1-1: 39
|
VHF (range in miles) |
UHF (range in miles) |
MODEL |
PRICE |
|
30 |
20 |
A |
$40 |
|
45 |
35 |
B |
$50 |
|
60 |
40 |
C |
$60 |
|
75 |
55 |
D |
$70 |
Find the least cost antenna that receives VHF Channel 19 (25, 35) and UHF Channel 38 (-20, -32) from Home (0, 0).
Step 1) find the distances d1 and d2
Step 2) find the antenna models that can receive both a UHF signal at d1 distance AND a VHF signal at d2 distance.
Step 3) select the least expensive such antenna.
d1 = sqrt ( (-20 - 0 )2 + (-32 - 0)2 ) = sqrt (400 + 1024) = sqrt 1424 = 37.7 miles for UHF
d2 = sqrt ( (25 - 0 )2 + (35 - 0)2 ) = sqrt (625+ 1225) = sqrt 1850 = 43.0 miles for VHF
So, Models C and D will receive the UHF signal, while Models B, C and D will work for the VHF signal.
To get both stations, Models C and D will work. Model C is the least expensive of these choices.