Suppose the temperature x miles above ground level is given

Suppose the temperature x miles above ground level is given by T(x)=69-29x. Determine where the temperature is below 52 degrees. Assume that the domain of T is 0 which is < or = to x which is < or = to 6. Answer the following questions. Use the intersection of graphs method to estimate the altitudes where the temperature is below 52 degrees.

The solution set is {x ___ <x< or = to ____}

Round to the nearest hundredth. Simplify, type the answer as an integer or fraction.

What does the x – intercept on the graph of T represent?

a)    An altitude of 6 miles high

b)    Altitude where the temperature equals zero

c)    Ground level

Solve the first part symbolically.

Solution

T(x) = 69 -29x <52

69 -29x < 52

29x > 69 -52

29x >10

x > 10/29

x>0.345 miles

for x>0.345 temp is below 52 deg

a) T(x) = 69 -29x

x intercept : 0 = 69 - 29x

x = 69/29 = 2.38 miles where temp is 0 deg

b) temp at x =6

T(6) = 69 - 29*6 = -105 deg

c) at x = 2.38 miles temp equals zero.

d) Ground level : x =0

T(0) = 69 deg