8 math

Determine whether the system Ax - 2y + 6z = 8, 2x - + 3z = 5, 2 jc - y + 3z =4 is consistent. Sol. The given equations are 4 jc -2 y + 6z = 8 ...(1) 2x ~y + 3z = 5 ...(2) 2x - y + 3z = 4 ...(3) ..

.htm#bookmark33">Jo a Jo a putting x = a sin 0 so that dx = a cos 8 dQ = ba\} cos 2 9 dQ = abfi = Jo I ' Jo 2 2 L 2 J 0 2, 2 ; . . _ square units. Area of the elli..

Evaluate: ! f _ dx 2 f dx __ 3 f dx 1 9x 2 - tlx + 8 *3-2x-x 2 ' j 2 x 2 + x-1 4. r_ *L 5. f' * 3 + 2x + x 2 Joi-jc + x 2 ..

%2028.htm#bookmark78"> a * ft, ft * c and c x are also non-coplanar. - if! * uh - ' > . r, > ,-' kf Sol. Let ft x c = d then (b x c)x (c x a) - d x (c x a) = (i/- a) c ^(rf- c)a =[(b x c)-a] c -[(ft x c)-c]a > > > > -> ^ -> ->->- = [ft c a | c -1 b c c | a = [ft c a] c..

Prove that the following functions do not have maxima or minima. (i)/ (ii) log j: (iii) jc + 2 (iv) x 3 + jc 2 + jc +1. Sol. (0 Lety=e*. => ..

Assume that a spherical rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop. (LLT. 1997) Sol. Let r denote the rad..

Ifa + ft + c= 0, show that the angle 0 between the vectors b and c is given by - - -> 2 .2 2 a _ & _ c cos 8 =-. _ * 2\~b\\c\ - - -> _ -> > Sol. 7 a + ft + c = 0, a =-(6 + c). Nowa = a . a = [- (ft + c)]. [- (ft + c..

A (-1,0) and B (2,0) are two given points. A points/is moving in such a way that the angle B in the triangle AMB remains twice as large as the angle/4. Show that the locus of the point M is a hyperbola. Find the eccentricity of the hyperbola. (I.S.C. 1992) ..

Differentiate with respect tox. - 1. (0 (//) 6x 8 . (iii) x m (iv) t: J (v) Sx' VA L . (vi) V? , ' (Vit) 2 (viii) 4" ' ..

Perimeter of a polygon: P= N x S N= No of sides S= Length of the side. Perimeter of a triangle: P= a+b+c a,b,c are the side..