Question 1206903
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Circle equation
(x-h)^2 + (y-k)^2 = r^2
where,
(h,k) = center
r = radius


Let's place the radio transmitter at the origin. Meaning h = 0 and k = 0.
The radius is r = 21 in this case.
The circle equation will then update to x^2+y^2 = 441
Points inside the circle, or on the boundary, will get the radio signal. 


A = (0,25) is where you start from since it is 25 miles north of the transmitter.
B = (29,0) is where you are driving to, which is 29 miles east of the transmitter.
I'll skip a few steps, but you should find the equation of line AB is y = (-25/29)x + 25


We have this system of equations
{{{system(x^2+y^2 = 441, y = expr(-25/29)x + 25)}}}
Use substitution to plug the second equation into the first one to end up with {{{x^2+(expr(-25/29)x + 25)^2 = 441}}}


Skipping a few more steps, the solutions to that equation are approximately: x = 5.48588 and x = 19.24127
These are the x coordinates of the intersection points of the line and circle.
Since we're looking at approximate solutions, it seems reasonable to assume your teacher will allow you to use a graphing calculator to make quick work of this equation. 
Note: The exact solutions involve very large messy numbers.


If {{{5.48588 <= x <= 19.24127}}}, then points on line AB are inside the circle or on the circle's boundary. 
Otherwise, you'll be outside of the circle and won't pick up the signal.


Use those x values to determine the corresponding paired y values.
x = 5.48588 leads to y = 20.2708
Let point C be located at (5.48588, 20.2708)
x = 19.24127 leads to y = 8.4127
Let point D be located at (19.24127, 8.4127)


Diagram
*[illustration UploadedScreenshot_50.png]
The diagram was made with <a href="https://www.geogebra.org/calculator">GeoGebra</a> which is a useful tool to verify many types of math problems.


Use the distance formula to determine these approximate segment lengths
AB = 38.28838
CD = 18.1611
Then,
CD/AB = 18.1611/38.28838 = 0.47432


For roughly 47.432% of the trip, you'll be able to pick up this particular radio signal.
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