If r varies directly as p and inversely as q2, and r = 27 when p =3 and q = 2, find r when p = 2 and q= 3
k = r =

k = 36 and r = 8

Step-by-step explanation:

Given that r varies directly as p and inversely as q² then the equation relating them is

r = ← k is the constant of variation

To find k use the condition r = 27 when p  3 and q = 2, thus

27 = ( multiply both sides by 4 )

108 = 3k ( divide both sides by 3 )

k = 36

r = ← equation of variation

When p = 2 and q = 3, then

r = = = 8

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11