The variable x varies directly as the cube of y, and y varies directly as the square root of z. if x equals 1 when z equals 4, what is the value of z when x equals 27?

Step-by-step explanation:

According to the question,

∝          .......(1)

∝    .......(2)

From equation 1,2 let constant of proportionality be respectively.

⇒            .......(3)

⇒    .......(4)

From the above equations putting 4 into 3,

Let the new constant to the above equation be ,

Given,if x=1, when z=4

⇒

Now if x=27, then z=?

⇒

⇒

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.