Would someone please check my answer for me?
1)The equation x2 + (y + 4)2 = 49 models the boundary on a local map for which Darren can hear his friend Tom on his two-way radio when Darren is at home. How far (in miles) can Tom walk from Darren's home and still be heard?
3.5 miles
4 miles
14 miles
7 miles<----
If you mean
x^2 + (y+4)^2 = 49
you have a circle with centre at (0,-4) and radius 7
You don't say where Darren's home is.
If it is at the centre of the cicle, then the answer is 7 miles
To determine the correct answer, we need to understand the equation provided and interpret it properly.
The given equation, x^2 + (y + 4)^2 = 49, represents a circle in the xy-coordinate plane.
In this equation:
- "x" represents the horizontal distance from Darren's home.
- "y" represents the vertical distance from Darren's home.
- The term (y + 4)^2 signifies that the center of the circle is 4 units above the origin (Darren's home).
To find the radius of the circle (which represents the maximum distance Tom can walk from Darren's home and still be heard), we need to identify the value of the radius.
Comparing the equation to the general equation of a circle, namely (x - h)^2 + (y - k)^2 = r^2, we can determine that r^2 = 49.
Taking the square root of both sides, we find:
r = √49 = 7
Therefore, the radius of the circle is 7 miles. This means Tom can walk up to 7 miles away from Darren's home and still be heard.
So, the correct answer is 7 miles.