A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water flows in at a constant rate k and is lost through evaporation at a rate proportional to the surface area. (a) Find the differential equation satisfied by the volume V(t) of water in the pond at time t. (Use a for the coefficient of evaporation.) O dv = k - an dt = k + ax v -m(第)i = k - az(vt O dv dt AP O dt - CT AP O

Q: 1 dt. 1+ vt Let G(x) Find G'(9).

A: Given that: G(x) = ∫2x211+tdt

Q: The flow system shown in the figure is activated at time t== 0. Let Q.(t) denote the amount of…

A: As this problem is related to differential equation, hope you know how to find inverse of a matrix,…

Q: nd ifzxy+In(x) . x-r-I and y=e dt

A:

Q: find dy/dt. y = (esin (t/2))3

A:

Q: A particle is moving along a straight line. At time t seconds it's displacement , x meter from a…

A:

Q: Solve: ds/dt = t In s?t + 8t2.

A: Solution

Q: A tank initially contains 60 litres of pure water. Brine containing 2 gm of salt per litre is…

A: Using the given data.

Q: A tank contains 200 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A:

Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…

Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

A:

Q: The velocity dx/dt of a chemical reaction is proportional to (a-x), where x is the amount…

A: Solution :-

Q: (4) Suppose the acceleration of an object is given by a(t) = t m/s. Its initial velocity is v(0) = 5…

A:

Q: dT +kT =200k, where k is a constant. dt Solve A. T=ce" + 200 B.T= ce–200 C. T=ce +200 D. T= ce"+200e…

A: See the detailed solution below.

Q: Find a solution to dA/dt=5A If A(0) =4. A(t)=?

A: Given that  dA/dt=5A If A(0) =4. To find A(t)

Q: Ex.: Solve dx dy 2=t.... dt dt dx dy -+2 +2-y=0... y = 0.. dt dt

A: