SOLUTION: The gas mileage for a certain vehicle can be approximated by m = −0.04x2 + 3.6x − 49, where x is the speed of the vehicle in mph. Determine the speed(s) at which the ca

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: The gas mileage for a certain vehicle can be approximated by m = −0.04x2 + 3.6x − 49, where x is the speed of the vehicle in mph. Determine the speed(s) at which the ca      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1009294: The gas mileage for a certain vehicle can be approximated by m = −0.04x2 + 3.6x − 49, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 30 mpg. Round to the nearest mph.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+m+=+-.04x%5E2+%2B+3.6x+-+49+
+30+=+-.04x%5E2+%2B+3.6x+-+49+
+-.04x%5E2+%2B+3.6x+-+79+=+0+
+-4x%5E2+%2B+360x+-+7900+=+0+
+-x%5E2+%2B+90x+-+1975+=+0+
Use quadratic formula
+x+=+%28+-90+%2B-+sqrt%28+90%5E2-4%2A%28-1%29%2A%28-1975%29+%29%29%2F%282%2A%28-1%29%29+
+x+=+%28+-90+%2B-+sqrt%28+8100+-+7900+%29%29%2F%28-2%29+
+x+=+%28+-90+%2B-+sqrt%28+200+%29%29%2F%28-2%29+
+x+=+%28+-90+%2B+14.142+%29%2F%28-2%29+
+x+=+37.93+
38 mi/hr
------------
and, also:
+x+=+%28+-90+-+14.142+%29%2F%28-2%29+
+x+=+%28+-+104.142+%29+%2F+%28+-2+%29+
+x+=+52.07+
52 mi/hr
--------------
check:
+30+=+-.04x%5E2+%2B+3.6x+-+49+
+30+=+-.04%2A38%5E2+%2B+3.6%2A38+-+49+
+30+=+-.04%2A1444+%2B+136.8+-+49+
+30+=+-57.76+%2B+136.8+-+49+
+30+=+30.04+
close enough
You can check the other solution