Chapter 11 QuaDraTiC appliCaTionS 4351000 20 000 1000 20 000 55 400
2000 55rrr^2
rr−++=−
=,,.( ).^22
2
2
2200
055 2000 2200
2000 2000 4−
=−−=−− ±− −.
()()(rrr^5552200
255
2000 4 000 000 48 400
11
2000.)()
(.)
,, ,−= ±+= ±± ≈ ± ≈
−4 048 400
112000 2012 063617
11365
2000 2012,,. ,. 0063617
11
isnegative
The plane would have averaged about 365 mph without the wind.
- Let r represent the plane’s average speed without the wind. The plane’s
average speed from Minneapolis to Atlanta (against the headwind) is
r − 30. The plane’s average speed from Atlanta to Minneapolis (with the
tailwind) is r + 30. The total time in the air is 512 hours and the distance
between Atlanta to Minneapolis is 900 miles. The time in the air from
Minneapolis to Atlanta is^900
r – 30
hours, and the time in the air fromAtlanta to Minneapolis is^900
r + 30hours. The time in the air from Minne-
apolis to Atlanta plus the time in the air from Minneapolis to Atlanta is
5512 .= 5 hours. The equation to solve is^900
30900
3055
rr .
– +
+ = . The LCD is
(r − 30)(r + 30).()rr() ()() ()(
rrr
r−+ r
−+− +
+30 30 900 =−
3030 30 900
3030 rr
rrrr+
++ −= −+30 55
900 30 900 30 55 30 30)( .)
()().[()()]]
,,.( )
.900 27 000 900 27 000 55 900
1800 55rrr^2
rr++−=−
=^22
2
24950
055 1800 4950
1800 1800 4−
=−−=−− ±− −.
()()(rrr^5554950
255
1800 3 240 000 108 900
11180.)()
(.)
,, ,−= ±+=^003 348 900
11
1800 1830
11330 1800 1830
11±= ± = −,, isnnegative
The plane’s average speed without the wind was 330 mph.