Answer :
Sure! Let's solve this question step-by-step.
1. Understanding the Problem: We're told that [tex]\( f \)[/tex] varies inversely as [tex]\( g \)[/tex]. This means as one increases, the other decreases. Mathematically, this relationship can be expressed as [tex]\( f \times g = k \)[/tex], where [tex]\( k \)[/tex] is a constant.
2. Finding the Constant [tex]\( k \)[/tex]: We're given that [tex]\( f = 7 \)[/tex] when [tex]\( g = 56 \)[/tex]. Substituting these values into the inverse variation formula:
[tex]\[
7 \times 56 = k
\][/tex]
Multiplying these gives:
[tex]\[
k = 392
\][/tex]
3. Finding the New Value of [tex]\( g \)[/tex] when [tex]\( f = 8 \)[/tex]: We need to find [tex]\( g \)[/tex] when the new value of [tex]\( f \)[/tex] is 8. Using the constant [tex]\( k \)[/tex] we found, the equation becomes:
[tex]\[
8 \times g = 392
\][/tex]
To find [tex]\( g \)[/tex], we divide both sides by 8:
[tex]\[
g = \frac{392}{8}
\][/tex]
Dividing gives:
[tex]\[
g = 49
\][/tex]
4. Conclusion: Therefore, the value of [tex]\( g \)[/tex] when [tex]\( f = 8 \)[/tex] is 49.
The correct answer is B. 49.
1. Understanding the Problem: We're told that [tex]\( f \)[/tex] varies inversely as [tex]\( g \)[/tex]. This means as one increases, the other decreases. Mathematically, this relationship can be expressed as [tex]\( f \times g = k \)[/tex], where [tex]\( k \)[/tex] is a constant.
2. Finding the Constant [tex]\( k \)[/tex]: We're given that [tex]\( f = 7 \)[/tex] when [tex]\( g = 56 \)[/tex]. Substituting these values into the inverse variation formula:
[tex]\[
7 \times 56 = k
\][/tex]
Multiplying these gives:
[tex]\[
k = 392
\][/tex]
3. Finding the New Value of [tex]\( g \)[/tex] when [tex]\( f = 8 \)[/tex]: We need to find [tex]\( g \)[/tex] when the new value of [tex]\( f \)[/tex] is 8. Using the constant [tex]\( k \)[/tex] we found, the equation becomes:
[tex]\[
8 \times g = 392
\][/tex]
To find [tex]\( g \)[/tex], we divide both sides by 8:
[tex]\[
g = \frac{392}{8}
\][/tex]
Dividing gives:
[tex]\[
g = 49
\][/tex]
4. Conclusion: Therefore, the value of [tex]\( g \)[/tex] when [tex]\( f = 8 \)[/tex] is 49.
The correct answer is B. 49.
