Yis inversely proportional to the square of x.
a table of values for x and y is shown.

a) express y in terms of x.
b) work out the positive value of x when y = 25

To find the value of and we have to find the proportionality constant. The y in terms of x is and positive value of .

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.

Then,

Therefore, y in terms of x is .

(b) we have an expression of

Putting the value of , we get:

Therefore, the positive value of .

Learn more about Proportion and ratio here:

link

Step-by-step explanation:

If is inversely propotional to the square of , then the relation would be like

Where 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

Replacing this constant, the expression between variables is

Which is the answer to a).

Now, if the value of would be

Therefore, the answer to b) is

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐