Newton's Law of cooling is described by the differential equation dT := k(T – T,) Suppose an object has an initial temperature of 350 F and that dt after twenty minutes in a room that is 68° F the temperature has lowered to 275° F. Find the temperature of the object at any time t.

Q: How long will it take the voltage to drop to 40 percent of its original value?

A:

Q: At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat…

A: Newton's cooling law ,differential equation for temperature asdTdt=k(T-Ta)

Q: The growth of a new restaurant depends on the number of its regular customers as p'(t) = .05√p(t)…

A: TA differential equation is a equation that connects the derivatives of one or more unknown…

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

A:

Q: A population is modeled by the differential equation dP = 1.005P1- dt P 7500 For what value(s) of P…

A: The Given Differential equation is: dPdt = 1.005P1-P7500

Q: An L-R-C circuit has the following differential equation: (q = charge on capacitor) with q (0) = 1…

A:

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A:

Q: The Pacific halibut fishery has been modeled by the differential equation dt where y(t) Is the…

A: the solution of equation y(t) = M/(1+Ae-kt) where A = (M - y(0))/y(0)            A = (9 * 107 -…

Q: A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has…

A:

Q: Consider the following model for a population that is changing due to births, deaths, immigration,…

A:

Q: When predicting population growth, demographers must consider birth and death rates as well as the…

A:

Q: What differential equation corresponds to an RC circuit with a resistor of R = 100 and a capacitor…

A:

Q: Assume that in the absence of immigration and emigration, the growth of a country's population P(t)…

A: In the absence of immigration and emigration the growth rate of the country is given by dP/dt = kP…

Q: Use exponential shift to find the general solution of the differential equation. (D+1)°y = 0

A:

Q: Find the differential equation of the exponential curve y = A(33x) where A is an arbitrary constant.…

A:

Q: If the rate of change of N is inversely proportional to sec(x)- N where (-<x<). If N(O)=3, and N() =…

A: Note:- These are multiple questions and according to company guideline we can do maximum 1 questions…

Q: A constant-stirred tank reactor (CSTR), initially filled with 20 kg of salt, is diluted with enough…

A: Step:-1 Given that  dSdt =180 s +40 ---(1) and initially the amount of salt = 20 kg that is, S0=20…

Q: Solve the differential equation y' = x¹y subject to the condition that y = e¹ when x = 0. e4 y(x):…

A: The detailed solution is given below Thank you

Q: In a city of a fixed population of "P" people , the rate of change (with respect to timet) of the…

A: Given Data: A city has a fixed population is P. Also given, the rate of change (with respect to…

Q: A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has…

A: Given dMdt=a-k1M  ....(1) a Assume M0=0 To find Mt, integrate the given differential equation…

Q: From the Newton's law of cooling, the cooling rate of a body is proportional to the difference…

A: We will use variable separable method to solve the differential equation.

Q: The differential equation governing the free response of an accelerometer is given as: 4.6 x 10-12 i…

A: Given differential equation, 4.6×10-12x¨+5×10-7x˙+0.4=0 Lets write given equation in second order…

Q: A population of wild horses is represented by the logistic differential equation dP/dt =…

A: Given: The logistic differential equation is, dpdt=0.08p-0.00004p2          (1) To find: A) The…

Q: A vessel with liquid at 18 C is placed in a cooler held at 3 C, and after 3 minutes the temperature…

A: According to the given information, Vessel with liquid at 18C is placed in cooler at 3C After 3…

Q: The rate of change of the weight of a cow is proportional to 1200 W, where time, t, is measured in…

A: We want to find differential equation of W(t).

Q: the rate of change in the value of bills investment in bitcoin obeys the differential equation…

A: We have to find bill invest initially in bitcoin 6 years ago , the rate of change in bill's…

Q: In a liquid culture, the number of bacteria grows at a proportional rate depending on the number of…

A:

Q: The tank in the figure contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

A: Given that, The tank contains 4000 L of water in which initially 50 kg of salt is dissolved. Brine…

Q: Suppose a pendulum with length LL (meters) has angle θθ (radians) from the vertical. It can be shown…

A: NOTE : As per Bartleby rules, only three parts have to be answered. Please upload other parts…

Q: Suppose that the number x(t) (with t in months) of alliga- tors in a swamp satisfies the…

A:

Q: Let y(t) be the size of a colony of bacteria after t hours. Suppose the rate of growth of the colony…

A: We will find out the required solution

Q: A constant-stirred tank reactor (CSTR), initially filled with 20 kg of salt, is diluted with enough…

A: Given:  ds = (180s+40)dt ds = change in the mass of the salt in CSTR,  in kg Given: At t =0 sec,…

Q: A lamb that weighs 10 pounds at birth gains weight at the rate dw = k(200 – w) dt where w is the…

A: Since you find that  w(t) = 120-190e-kt  where, w(t) = weight of lamb in pounds at t years

Q: Suppose a population P(t) satisfies logistic differential equation dP/dt=0.1P(1-(P/2000))…

A: SOLUTION-

Q: The rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where t…

A: Just I have used the proportionality rule and easily find the required differential equation. Last…

Q: Verify that the general solution satisfies the differential equation. Then find the particular…

A:

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

A:

Q: Find the order and degree of the differential equation:

A: Given,                d2ydx2+5dydx4=13sinx

Q: The population of fish in a lake grows logistically according to the differential equation where t…

A: Logistic growth model of fish is given by dydt=0.1y1-y2500                      (1) Initially lake…

Q: The population y(t) of a certain microorganism grows continuously and quadrupling time is found to…

A: In this question, the concept of the derivative is applied. Derivative We can use a derivative to…

Q: Suppose that a large mixing tank initially holds 700 gallons of water in which 50 pounds of salt…

A: Given: A tank containing 700 gallons of water in which 50 pounds of salt is dissolved. Rate at which…

Q: A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has…

A: Consider a first order differential equation isdMdt=a-k1M, where a&gt;0,k1 is the fraction of…

Q: Let f(t) be the balance in a savings account at the end of t years. Suppose that y = f(t) satisfies…

A: Given differential equation:- y'=0.04y+2000

Q: The differential equation governing the decay of a certain radioactive substance through time is dq…

A:

Q: Show that the differential equation x¹y³ + x(1+y¹)y' = 0 is not exact, but becomes exact when…

A:

Q: A ball is thrown from the ground and after t second is at a distance meter from the ground, where…

A: Consider the given equation. s=at-bt2 As we have given the value of a and b is 5, 1. Put the values…

Q: A farmer selected a variety of a fast-growing vegetable which matures based on the differential…

A:

Q: The implementation of a good harvesting policy for fisheries is crucial to ensure a sustainable…

A:

Q: find general solution for ordinary differential equation y" + y' = sec t when - T/2 < t< T/2 %3D

A: Given: y'''+y'=sect, when -π2&lt;t&lt;π2 To Find: The general solution for the given Ordinary…