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?

Guest Sep 28, 2021

#1**+1 **

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

ElectricPavlov Sep 28, 2021