The problem states that for every 2 psi drop in pressure, the temperature rises by 3 degrees. This indicates a linear relationship between temperature and pressure, T = mP + c.

Here are the solutions to your questions: Question 3 1. Derive the formula which shows the interrelationship between pressure and temperature. Let P be the pressure in psi and T be the temperature in degrees. The problem states that for every 2 psi drop in pressure, the temperature rises by 3 degrees. This indicates a linear relationship between temperature and pressure, T = mP + c. Step 1: Determine the slope (m). The change in pressure is P = -2 psi (pressure drops). The change in temperature is T = +3 degrees (temperature rises). The slope m is given by: m = ( T)/( P) = (3)/(-2) = -(3)/(2) Step 2: Use the given point to find the y-intercept (c). We are given that when the pressure is P = 2 psi, the temperature is T = -12 degrees. Substitute these values and the slope into the linear equation T = mP + c: -12 = (-(3)/(2))(2) + c -12 = -3 + c Step 3: Solve for c. c = -12 + 3 c = -9 Step 4: Write the final formula. Substitute the slope m = -(3)/(2) and the y-intercept c = -9 into T = mP + c: T = -(3)/(2)P - 9 The formula showing the interrelationship between pressure and temperature is: T = -(3)/(2)P - 9 2. Draw the graph of the above function, show the intersection points on the graph with the axes precisely. The function is T = -(3)/(2)P - 9. To draw the graph, we find the intercepts with the axes. Step 1: Find the T-intercept (where P=0). Substitute P=0 into the equation: T = -(3)/(2)(0) - 9 T = -9 The T-intercept is (0, -9). Step 2: Find the P-intercept (where T=0). Substitute T=0 into the equation: 0 = -(3)/(2)P - 9 Add 9 to both sides: 9 = -(3)/(2)P Multiply by -(2)/(3) to solve for P: P = 9 × (-(2)/(3)) P = -3 × 2 P = -6 The P-intercept is (-6, 0). Step 3: Draw the graph. Plot the two intercepts (0, -9) and (-6, 0) and draw a straight line through them. The horizontal axis represents Pressure (P in psi) and the vertical axis represents Temperature (T in degrees). ` ^ T (degrees) | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |