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Solve for [tex]\( k \)[/tex], the constant of variation, in an inverse variation problem, where [tex]\( x = 3.3 \)[/tex] and [tex]\( y = 24 \)[/tex].

A. [tex]\( k = 79.2 \)[/tex]

B. [tex]\( k = 7.3 \)[/tex]

C. [tex]\( k = 20.7 \)[/tex]

D. [tex]\( k = 0.14 \)[/tex]

Sagot :

GinnyAnsweridn
To determine the constant of variation [tex]\( k \)[/tex] in an inverse variation problem, where [tex]\( y \)[/tex] varies inversely with [tex]\( x \)[/tex], you can use the relationship:

[tex]\[ y = \frac{k}{x} \][/tex]

Given:

[tex]\[ x = 3.3 \][/tex]
[tex]\[ y = 24 \][/tex]

we need to solve for [tex]\( k \)[/tex].

1. Start with the relationship for inverse variation:

[tex]\[ y = \frac{k}{x} \][/tex]

2. Substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] into the equation:

[tex]\[ 24 = \frac{k}{3.3} \][/tex]

3. Solve for [tex]\( k \)[/tex] by multiplying both sides by [tex]\( 3.3 \)[/tex]:

[tex]\[ k = 24 \times 3.3 \][/tex]

4. Perform the multiplication:

[tex]\[ k = 79.2 \][/tex]

Thus, the correct value for the constant of variation [tex]\( k \)[/tex] is:

[tex]\[ k = 79.2 \][/tex]

So, the correct option is:
[tex]\[ k = 79.2 \][/tex]
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