If the normal drawn at the point $P$ on the curve $y^2=x^3-x+1$ makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the curve at $P$ is

If a balloon lying at an altitude of 30 m from an observed at a particular instant is moving horizontally. At the rate of $1 \mathrm{~m} / \mathrm{s}$ away from him, then the rate at which the balloon is moving away directly from the observer at the 40 th second is (in m/s) .

The approximate value of $\sqrt{6560}$ is

The radius of a cone of height 9 units is changed from 2 units to 2.12 units. The exact change and approximate change in the volume of the cone are respectively