Show that the conical tent of given capacity will require the least amount of canvas if its height is √2 times its base radius.
Let the base radius of the conical tent be \( r \) and its height be \( h \). Given that \( h = \sqrt{2} r \), we need to minimize the canvas required, which corresponds to the lateral surface area.
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, and
find vector
such that
and
Find 'c' of Cauchy's mean value theorem for the function f(x) = 2.ln(x) and g(x) = x²-1 in the interval [2,3].
Given a point on the axis of the parabola y² = 2px at a distance a from the vertex, find the abscissa of the point of the curve closest to it.
If A is a square matrix, such that A² =A, then find (I + A)³ - 7A.
Prove that
is independent of a, b, c.
Find and
for the function x² sin(y³)+xe3z-cos(z²)=3y-6z+8