Differential Geometry | Topology Answers

Find the moment of inertia and the radius of gyration for y = 2√x, y = 0, x = 4; about x = 0

Find the centroid of the area bounded by

x² + y² = 25, x + y = 5

Find the centroid of the area bounded by

y² = x³, y = 2x

Find the centroid of the area bounded by

x + 2y = 6, x= 0 y= 0

Find the mass of the solid bounded by z = 1 and , z = x² + y² the density function

being d (x, y, z) = | x |

Find the centre of gravity of a thin sheet with density d(x, y) = y, bounded by the

curves y = 4x² and x = 4.

A particle moves so that its position vector ˜r at time t is = ˜r ˜a coswt +˜bsinwt, where w is a constant and ˜a and ˜b are constant vectors. Show that (a) ˜ ˜ r × r˙ is independent of t, ˜

Differentiate with respect to the variable 

y=x³ - x² + x + 5. dy/dx

y=x³ + 7x² - 4x + 8 dy/dx

s=17t³ - 5t² - 5t - 3 ds/dt

y= x^3 - x^2 + x + 5, find  dy/dx.

y=4x^3 + 7x^2 - 4x + 8, find  dy/dx.

s=17t^3 - 5t^2 - 5t - 3, find  ds/dt.

Let a(s) = (x(s), y(s), 0) be a unit speed curve. Prove that

K = |x'y" – x''y'l.