The solution of `(d v)/(dt)+k/m v=-g` is

If the solution of the equation (d^(2)x)/(dt^(2))+4(dx)/(dt)+3x = 0 given that for t = 0, x = 0 and (dx)/(dt) = 12 is in the form x = Ae^(-3t) + Be^(-t) , then

18 % ( w/V) solution of urea ( Mol mass = 60) is

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 constants. If v and x are both initially zero, find v in terms of x.

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)

The frequency of oscillations of a mass m suspended by spring is v_(1) . If the length of the spring is cut to one- third, the same mass oscillates with frequency v_(2) . Determine the value of (v_(2))/(v_(1)) .

A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)],V=[(a^2),(0),(0)] If there is a vector matrix X, such that AX = U has infinitely many solutions, then prove that BX = V cannot have a unique solution. If a f d != 0 . Then,prove that BX = V has no solution.

Let u-=a x+b y+a b3=0,v-=b x-a y+b a3=0,a ,b in R , be two straight lines. The equations of the bisectors of the angle formed by k_1u-k_2v=0 and k_1u+k_2v=0 , for nonzero and real k_1 and k_2 are u=0 (b) k_2u+k_1v=0 k_2u-k_1v=0 (d) v=0