Question

Maria is walking near a radio transmitter antenna. She begins 3 km west and 4km south of the transmitter, and walks directly toward a point 5 km due north of the transmitter. Maria walks at a constant speed of 4km/hr. During her walk, for how much time was she within 3km of the transmitter. ( Please show work so i cant understand )THanks :)

Answer 1

were you able to get started at all?

Answer 2

i got the points down to it

Answer 3

which points do you have

Answer 4

(3,-4) (0,5)

Answer 5

well she actually starts at (-3,-4) because she is west of the transmitter

I put the transmitter at (0,0)

Answer 6

yes yes my bad

Answer 7

what is the equation of the line through (-3,-4) and (0,5)

Answer 8

i dont know

Answer 9

how about the slope of that line?

Answer 10

slope is 9/3 =3

Answer 11

notice how (0,5) is on the line

that is the y-intercept

Answer 12

m = 3
b = 5

so the equation is y = 3x+5

Answer 13

we'll use that to determine the points of intersection between that line and the circle

Answer 14

it asks us: " During her walk, for how much time was she within 3km of the transmitter. "

so essentially we'll have a circle with radius 3 and center (0,0)

and we want to know how long she's been in this 3 km circle

Answer 15

what is the equation of this circle?

Answer 16

its x^2+y^2=r^2

Answer 17

hello?

Answer 18

sorry about that

you are close, but what is r?

Answer 19

i dont know

Answer 20

r is the radius of the circle

Answer 21

which in this case is 3

Answer 22

ok

Answer 23

therefore,

x^2+y^2=r^2

x^2+y^2=3^2

x^2+y^2=9

is the equation of the circle

Answer 24

now let's graph the line y = 3x+5 and the circle x^2+y^2=9 together