Get the most out of your questions with the extensive resources available on IDNLearn.com. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.
[tex]$y$[/tex] varies directly with [tex]$x$[/tex]. [tex]$y$[/tex] is 42 when [tex]$x$[/tex] is 7. What is [tex]$x$[/tex] when [tex]$y$[/tex] is 18?
Certainly! To find the value of [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is 18 given that [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], follow these steps:
1. Determine the constant of proportionality [tex]\( k \)[/tex]: Since [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we can express this relationship as [tex]\( y = kx \)[/tex] where [tex]\( k \)[/tex] is the constant of proportionality.
From the given information, [tex]\( y = 42 \)[/tex] when [tex]\( x = 7 \)[/tex]. Substituting these values into the equation [tex]\( y = kx \)[/tex]: [tex]\[
42 = k \cdot 7
\][/tex] To find [tex]\( k \)[/tex], solve for [tex]\( k \)[/tex] by dividing both sides of the equation by 7: [tex]\[
k = \frac{42}{7} = 6
\][/tex] So, the constant of proportionality [tex]\( k \)[/tex] is 6.
2. Use the constant of proportionality to find [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is 18: Now that we know [tex]\( k = 6 \)[/tex], we can use this to find [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is 18.
Using the direct variation formula [tex]\( y = kx \)[/tex], substitute [tex]\( y = 18 \)[/tex] and [tex]\( k = 6 \)[/tex]: [tex]\[
18 = 6 \cdot x
\][/tex] To find [tex]\( x \)[/tex], isolate [tex]\( x \)[/tex] by dividing both sides of the equation by 6: [tex]\[
x = \frac{18}{6} = 3
\][/tex]
Therefore, when [tex]\( y \)[/tex] is 18, the corresponding value of [tex]\( x \)[/tex] is 3.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! IDNLearn.com is your reliable source for answers. We appreciate your visit and look forward to assisting you again soon.
