" (ii) "quad alpha(nu)=3y^(3)-4y+sqrt(11)" at "y=2

Find the value of each of the following polynomials at the indicated value of variables : q(y) = 3y^(3) - 4y + sqrt(11) at y = 2.

Find the value of the following polynomials at the indicated value of variables: q(y) = 3y^3- 4y +sqrt11 at y = 2.

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (A) sqrt(3)x^2 + sqrt(3)y^2 - 4x +4 sqrt(3)y = 0 (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

If tan alpha=(x)/(y) , then show that x "cosec" (alpha)/(3)- y "sec" (alpha)/(3)=3 sqrt(x^(2)+y^(2))(0 lt alpha lt (pi)/(2))

If (x^3+y^3) alpha(x^3-y^3) prove that (x^2+y^2) alpha(x^2-y^2) .

An equilateral triangle whose two vertices are (-2, 0) and (2, 0) and which lies in the first and second quadrants only is circumscribed by a circle whose equation is : (B) sqrt(3)x^2 + sqrt(3)y^2 - 4x - 4 sqrt(3)y = 0 (C) sqrt(3)x^2 + sqrt(3)y^2 - 4y + 4 sqrt(3)y = 0 (D) sqrt(3)x^2 + sqrt(3)y^2 - 4y - 4 sqrt(3) = 0

On the ellipse 2x^(2)+3y^(2)=1 the points at which the tangent is parallel to 4x=3y+4 are ( i )((2)/(sqrt(11)),(1)/(sqrt(11))) or (-(2)/(sqrt(11)),-(1)/(sqrt(11))) (ii) (-(2)/(sqrt(11)),(1)/(sqrt(11))) or ((2)/(sqrt(11)),-(1)/(sqrt(11))) (iii) (-(2)/(5),-(1)/(5)) (iv) ((3)/(5),(2)/(5)) or (-(3)/(5),-(2)/(5))

If alpha=tan^(-1)((sqrt(3)x)/(2y-x)),beta=tan^(-1)((2x-y)/(sqrt(3y)))" then "alpha-beta=