Related questions with answers

A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to minimize the combined area of the circle and the square?

Calculate $\frac{d y}{d x}$ . You need not expand your answers. $y=\frac{\sqrt{x}+1}{\sqrt{x}-1}$

A fluid with a density of 2000 kg/m $^{3}$ flows steadily between two flat plates. The bottom plate is fixed and the top one moves at a constant speed in the x direction. The velocity is $\mathrm{V=0.20 y \hat{i} m / s}$ where y is in meters. The acceleration of gravity is $\mathrm{g}=-9.8 \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}^{2}$ . The only nonzero shear stresses, $\tau_{y x}=\tau_{x y}$ , are constant throughout the flow with a value of 5 N/m $^{2}$ . The normal stress at the origin (x = y = 0) is s $\sigma_{x x}=-100 \mathrm{kPa}$ . Use the x and y components of the equations of motion to determine the normal stress throughout the fluid. Assume that $\sigma_{x x}=\sigma_{y y}$ .