SOLUTION: The relationship between the air temperatur t (in degrees Fahrenheit) and the altitude h ( in feet above sea level) is approcimately linear. At 1000 ft, the temperature is 60*. At

Algebra ->  Algebra  -> College  -> Linear Algebra -> SOLUTION: The relationship between the air temperatur t (in degrees Fahrenheit) and the altitude h ( in feet above sea level) is approcimately linear. At 1000 ft, the temperature is 60*. At       Log On


   


Question 28699: The relationship between the air temperatur t (in degrees Fahrenheit) and the altitude h ( in feet above sea level) is approcimately linear. At 1000 ft, the temperature is 60*. At 5000ft the temperature is 42*. Express t in therms of h. Use proper or improper fractions or exact decimals only no decimal approcimations.
Answer by josmiceli(6784) About Me  (Show Source):
You can put this solution on YOUR website!
If it's a linear relation then
t = mh +k where m is the slope and t = k when h = 0
%28t+-+60%29+%2F+%28h+-+1000%29+=+%2842+-+60%29+%2F+%285000+-+1000%29
this is the same as
%28y+-+y%5B2%5D%29+%2F+%28x+-+x%5B2%5D%29+=+%28y%5B1%5D+-+y%5B2%5D%29+%2F+%28x%5B1%5D+-+x%5B2%5D%29
%28t+-+60%29+%2F+%28h+-+1000%29+=+-18+%2F+4000%29
multiply both sides by (h - 1000)
+t+-+60+=+-%284.5+%2A+10%5E-3%29%2Ah+%2B+4.5
+t+=+-%284.5+%2A+10%5E-3%29%2Ah+%2B+64.5
check
when h = 1000
+t+=+-%284.5+%2A+10%5E-3%29%2A10%5E3+%2B+64.5
t+=+-4.5+%2B+64.5
t+=+60
when h = 5000
+t+=+-%284.5+%2A+10%5E-3%29%2A5%2A10%5E3+%2B+64.5
+t+=+-%285+%2A+4.5%29+%2B+64.5
+t+=+-22.5+%2B+64.5
+t+=+42
OK