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$3. Fill in the blanks(i) The simplest form of the ratio \frac{(x+y)\left(x^{2}+x y+y^{2}\right)}{x^{3}-y^{3}} is(ii) In a ratio x: y ; x is called(iii) In a ratio a: b ; b is called(iv) In a proportion a: b:: x: y ; a and y are called(v) In a proportion p: q:: m: n ; q and m are called(vi) In proportion 7: 4:: p: 8 p= (vii) If 6: m: 0: 9: 12 then m= (viii) If x and y varies directly then x= (ix) If v varies directly as u^{3} then u^{3}= (x) If w varies inversely as p^{2} then k= (xi) A third proportional of 12 and 4 is(xii) The fourth proportional of 1565 is(xiii) The mean proportional of 4 m^{2} n^{4} and p^{6} is(xiv) The continued proportion of 4 m and 9 is$

$(iv) In a proportion a: b:: c: d b and c are called(a) means(b) extremes(c) fourth proportional(d) None of these$

$Example 1: If y varies jointly as x^{2} and z and y=6 when x=4 z=9 . Write y as a function of x and z and determine the value of y when x=-8 and z=12 .$

$10. Complete the following:(iii) If \frac{9 p q}{2 l m}=\frac{18 p}{5 m} then 5 q=$

$3. If y varies directly as x^{3} and inversely as z^{2} and t and y \doteq 16 when x=4 z=2 t=3 . Find the value of y when x=2 z=3 and t=4 .$

$4. Find the value of p if the ratios 2 p+5: 3 p+4 and 3: 4 are equal.$

$8. If y \propto \frac{1}{x} and y=4 when x=3 find x when y=24 .$