Question

Suppose that y varies directly as the square root of x, and that y = 29 when x = 100. What is y when x = 123? Round your answer to two decimal places if necessary

Answer 1

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form

y=kx

where

k is the constant of proportionality

In this problem we have that

`y=k√(x)`

when y=29, x=100

step 1

find the value of k

substitute the given values in the expression above

`\begin{gathered} 29=k√(100) \\ 29=10k \\ k=2.9 \end{gathered}`

step 2

we have the equation

`y=2.9√(x)`

For x=123

substitute the value of x and solve for y

`\begin{gathered} y=2.9√(123) \\ y=32.16 \end{gathered}`