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

Respuesta :

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

[tex]y=k\sqrt{x}[/tex]

when y=29, x=100

step 1

find the value of k

substitute the given values in the expression above

[tex]\begin{gathered} 29=k\sqrt{100} \\ 29=10k \\ k=2.9 \end{gathered}[/tex]

step 2

we have the equation

[tex]y=2.9\sqrt{x}[/tex]

For x=123

substitute the value of x and solve for y

[tex]\begin{gathered} y=2.9\sqrt{123} \\ y=32.16 \end{gathered}[/tex]