D = 0.2 when p = 10. find the P = 18

p when d
= 1.1

1 answer

To find \( D \) when \( P = 18 \) and given that \( D = 0.2 \) when \( P = 10 \) and we want to find \( D = 1.1 \), we can assume a proportional relationship between the values.

Given:

  • \( D_1 = 0.2 \) when \( P_1 = 10 \)
  • We want to find \( D_2 \) when \( P_2 = 18 \)

Step 1: Determine the relationship between \( D \) and \( P \).

Since we do not have a specific functional form, we'll use a simple proportionality for this case, assuming the form \( D \cdot P = k \) (where \( k \) is a constant).

Step 2: Calculate the constant \( k \).

From \( D_1 \) and \( P_1 \): \[ k = D_1 \cdot P_1 = 0.2 \cdot 10 = 2 \]

Step 3: Compute \( D \) for \( P = 18 \).

Now for \( P_2 = 18 \): \[ D_2 \cdot P_2 = k \] \[ D_2 \cdot 18 = 2 \] \[ D_2 = \frac{2}{18} = \frac{1}{9} \approx 0.1111 \]

Step 4: Relate \( D_1 \) to \( D_2 \) based on proportionality.

To find \( P \) when \( D = 1.1 \): Using \( D \cdot P = 2 \): \[ 1.1 \cdot P = 2 \] \[ P = \frac{2}{1.1} \approx 1.818 \]

In conclusion, when \( D = 1.1 \), the corresponding \( P \) is approximately \( 1.818 \).