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Sagot :
Using linear functions, it is found that:
a) Clouds will not form at an altitude below 1.136 miles.
b) The analytical solution to the inequality is x > 1.136.
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The linear function for the temperature at an altitude of x miles is:
[tex]T(x) = T(0) - 19x[/tex]
In which
- T(0) is the ground level temperature.
- The ground level temperature is 65ºF, thus [tex]T(0) = 65[/tex], and:
[tex]T(x) = 65 - 19x[/tex]
The function for the dew point is:
[tex]D(x) = D(0) - 5.8x[/tex]
The ground level dew point is 50ºF, thus:
[tex]D(x) = 50 - 5.8x[/tex].
Item a:
- Clouds will not form if the temperature is above the dew point.
- In the sketch, temperature is in blue and the dew point is in red.
- The intersection is at an altitude of 1.136 miles.
- Before, the temperature is above.
- Thus, clouds will not form at an altitude below 1.136 miles.
Item b:
Analytically, we have to solve the following inequality:
[tex]T(x) > D(x)[/tex]
[tex]65 - 19x > 50 - 5.8x[/tex]
[tex]-13.2x < -15[/tex]
[tex]13.2x > 15[/tex]
[tex]x > \frac{15}{13.2}[/tex]
[tex]x > 1.136[/tex]
A similar problem is given at https://brainly.com/question/12965245

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