h=11.2-0.125 d The ceiling height, h, in feet, for a particular room in a house a distance of d feet from the west wall is given by the equation. In order for the ceiling height to decrease by 1 foot, how much does the distance from the west wall change in feet? Choose 1 answer: (A) 0.125 (B) 8 (c) 11.2 (D) 89.6

Question

h=11.2-0.125 d The ceiling height,  h, in feet, for a particular room in a house a distance of  d feet from the west wall is given by the equation. In order for the ceiling height to decrease by 1 foot, how much does the distance from the west wall change in feet? Choose 1 answer: (A) 0.125 (B) 8 (c) 11.2 (D) 89.6

Bytelearn · Accepted Answer

Given Equation: We are given the equation h = 11.2 - 0.125d, where h is the ceiling height in feet and d is the distance from the west wall in feet. We want to find out how much d needs to change for h to decrease by 1 foot.Denote Initial Heights: Let's denote the initial height as h1 and the height after the decrease as h2. We know that h2 = h1 - 1 because the height decreases by 1 foot. Let's denote the initial distance from the west wall as d1 and the distance after the change as d2.Substitute and Simplify: Using the given equation for the initial height, we have h1 = 11.2 - 0.125d1. For the height after the decrease, we have h2 = 11.2 - 0.125d2.Isolate d2: Since h2 = h1 - 1, we can substitute the expressions for h1 and h2 to get 11.2 - 0.125d2 = (11.2 - 0.125d1) - 1.Final Calculation: Simplifying the equation, we get 11.2 - 0.125d2 = 11.2 - 0.125d1 - 1. The 11.2 on both sides of the equation cancel out, leaving us with -0.125d2 = -0.125d1 - 1.To isolate d2, we divide both sides of the equation by -0.125. This gives us d2 = d1 + (1 / -0.125).Calculating the right side of the equation, we have d2 = d1 + (1 / -0.125) = d1 - 8. This means that the distance from the west wall must increase by 8 feet for the ceiling height to decrease by 1 foot.

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