Find answers to your questions and expand your knowledge with IDNLearn.com. Get the information you need from our community of experts who provide accurate and thorough answers to all your questions.

2. If [tex]$x$[/tex] is inversely proportional to [tex]$y$[/tex], and [tex]$x = 60$[/tex] when [tex]$y = 0.5$[/tex], find [tex]$x$[/tex] when [tex]$y = 12$[/tex].

A. 0.4
B. 2.5
C. 25
D. 360


Sagot :

To solve this problem, we need to use the concept of inverse proportionality. When two quantities are inversely proportional to each other, their product is always a constant. Mathematically, if [tex]\(x\)[/tex] is inversely proportional to [tex]\(y\)[/tex], then [tex]\(x \cdot y = k\)[/tex], where [tex]\(k\)[/tex] is a constant.

Given the problem:
- [tex]\( x = 60 \)[/tex] when [tex]\( y = 0.5 \)[/tex].

Let's first find the constant [tex]\( k \)[/tex]:

[tex]\[ k = x \cdot y = 60 \cdot 0.5 = 30 \][/tex]

Now, we need to find [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex]. According to the inverse proportionality:

[tex]\[ x \cdot y = k \][/tex]

Substituting the known values:

[tex]\[ x \cdot 12 = 30 \][/tex]

Solving for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{30}{12} \][/tex]
[tex]\[ x = 2.5 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 12 \)[/tex] is:

[tex]\[ \boxed{2.5} \][/tex]