The velocity v of a parachute falling vertically satisfies the equation `v(dv)/(dx)=g(1-v^2/k^2)`, where g and k are positive constants, if both v and x are zero initially, find v in terms of x.

In the figure, a vectors x satisfies the equation x-w=v. then, x is equal to

The functions u=e^(x).sinx and v=e^(x).cosx satisfy the equation

Show that int_(0)^(npi+v)|sinx|dx=2n+1-cosv , where n is a positive integer and 0levltpi .

Evaluate : int(x^2-1)/(x^4+kx^2+1)dx , where k is any constant.

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation (d V(t))/(dt) =-k(T-t) , where k"">""0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is : (1) T^2-1/k (2) I-(k T^2)/2 (3) I-(k(T-t)^2)/2 (4) e^(-k T)

For the equation P prop m^(x).v^(y) where P is momentum, m is mass and v velocity. Then the value of x and y are

In van der Waal's equation : (P+ (a)/(V^(2)))(V-b)= RT what are the dimensions of constant 'a' and 'b' ?

Check the correctness of the physical relation: v= sqrt((2GM)/(R)) , where v is velocity, G is gavitational constant, M is mass and R is radius of the earth.