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Answer:
[tex]y = 1.4[/tex]
Step-by-step explanation:
Given
[tex]y = width[/tex]
[tex]x = length[/tex]
[tex]y = 3;\ when\ x = 14[/tex]
Required
Find y when x = 30
Being an inverse variation, we have:
[tex]y\ \alpha\ \frac{1}{x}[/tex]
Convert the variation to an equation
[tex]y = \frac{k}{x}[/tex]
First, we solve for k
Make k the subject to solve for k
[tex]k = xy[/tex]
[tex]y = 3;\ when\ x = 14[/tex]
So, the value of k is:
[tex]k = 14 * 3[/tex]
[tex]k = 42[/tex]
To solve for y when x = 30
Substitute 30 for x and 42 for k in [tex]k = xy[/tex]
[tex]42 = 30 * y[/tex]
Make y the subject
[tex]y = \frac{42}{30}[/tex]
[tex]y = 1.4[/tex]
The width of the rectangle would be as follows:
[tex]1.4[/tex] inches
Inverse proportion occurs when one value increases and the other decreases.
The width, [tex]y[/tex], of a rectangle with a fixed area varies inversely with its length, [tex]x[/tex].
So, [tex]y=\frac{k}{x}[/tex] where [tex]k[/tex] is the constant.
The width is [tex]3[/tex] inches when the length is [tex]14[/tex] inches.
So,
[tex]3=\frac{k}{14} \\k=42y=\frac{42}{x}\\Put x=30[/tex]
Therefore, [tex]y=\frac{42}{30}=1.4[/tex] inches
Thus, Width is [tex]\boldsymbol{1.4}[/tex] inches when the length is [tex]30[/tex] inches.
Find out more information about inverse proportion here: https://brainly.com/question/2548537