An amount allocated, X will be distributed to households affected by the flood disaster. Given that the distribution calculation formula is that X changes directly with the square of Y and inversely with Z + 3. Given X= 8 000 when Y=80 and Z=47. (a) Express X in terms of Y and Z.

The distribution calculation formula states that: X is directly proportional to Y^2 X is inversely proportional to Z+3 Using the proportionalities, we can write: X = k * Y^2 / (Z+3) where k is a constant of proportionality. To determine the value of k, we can use the values given in the problem: X= 8,000, Y = 80, and Z = 47. Substituting these values into the equation above, we get: 8,000 = k * 80^2 / (47+3) Simplifying, we get: 8,000 = k * 6400 / 50 k = 8,000 * 50 / 6400 k = 62.5 Now we can substitute this value of k back into the equation: X = 62.5 * Y^2 / (Z+3) Therefore, X in terms of Y and Z is: X = 62.5 * Y^2 / (Z+3)