Answer:
Step-by-step explanation:
If [tex]y[/tex] is inversely propotional to the square of [tex]x[/tex], then the relation would be like
[tex]y=\frac{K}{x^{2} }[/tex]
Where [tex]K[/tex] is the constant of propotionality.
Now, we need to use a pair from the table to find the constant of proportionality, we are gonna use [tex](1,4)[/tex]
[tex]y=\frac{K}{x^{2} }\\4=\frac{K}{(1)^{2} } \\K=4[/tex]
Replacing this constant, the expression between variables is
[tex]y=\frac{4}{x^{2} }[/tex]
Which is the answer to a).
Now, if [tex]y=25[/tex] the value of [tex]x[/tex] would be
[tex]y=\frac{4}{x^{2} }\\25=\frac{4}{x^{2} }\\x^{2} =\frac{4}{25}\\ x=\sqrt{\frac{4}{25} }\\ x=\frac{2}{5}[/tex]
Therefore, the answer to b) is [tex]x=\frac{2}{5}[/tex]
To find the value of [tex]x[/tex] and [tex]y[/tex] we have to find the proportionality constant. The y in terms of x is [tex]y=\frac{2}{\sqrt{x}}[/tex] and positive value of [tex]x=\frac{2}{5}[/tex].
Given:
From the given problem y is inversely proportional to the square of x.
A table of values for x and y is shown.
From the table:
(a) As we know that, y is inversely proportional to the square of x,
Here k is proportionality constant.
[tex]y\propto\frac{1}{\sqrt{x}}[/tex]
Then, [tex]1\times \sqrt4 =2\times \sqrt{1}=2=k[/tex]
Therefore, y in terms of x is [tex]y=\frac{2}{\sqrt{x}}[/tex].
(b) we have an expression of [tex]y=\frac{2}{\sqrt{x}}[/tex]
Putting the value of [tex]y=25[/tex], we get:
[tex]25=\frac{4}{{x^2}}\\x^2=\frac{4}{25}\\\\x=\sqrt{\frac{4}{25}}\\x=\frac{2}{5}[/tex]
Therefore, the positive value of [tex]x=\frac{2}{5}[/tex].
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