A ladder 5 m in length is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of $2 \mathrm{~m} / \mathrm{sec}$. How fast is the height on the wall decreasing when the foot of the ladder is 4 m away from the wall?

If the equation $\cos ^4 \theta+\sin ^4 \theta+\lambda=0$ has real solutions for $\theta$, then $\lambda$ lies in the interval

The equation of the tangent to the parabola $y^2=8 x$, which is parallel to the line $4 x-y+3=0$ is

The centroid of tetrahedron with vertices $\mathrm{P}(5,-7,0), \mathrm{Q}(\mathrm{a}, 5,3), \mathrm{R}(4,-6, b)$ and $\mathrm{S}(6, \mathrm{c}, 2)$ is $(4,-3,2)$, then the value of $2 a+3 b+c$ is equal to