Answer :
Certainly! Let's work through this step-by-step:
a) We are told that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex]. This means the relationship can be described by the equation:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is a constant. To find the value of [tex]\( k \)[/tex], we use the information given: when [tex]\( y = 6 \)[/tex], [tex]\( x = 8 \)[/tex].
Substitute these values into the equation:
[tex]\[ 6 = \frac{k}{8} \][/tex]
To solve for [tex]\( k \)[/tex], multiply both sides of the equation by 8:
[tex]\[ k = 6 \times 8 \][/tex]
[tex]\[ k = 48 \][/tex]
So the equation connecting [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:
[tex]\[ y = \frac{48}{x} \][/tex]
b) To find the value of [tex]\( y \)[/tex] when [tex]\( x = 12 \)[/tex], use the equation we found:
[tex]\[ y = \frac{48}{x} \][/tex]
Substitute [tex]\( x = 12 \)[/tex] into the equation:
[tex]\[ y = \frac{48}{12} \][/tex]
[tex]\[ y = 4 \][/tex]
So, when [tex]\( x = 12 \)[/tex], the value of [tex]\( y \)[/tex] is 4.
a) We are told that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex]. This means the relationship can be described by the equation:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is a constant. To find the value of [tex]\( k \)[/tex], we use the information given: when [tex]\( y = 6 \)[/tex], [tex]\( x = 8 \)[/tex].
Substitute these values into the equation:
[tex]\[ 6 = \frac{k}{8} \][/tex]
To solve for [tex]\( k \)[/tex], multiply both sides of the equation by 8:
[tex]\[ k = 6 \times 8 \][/tex]
[tex]\[ k = 48 \][/tex]
So the equation connecting [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:
[tex]\[ y = \frac{48}{x} \][/tex]
b) To find the value of [tex]\( y \)[/tex] when [tex]\( x = 12 \)[/tex], use the equation we found:
[tex]\[ y = \frac{48}{x} \][/tex]
Substitute [tex]\( x = 12 \)[/tex] into the equation:
[tex]\[ y = \frac{48}{12} \][/tex]
[tex]\[ y = 4 \][/tex]
So, when [tex]\( x = 12 \)[/tex], the value of [tex]\( y \)[/tex] is 4.
