Verify that (A^-1)^T = (A^T)^-1 for A =\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

Find the locus of z if |3z - 5| = 3 |z + 1| where z = x + iy.

Solve: 2x+2^x-1+2^x-2 = 7x+7^x-1+7^x-2

Evaluate \(cos\left[ { cos }^{ -1 }\left( \frac { -\sqrt { 3 } }{ 2 } +\frac { \pi }{ 6 } \right) \right] \)

Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

If \(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } =0\) then show that \(\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } =\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } =\overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \)

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lies in the plane containing \(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \)

A cylindrical hole 4 mm in diameter and 12 mm deep in a metal block is reboared to increase the diameter to 4.12mm. Estimate the amount of metal removed

Find two numbers whose sum is 100 and whose product is a maximum.

If w = xy + z where x = cos t; y = sin t; z = t find \(\frac{dw}{dt}\)

If w=xy+z and x=cot, y=sint, z=t then find \(\frac { dw }{ dt } \)

Evaluate \(\int _{ 3 }^{ 6 }{ \frac { \sqrt { x } }{ \sqrt { 9 } -x+\sqrt { x } } dx } \)

Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 0 }xdx } \)

Form the D.E of the family of curves c(y + c)² = x², where c is the parameter.

Solve :(x²-yx²)dy+(y²+x²y²)dx=0