24. DısCHARGING Water FROM A TANK A container that has a constant cross section A is filled with water to height H. (See the accompanying figure.) The water is discharged through an opening of cross section B at the base of the container. By using Torricelli's Law, it can be shown that the height h of the water at time t satisfies the initial- value problem dh B / 2gh A h(0) = H dt a. Find an expression for h. b. Find the time T it takes for the tank to empty. c. Find T if A = 4 (ft²), B = 1 (in.²), H = 16 (ft), and t = 32 (ft/sec²). A ft H ft B in.?

Q: A point moves along the curve y = √x in such a way that the y-component of the position of the point…

A:

Q: Y = KN 1 + N² where k is a positive constant. What nitrogen level gives the best yield? 3. The…

A:

Q: C/G An 8 lb weight stretches a spring 1.5 inches. It is attached to a dashpot with damping constant…

A:

Q: d'u =16- for all 0sxs10 and t20

A: Solution

Q: where and dt=2' y(0) = 1, y(0.1) = 1.01, y(0.2) = 1.022 (03)

A:

Q: d. To simplify calculations, a student uses a tangent line approximation to P(t) at 1=0 as a model…

A: (d)

Q: 1 A population of giant tortoises is modelled by the delay differential dN (t)=bN(t-T)-c[N(t-T)]² -…

A: Given:A population of giant tortoises is modelled by the delay differential  where and are…

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: A tank holds 2000 liters of water in which 400 grams of salt have been dissolved. Saltwater with a…

A:

Q: Determine the value of v that minimizes E.

A: Given that the problem is : Differentiating the E(V) :

Q: A model for the populations of two interacting species of animals is dx = k₁x(α - x) dt k2xy. dy dt…

A:

Q: 1. A 64 lb object stretches a spring 4 ft in equilibrium. It is attached to a dashpot with damping…

A:

Q: Over the first two years, at what time t is the amount of honey in the hive the most? What is this…

A: Maxima and minima of a real-valued function is a very important application of differentiation. At…

Q: This exercise is bout section 4.7 The rate (in mg carbon/m /h ) at which photosynthesis takes place…

A:

Q: 25. Kinetic energy If a variable force of magnitude F(x) moves an object of mass m along the x-axis…

A:

Q: Use the method of variation of parameters to find the general solution of each of the following…

A: This question is about ordinary differential equation.

Q: y=-sinx . 3π X 2 元 2. 2 N/2

A: Given: y=-sinx

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.