To solve for [tex]\( y \)[/tex] given the conditions, we need to follow the steps for dealing with direct variation. Here's the step-by-step process:
1. Understand Direct Variation:
If [tex]\( y \)[/tex] varies directly as [tex]\( x \)[/tex], it means [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
2. Find the Constant of Variation (k):
We are given that [tex]\( y = 13 \)[/tex] when [tex]\( x = 27 \)[/tex]. Substitute these values into the direct variation formula to determine [tex]\( k \)[/tex]:
[tex]\[
13 = k \cdot 27
\][/tex]
Solving for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{13}{27}
\][/tex]
3. Find the New Value of y:
Now, we're asked to find [tex]\( y \)[/tex] when [tex]\( x = 44 \)[/tex]. Use the constant [tex]\( k \)[/tex] and substitute [tex]\( x = 44 \)[/tex] back into the direct variation equation:
[tex]\[
y = k \cdot 44
\][/tex]
Substituting the value of [tex]\( k \)[/tex]:
[tex]\[
y = \left(\frac{13}{27}\right) \cdot 44
\][/tex]
Calculating [tex]\( y \)[/tex] gives us:
[tex]\[
y \approx 21.185185185185183
\][/tex]
4. Round the Answer:
Finally, we need to round [tex]\( y \)[/tex] to the nearest hundredth. Rounding [tex]\( 21.185185185185183 \)[/tex] to two decimal places:
[tex]\[
y \approx 21.19
\][/tex]
Thus, when [tex]\( x = 44 \)[/tex], the value of [tex]\( y \)[/tex] is:
[tex]\[
y \approx 21.19
\][/tex]
