‘x’ varies directly with the cube of ‘y’, and inversely with the square of ‘z’. If x = 1/36 when y = 2 and z = 3, then what is the value of 800x when y = 3 and z = 5?

Question

Accepted Answer

Given that x varies directly with the cube of y and inversely with the square of z, we can write the relation as:

x = k * (y^3) / (z^2)

where k is the constant of proportionality.

Step 1: Find k using the given values x = 1/36, y = 2, z = 3.

x = k * (2^3) / (3^2)
1/36 = k * 8 / 9

Multiply both sides by 9:
9 * (1/36) = 8k
1/4 = 8k

Divide both sides by 8:
k = 1/32

Step 2: Find x when y = 3 and z = 5.

x = (1/32) * (3^3) / (5^2)
= (1/32) * 27 / 25
= 27 / (32 * 25)
= 27 / 800

Step 3: Find 800x:

800x = 800 * (27 / 800) = 27

Therefore, the value of 800x is 27.

Answer

Answer

Answer