A beaker of liquid was placed in a fridge. The rate of cooling is given by dT — k(Т — Тр), k> 0 dt where TF is the constant temperature in the fridge and T is the temperature of the liquid at time t. • The constant temperature in the fridge is 4°C. • When first placed in the fridge, the temperature of the liquid was 25°C. • At 12 noon, the temperature of the liquid was 9.8°C. • At 12:15pm, the temperature of the liquid had dropped to 6.5°C. Find the particular solution and determine the value of t. Hence at what time, to the nearest minute, was the liquid placed in the fridge? Comment on your finding.

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Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

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Q: When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of…

A: Solution:GivenC(t)=P(1.05)t

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A: Given :               h(t) = 15 - 4.9t2v(0) = 15 m/sAverage velocity = area under velocitytime…

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A: Given  , Rate if drain: dV/dt = - 1.8L/min By integrating the equation we get the volume.

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Q: a. Water is flowing into a conical tank at a constant rate of 3 cubic meters per second. The cone…

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Q: A body of mass 1 slug is dropped with an initial velocity of 1 ft/sec and encounters a force  due to…

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Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A: A 2‐lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

Q: Find the maximum rate of change of f(s,t)=te^(st) at the point (0,−5).

A: We have to solve

Q: = 4000 1 0 代 50 50

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Q: The equation for the amount Q of an antibiotic in the bloodstream at time t is Q = Ae-kt. %3D dQ 1.…

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Q: A particle moves along the x-axis so that at time t >0 its position is given by x (t) =t² – 10t +…

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Q: The position of a particle at time t is s(t) = 4t^3. Compute the average velocity over the time…

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Q: An observer moves so that his position, velocity, and acceleration at time t are given by the…

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Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

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Q: 2. Matter cools governed by = -k(T – B) where ß is the dt temperature. Clearly T(0)=25 degrees and…

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Q: A particle moves along the x-axis so that at any time t ≥ 0 its velocity is given by…

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Q: .................... ..................... A new fast-food firm predicts that the number of…

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Q: 2. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

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Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 3…

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Q: A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times…

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Q: The velocity is equal to the rate of change of distance x (m), dx v(t) dt (1.1) a. Substitute Eq.…

A: After substituting Eq. (1.2) to Eq. (1.1), we have dxdt=gmc1−e−cmt

Q: The position of a particle at time t is s(t) = 4t^3. compute the average velocity over the time…

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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.