital are judged to have excellent access to the hospital, those located exactly 10 km away have acceptable access, any anyone living further than 10 km away has poor access.
a) If the hospital is located at coordinates (0,0) find the equation that describes all locations where people of the region have acceptable access to the hospital.
How would i find the equation?
b) The village of Kericho is located at coordinates (-4,9). What quality of access to the hospital of do the residents have? Explain.
What do i have to do or what formula to use in order to figure out the answer?
You need a circle here.
x^2 + y^2 = r^2
x^2 + y^2 = 100
a) To find the equation that describes all locations where people have acceptable access to the hospital, we need to consider the distance between each location and the hospital.
Given that people located exactly 10 km away from the hospital have acceptable access, we can use the distance formula to calculate the distance between any point (x, y) and the hospital located at coordinates (0, 0).
The distance formula is:
d = sqrt((x - x0)^2 + (y - y0)^2)
where (x, y) represents the coordinates of the point, and (x0, y0) represents the coordinates of the hospital.
In this case, we have (x0, y0) = (0, 0). So the distance formula simplifies to:
d = sqrt(x^2 + y^2)
We want to find the equation that describes all locations where people have acceptable access, meaning they are exactly 10 km away from the hospital. Therefore, we can set up the following equation:
sqrt(x^2 + y^2) = 10
This equation represents the boundary between acceptable access (within 10 km) and poor access (further than 10 km) to the hospital.
b) To determine the quality of access to the hospital for the residents of the village of Kericho located at coordinates (-4,9), we need to calculate the distance between this location and the hospital at (0,0).
Using the distance formula:
d = sqrt((-4 - 0)^2 + (9 - 0)^2)
= sqrt(16 + 81)
= sqrt(97)
≈ 9.85 km
Since the distance between Kericho and the hospital is less than 10 km, the residents of Kericho have acceptable access to the hospital.