2. Matter cools governed by = -k(T – B) where ß is the dt temperature. Clearly T(0)=25 degrees and the constant k=0.5. In steps of 5 degrees determine T(40)

Q: It takes a total of 12 hours to drain a tank by opening a valve at the bottom. The depth h (in…

A:

Q: Solve for y: O y = Oy = x = 4ln(y - 8). 1 4 ln(x - 8) x+8 4 O y = e-4x + 8 O y = 4 ln(x - 8) Oy =…

A:

Q: The population of a certain kind of insect change directly proportional to its present population at…

A: The growth model will be modeled by : P(t)=P0 ekt  where, P0 : initial population P(t) : population…

Q: The mess in a restaurant can be measured by M(t). Assume that M(O) = 0, the restaurant starts out…

A: Let's consider a differential equation as follows:If M(t)=F(t), then equation 1 will be satisfied.

Q: AB1: Find g(2), g'(2), and g"(2).

A: Given that gx=∫-2x2ftdt Now we have to find g2, g'2 and g''2 In the interval -2,2, fx=4-x2In the…

Q: jn= 16, α=0.05

A:

Q: L=2-36X, y'co) =5, and ylo)=S x)

A:

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: Find Y = Coth 1 (x)

A: Given that y=coth-1x find dydx

Q: An evergreen nursery usually sells a certain shrub after 6 years if growth and shaping. The growth…

A:

Q: A tank initially contains 100 litres of water in which 10 kg of a salt is dissolved. A solution…

A: Here Q(t) denotes the amount of salt in the tank at time t. ⇒dQdt represents the rate of change of…

Q: A runner's speed is given by the function s(h)=2h and the associated time is given by the function…

A: Given:- Runner' speed sh=2h Time th=34h Let dh represents distance of runner travel

Q: Find the differential of the function y = f(x). f(x) = 7x5/6 + 2x2/3 %3D %3D

A:

Q: x2 + a Consider the function Find the value of the constant a so that y' (1) = 0.64

A:

Q: nt A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 750.19 cos( r24 man,…

A:

Q: Determine the value of x for which f(x) = x³9x² + 5x-e7 +11″ has the lowest instantaneous rate of…

A:

Q: According to Newton's Law of Cooling, the temperature T of an (as a function of time t) is given by…

A: Given, T(t)=Ts+D0e-ktwhere k=0.05

Q: Find the population y(t) of the birth rate is proportional to y(t) and the death rate is propors-…

A:

Q: Find f. f ″(x) = 20x3 + 12x2 + 8,    f(0) = 6,    f(1) = 3 f(x) =

A: To solve the following

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.