Question

For altitudes up to 36,000 feet, the relationship between ground temperature and atmospheric

temperature can be described by the formula t = -0.0035a +g, in which t is the atmospheric

temperature in degrees Fahrenheit,a is the altitude, in feet, at which the atmospheric temperature is

measured and g is the ground temperature in degrees Fahrenheit. Solve the equation for a. If the

atmospheric temperature is -30.5 °F and the ground temperature is 50 °F, what is the altitude?

The equation for a is a =

If the atmospheric temperature is -305 °F and the ground temperature is 50 °F, then

feet

a =

Answer 1

The equation for a is
`a=-(2000)/(7)*(t-g)`

The altitute is 101,428.57 feet

Explanation:

You know that the relationship between ground temperature and atmospheric temperature can be described by the formula

t = -0.0035a +g

where:

• t is the atmospheric temperature in degrees Fahrenheit
• a is the altitude, in feet, at which the atmospheric temperature is measured
• g is the ground temperature in degrees Fahrenheit.

Solving the equation for a:

-0.0035a +g=t

-0.0035a= t - g

`a=(t-g)/(-0.0035)`

`a=-(2000)/(7)*(t-g)`

The equation for a is
`a=-(2000)/(7)*(t-g)`

If the atmospheric temperature is -305 °F and the ground temperature is 50 °F, then t= -305 °F and g= 50 °F

Replacing in the equation for a you get:

`a=-(2000)/(7)*(-305-50)`

`a=-(2000)/(7)*(-355)`

a= 101,428.57

The altitute is 101,428.57 feet