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Math Asked by a SnapAndSolve user · about 4 hours ago

(a) Find a relationship of the form T = mx + b where T is degrees Fahrenheit and x is altitude in thousands...

(a) Find a relationship of the form T = mx + b where T is degrees Fahrenheit and x is altitude in thousands of feet.
(b) Find the boiling point at an altitude of 3,800 feet.
(c) Find the altitude if the boiling point is 196°F.
(d) Graph T and illustrate the answers to (b) and (c) on the graph.
(d) Graph T. Choose the correct graph below.

Answer

  1. (a) To find the relationship T = mx + b, we use the points (0, 212) and (10, 193.6). The slope m is calculated as:
    m = (193.6 - 212) / (10 - 0) = -1.84.
    Using the point (0, 212), the equation becomes:
    T = -1.84x + 212.

  2. (b) For an altitude of 3,800 feet (or 3.8 thousand feet), substitute x = 3.8 into the equation:
    T = -1.84(3.8) + 212 = 205°F.

  3. (c) To find the altitude where the boiling point is 196°F, set T = 196:
    196 = -1.84x + 212.
    Solving for x gives:
    x = (212 - 196) / 1.84 = 8.7 thousand feet.

  4. (d) The correct graph is option D, which shows a linear decrease in temperature with increasing altitude, consistent with the equation T = -1.84x + 212.

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