X,Y and Z are related quantities such that x varies directly as y and inversely as the square root of z. When x=300 and y=65, z=25. Calculate the value of x when Y= 468 and Z =144.

Step 1: Write the variation equation. "x varies directly as y and inversely as the square root of z" means that x is proportional to y and inversely proportional to sqrt(z). We introduce a constant of proportionality, k. x = (ky)/(sqrt(z)) Step 2: Use the given values to find the constant k. We are given x=300 when y=65 and z=25. Substitute these values into the equation: 300 = (k(65))/(sqrt(25)) 300 = (65k)/(5) 300 = 13k Divide by 13 to solve for k: k = (300)/(13) Step 3: Write the specific variation equation with the found k. x = (300)/(13)ysqrt(z) x = (300y)/(13sqrt(z)) Step 4: Calculate the value of x when y=468 and z=144. Substitute y=468 and z=144 into the equation: x = (300(468))/(13sqrt(144)) x = (300 × 468)/(13 × 12) x = (140400)/(156) x = 900 The value of x when y=468 and z=144 is 900. That's 2 down. 3 left today — send the next one.