supposed that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the radius of the drop increases at a constant rate. dv/dt=1 the radius increases at a constant rate because the equation simplifies to dr/dt= ____, a constant  K x S S+k S-k

Q: A 20-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3…

A:

Q: 4. A rock thrown vertically upward from the surface of the moon reaches a height of h = 8t – 0.8t2…

A:

Q: 1. A spherical balloon is being filled with helium such that its radius is changing at a constant…

A: Given,            A spherical balloon is filled with helium gas and radius is increasing with rate…

Q: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then…

A:

Q: :-In an oil refinery, a storage tank contains 200 gal of gasoline that initially has 100 Ib of an…

A:

Q: A bug is moving along the right side of the parabola y=x at a rate such that its distance from the…

A: see the calculation below

Q: In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to…

A: Given, M denotes total amount of subject to be memorized A(t) denotes amount memorized in time t…

Q: Professor Mike starts an experiment using bacteria with a population of n. It is found that the rate…

A: We will solv

Q: 39. The conical watering pail in Figure 17 has a grid of holes. Water flows out through the holes at…

A:

Q: dx kx, x(t,)=x, dt where k is a constant of proportionality, serves as a model for diverse phenomena…

A: Topic:- function

Q: A radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t)…

A: We are given the differential equation (rate of disintegration) . First  we will find the equation…

Q: d) A population of size x is decreasing according to the law dx -x dt 250 where t denotes the time…

A: The solution is given as

Q: Consider the ideal gas law PV = kT, where k > 0 is a constant. av a.) Determine the rate of change…

A:

Q: 10. If an initially resting object is accelerating with a constant power, then its acceleration a(t)…

A:

Q: A tank contains 1 kilogram of salt dissolved in 100 liters of water. A salt solution of 0.1 kg…

A:

Q: 39. A population P, grows at the rate P'(t) = 5(t +1) In /t +1 %3D thousand individuals per year at…

A:

Q: b) A population of size x is decreasing according to the law dx -x dt 250 where t denotes the time…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A population of insects increases at a rate 290 + 10t + 0.3t² insects per day (t in days). Find the…

A:

Q: a. What is the constant rate of change of y with respect to x? 1.5 Preview b. Write a formula that…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then…

A:

Q: 03/ The dimensions of a rectangular solid at a given instant (t.) are : L(t) 13 cm. W(t)-9 cm. H(t.)…

A: Given problem:- The dimensions of a rectangular solid at a given instant (t0) are: L(t )=13 cm.…

Q: A 50-gal barrel is filled completely with pure water. Saltwater with a concentration of 0.3 lb/gal…

A: Given function is, Qt=151-e-0.04t.....(1) To determine the amount of salt in the barrel after 5…

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in…

A:

Q: An object travels in a straight line with velocity v(t) = 6 − 3t over the timeinterval [0, 5]. Find…

A: We first find the t intercept of v(t)=6-3t  for that, we plug v(t)=0 and solve for t For t<2 ,…

Q: A single flu infected individual enters a community of n susceptible individuals. Let x be the…

A: Solve the following

Q: =) A cup of water with a temperature of 90°C is placed in a room with a constan temperature of 24°…

A: given T=90oC , To=24oC, dT=90-55=35oC , dT=15 min, dTdt=k(T-To)3515=k(90-24)73=66kk=73×66=7198k=7198…

Q: dx • A population is modeled by the equation dt ka (a – x), %3D where a and k are positive…

A: The given D.E. is dxdt=kxa−x.

Q: A population grows at a rate P'(t) = 500te-0.2t P(t) is the population after t months. What is the…

A: To find the average growth rate  of the first 6 months we need to find  16-0∫06P'(t)dt=16∫06P'(t)dt…

Q: Please show all work

A:

Q: Consider the problem of draining a hemispherical tank of radius H* feet that is full of water and…

A:

Q: Laboratory department detects the concentration C of impurity of an oil purifier changes b + dm - Cm…

A: Given - Laboratory department detects the concentration C of impurity of an oil purifier changes…

Q: The population function N(t) of a speci (in thousands) follows the differential dN = N(700 – N)(N –…

A:

Q: The figure shows an 11-foot ladder leaning against a wall. (a) Use the Pythagorean theorem to find…

A: Answer

Q: Vx. As the particle passes through the point (4, 2), its x-coordinate increases at a rate of A…

A:

Q: d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A:

Q: ! d. Suppose that the cylindrical tank in the accompanying figure is filled to a depth of 4 feet at…

A:

Q: The growth of malignant tumors can be modeled using the Gompertz model. dP dt r.P. where r>0 is the…

A: *answer:

Q: The rate at which the remainder of a substance dissolves in a small quantity of water is inversely…

A: The linear differential equations can be solved by separation of variables. The variables are…

Q: 6- The dimension of a solid rectangular at given instant ( to ) are (L = 13 cm) ,(W = 9 cm ) and ( H…

A:

Q: n a culture of yeast the rate of growth dy/dt is proportional to its population present at any time…

A:

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a…

A:

Q: Laboratory department detects the concentration C of impurity of an oil purifier changes with time t…

A: Integrating factor: The integrating factor of linear differential equation dydx + Py = Q is e∫P dx.…

Q: A population grows at a rate P'(t) = 500te-0.2t P(t) is the population after t months. What is the…

A: Population growth at a rate P’(t) = 500te-0.2t2 Where P(t) is the population after t months Evaluate…

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that…

A: Given function, B(t)=3.1+0.25 sin 2πt5.3

Q: 1. A population of insects at a rate of 200 +10t +0.25t² insects per day (t in days). Find the…

A:

Q: A Sliding Ladder A 25 ft ladder leaning against a wall begins to slide. How fast is the top of the…

A: This question is based on application of derivative.

Q: What is the rate equation for Newton's Law of Cooling? T is the temperature of the body and Tm is…

A:

Q: A tank contains 240 liters of fluid in which 30 grams of salt is dissolved. Pure water is then…

A: We have to find the rate at which the number of grams of salt in the tank is changing at time t and…

Q: (iii) The volume of air, V mL , in a spherical balloon at time t seconds, is decreasing dV at a rate…

A:

Q: A culture initially has Po number of bacteria. At t = 2hour the number of bacteria is measured to be…

A:

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.