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A small radio transmitter broadcasts in a 50 mile radius. If you drive along a straight line from a city 61 miles north of the transmitter to a second city 56 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?

 Sep 28, 2021
 #1
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Circle equation    x^2 + y^2 = 2500

 

Line equation between cities     y = -61/56 x  -61     sub this into the circle equation to solve for x

 

x^2  +  ( -61/56 x  +61 ) ^2   -2500 = 0

2.18654x^2 -132.8928x +1221 =0     Now use quadratic Formula  ( or a quadratic formula calculator available online)

                                                                    to find   x =   49.4938  and  11.2825      

                                                                               total x distance = 38.211 miles out of     56  'x' direction miles

 

38.211 / 56 = 68.23% of the route

 

 Sep 28, 2021

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