Questions: (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 4,400 feet. (c) Find the altitude if the boiling point is 202.5 degrees F. (d) Graph T and illustrate the answers to (b) and (c) on the graph. (a) Choose the correct relationship below A. T=-184 x+212 B. T=1.84 x+212 C. T=-1.84 x-212 D. T=1.84 x-212

(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 4,400 feet. (c) Find the altitude if the boiling point is 202.5 degrees F. (d) Graph T and illustrate the answers to (b) and (c) on the graph. (a) Choose the correct relationship below A. T=-184 x+212 B. T=1.84 x+212 C. T=-1.84 x-212 D. T=1.84 x-212
Transcript text: (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 4,400 feet. (c) Find the altitude if the boiling point is \(202.5^{\circ} \mathrm{F}\). (d) Graph \(T\) and illustrate the answers to (b) and (c) on the graph. (a) Choose the correct relationship below A. \(T=-184 x+212\) B. \(T=1.84 x+212\) C. \(T=-1.84 x-212\) D. \(T=1.84 x-212\)
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Solution

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Solution Steps

Step 1: Identify the correct relationship

The problem provides four options for the relationship between temperature \( T \) in degrees Fahrenheit and altitude \( x \) in thousands of feet. We need to choose the correct one.

Step 2: Choose the correct option

The correct relationship is: \[ T = -1.84x + 212 \]

Step 3: Find the boiling point at an altitude of 4,400 feet

Convert the altitude to thousands of feet: \( x = 4.4 \). Substitute \( x = 4.4 \) into the equation: \[ T = -1.84(4.4) + 212 \] \[ T = -8.096 + 212 \] \[ T = 203.904 \]

Step 4: Find the altitude if the boiling point is \( 202.5^{\circ} \mathrm{F} \)

Set \( T = 202.5 \) and solve for \( x \): \[ 202.5 = -1.84x + 212 \] \[ -1.84x = 202.5 - 212 \] \[ -1.84x = -9.5 \] \[ x = \frac{-9.5}{-1.84} \] \[ x \approx 5.1630 \]

Final Answer

  1. The correct relationship is \( T = -1.84x + 212 \).
  2. The boiling point at an altitude of 4,400 feet is approximately \( 203.904^{\circ} \mathrm{F} \).
  3. The altitude for a boiling point of \( 202.5^{\circ} \mathrm{F} \) is approximately 5,163 feet.

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