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Suppose [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex] and [tex]\( y = 35 \)[/tex] when [tex]\( x = 14 \)[/tex].

a) Find the equation that relates [tex]\( y \)[/tex] and [tex]\( x \)[/tex].

b) What is [tex]\( y \)[/tex] when [tex]\( x = 29 \)[/tex]?

Sagot :

GinnyAnsweridn
Sure! Let's solve this step-by-step.

### Step a) Find the equation that relates [tex]\( y \)[/tex] and [tex]\( x \)[/tex].

Since [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], it can be expressed in the form:

[tex]\[ y = kx \][/tex]

where [tex]\( k \)[/tex] is the constant of variation. To find [tex]\( k \)[/tex], we use the given values [tex]\( y = 35 \)[/tex] when [tex]\( x = 14 \)[/tex]:

[tex]\[ 35 = k \cdot 14 \][/tex]

Now, solve for [tex]\( k \)[/tex]:

[tex]\[ k = \frac{35}{14} \][/tex]

[tex]\[ k = 2.5 \][/tex]

So, the equation that relates [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:

[tex]\[ y = 2.5x \][/tex]

### Step b) What is [tex]\( y \)[/tex] when [tex]\( x = 29 \)[/tex]?

Using the equation [tex]\( y = 2.5x \)[/tex]:

[tex]\[ y = 2.5 \cdot 29 \][/tex]

[tex]\[ y = 72.5 \][/tex]

Therefore, when [tex]\( x = 29 \)[/tex], [tex]\( y \)[/tex] is:

[tex]\[ y = 72.5 \][/tex]
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