15. Each of the following temperature ranges is in degrees Fahrenheit. Use the formula F=95 C+32 to find the corresponding temperature range in degrees Celsius (using interval notation and assume inclusion).
16.The fuel efficiency (mpg rating) for cars has been increasing steadily since 1980 . The formula for a car's fuel efficiency for a given year between 1980 and 1996 is
E=0.36x+15.9
where E is miles per gallon and x is the number of years after 1980 .
a. In what years was the average fuel efficiency for cars less than 17 mpg (in interval form)?
b. In what years was the average fuel efficiency for cars more than 20 mpg (in interval form)?
Your temp conversion is wrong
F = (9/5)C + 32
E = 0.36 ( y-1980) +15.9
when does E reach 17 ?
17 -15.9 = .36 y - .36*1980
.36 y = 1.1 + 712.8 = 713.9
y = 713.9/.36
y = 1983
so y <1983
now do the same with E = 20
15. To find the corresponding temperature range in degrees Celsius using the formula F=95C+32, we need to solve the formula for C.
First, subtract 32 from both sides of the equation to isolate the term 95C:
F - 32 = 95C
Then, divide both sides of the equation by 95 to solve for C:
(F - 32) / 95 = C
Now we can use this formula to convert the temperature ranges from Fahrenheit to Celsius.
a. For a temperature range in Fahrenheit less than 17 degrees, we substitute 17 into the formula and solve for C:
(17 - 32) / 95 = C
-15 / 95 = C
C ≈ -0.1579
So, the corresponding temperature range in Celsius is approximately (-0.1579, 17].
b. For a temperature range in Fahrenheit more than 20 degrees, we substitute 20 into the formula and solve for C:
(20 - 32) / 95 = C
-12 / 95 = C
C ≈ -0.1263
So, the corresponding temperature range in Celsius is approximately (-0.1263, 20].
16. To find the years when the average fuel efficiency for cars was less than 17 mpg or more than 20 mpg, we need to substitute the given values into the formula E=0.36x+15.9 and solve for x.
a. For an average fuel efficiency of less than 17 mpg:
Substitute 17 into the formula and solve for x:
17 = 0.36x + 15.9
0.36x = 17 - 15.9
0.36x = 1.1
x = 1.1 / 0.36
x ≈ 3.0556
So, the average fuel efficiency for cars was less than 17 mpg between the years approximately 1983 and 1984.
b. For an average fuel efficiency of more than 20 mpg:
Substitute 20 into the formula and solve for x:
20 = 0.36x + 15.9
0.36x = 20 - 15.9
0.36x = 4.1
x = 4.1 / 0.36
x ≈ 11.3889
So, the average fuel efficiency for cars was more than 20 mpg between the years approximately 1991 and 1992.