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Given that [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex]:

a) Work out an equation connecting [tex]\( y \)[/tex] and [tex]\( x \)[/tex] when [tex]\( y = 7 \)[/tex] and [tex]\( x = 9 \)[/tex].

b) Work out the value of [tex]\( y \)[/tex] when [tex]\( x = 21 \)[/tex].

Sagot :

GinnyAnswer
Let's solve the problem step-by-step.

### Part (a) - Work out an equation connecting [tex]\( y \)[/tex] and [tex]\( x \)[/tex]

Since [tex]\( y \)[/tex] is inversely proportional to [tex]\( x \)[/tex], we can express their relationship using the equation:
[tex]\[ y = \frac{k}{x} \][/tex]
where [tex]\( k \)[/tex] is a constant of proportionality.

We are given the values [tex]\( y = 7 \)[/tex] and [tex]\( x = 9 \)[/tex]. We can use these values to find the constant [tex]\( k \)[/tex].

Plugging the given values into the equation:
[tex]\[ 7 = \frac{k}{9} \][/tex]

To find [tex]\( k \)[/tex], we multiply both sides of the equation by [tex]\( 9 \)[/tex]:
[tex]\[ k = 7 \times 9 = 63 \][/tex]

So, the equation connecting [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:
[tex]\[ y = \frac{63}{x} \][/tex]

### Part (b) - Work out the value of [tex]\( y \)[/tex] when [tex]\( x = 21 \)[/tex]

Now we need to find the value of [tex]\( y \)[/tex] for [tex]\( x = 21 \)[/tex] using the equation we derived in part (a):
[tex]\[ y = \frac{63}{x} \][/tex]

Substituting [tex]\( x = 21 \)[/tex]:
[tex]\[ y = \frac{63}{21} \][/tex]

Simplifying the right-hand side:
[tex]\[ y = 3 \][/tex]

So, the value of [tex]\( y \)[/tex] when [tex]\( x = 21 \)[/tex] is:
[tex]\[ y = 3 \][/tex]

### Summary
1. The equation connecting [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is [tex]\( y = \frac{63}{x} \)[/tex].
2. When [tex]\( x = 21 \)[/tex], [tex]\( y \)[/tex] is [tex]\( 3 \)[/tex].
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