According to Newton's Law of Cooling, if a body with temperature T, is placed in surroundings with temperature To, different from that of T,, the body will either cool or warm to temperature T(t) after t minutes, where T(t) = To + (T, - Tole -kt A metal pan with temperature 145°F is placed in a freezer with temperature 0°F. After 10 minutes, the temperature of the pan is 64°F. Use Newton's Law of Cooling to find the pan's temperature after 20 minutes. After 20 minutes the pan will have a temperature of

Q: (2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3. v' + t+ro If the…

A: This is a linear differential equation which have to be solved using integrating factor

Q: A mass m is accelerated by a time-varying force exp(-ßt)v², where v is its velocity. It also…

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Q: If a cup of coffee has temperature 94°C in a room where the ambient air temperature is 19°C, then,…

A: To find: The average temperature of the drink C during the first 26 minutes.  Given: The temperature…

Q: The speed, s, of an accelerating object moving on a strait line is given by the formula: s = so +…

A: The initial speed is 10 m/s and the speed at time t is 16 m/s, so s0=10 m/s and s=16m/s. The time…

Q: ;A species of rabbits has a growth rate of 0.5/ month. If a population of foxes inhabits the same…

A: Given :   dPdt=0.5P-150 Because Number of kills per day =5 Then Number of kills per month=150 Now,…

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a…

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Q: A certain vehicle can accelerate from a standing start to a speed of  v(t) = −0.21t2 + 16t  feet per…

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Q: A particle with velocity at any time t given by v(t)=e't moves in a straight line. How far does the…

A: solve the following

Q: Over a period of time, a hot object cools to the temperature of the surrounding air. This is…

A:

Q: 1. If a stone is thrown vertically upward frosthe surface of the moon with a velocity of 10 meters…

A: Follow the procedure given below.

Q: What is the velocity and distance covered in 5 seconds when acceleration is 0.02s^(-7/8)) m/s²,…

A: Given:    a = 0.02s(-7/8)     t = 5 sec

Q: it is known from experiments that the height (in meter) of a certain plant after t months is given…

A: Given: ht=t-t; 0≤t≤1 for finding given values, first we draw graph of given function on given…

Q: 4. A certain particle is travelling in a straight line governed by the equation a = v5 m / s?. If…

A: we know the first equation of motionv=u+atv=1+2v95  m/s

Q: A person's Body Mass Index is I = 2, where W is the body weight (in kilograms) and H is the body…

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Q: A ball is thrown upward from a height of 6.5 m at an initial speed of 61 m/sec. Acceleration…

A: here we have .................initial height .................initial velocity ..............gravity

Q: The population P (in thousands) of a colony of rabbits at time (t) years is given by P(t) = 5+…

A: It is given that, P(t)=5+ae-bt . It is also given that Initial population is P(t=0)=10,000…

Q: 1. An arrow is shot vertically up into the air with an initial vertical velocity of 60 m/s, and its…

A: Given; Initial velocity=60m/s   h=-5t2+60t.

Q: 4 The velocity of a particle travelling in a straight line is given by v(t) = 50 – 10e-0.5t m/s,…

A: Given data is : The velocity of the particle in a straight line is, vt=50-10e-0.5t

Q: a) The specific volume v of a gas can be expressed as a function of its pressure p and temperature T…

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to…

Q: The rate of growth, dP/dt of a population of bacteria is given by dP/dt=k sqrt of t, where P is the…

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Q: In an electric circuit containing a resistor and a capacitor with an initial charge qo, the charge q…

A: Given

Q: The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV =…

A: Given PV=8.31Twhere P is in kilopascal ,V is in liters ,and T is in kelvins Volume increases from…

Q: contains 60 gallons of pure water. A mixture consisting of 1 pound of salt per gallon is flowing…

A: Given that a tank contains 60 gallons of pure water. A mixture consisting of 1 pound of salt per…

Q: The marriage rate in a certain country in 1990 was 0.95%, and there were about 351,000 marriages…

A: 1990 corresponds to t=0 So, M0= 351000 And r= 0.95% = 0.0095 So the model is:

Q: If the brakes on a car give the car a constant negative acceleration of 24 m/s2, where is a positive…

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Q: A particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the…

A: The acceleration of a particle is the rate of changing of velocity at time. When the velocity…

Q: The air in a room with volume 180 m3 contains 0.2% carbon dioxide initially. Fresher air with only…

A: Given : Room volume = 180 m³ which initially contains 0.2% carbon dioxide

Q: 4. p = pRT is the perfect gas equation where p is pressure, p is density T is temperature and R is…

A: To Determine:  solve for the rate of change in pressure  Given:  P=ρRTis the perfect gas equation…

Q: The period T of a simple pendulum is given by T=2π√L/g where L is the length of the pendulum and g…

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Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time…

A: Given:The rate of change of concentration of a drug in blood with respect to time t is

Q: If a rock is thrown vertically upward from the surface ofMars with velocity 15 m/ s  , its height…

A: Given that a rock is thrown vertically upward from surface of Mars with velocity 15 m/s. Its height…

Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

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Q: An object is thrown upward at a speed of 70 feet per second by a machine from a height of 13 feet…

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Q: If a cup of coffee has temperature 93°C in a room where the ambient air temperature is 21°C, then,…

A: Given that: Temperature, T(t)=21+72e-t/48

Q: Over a period of time, a hot object cools to the temperature of the surrounding air. This is…

A:

Q: A liquid at a temperature of 120°F is placed in a room at 36°F. Its temperature T (in °F) at time t…

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Q: Over a period of time, a hot object cools to the temperature of the surrounding air. This is…

A: Answer:   The answer is as shown in below pic :

Q: At what speed should a fish swim upstream so as to reach its destination with the least expenditure…

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Q: A rectangular swimming pool 20 ft wide by 25 ft long and of uniform depth is being filled with…

A: Let l, b and h be the length, width and height of a rectangular swimming pool respectively.Then,…

Q: According to Newton's law of Cooling, if a body with temperature T1, is placed in surroundings with…

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Q: At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000…

A: We will find out the required values.

Q: A liquid at a temperature of 120°F is placed in a room at 36°F. Its temperature T (in °F) at time t…

A:

Q: 6. The acceleration of a body moving in a straight line is given in terms of timet by a(t) = 8-6t If…

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Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?. where k is a…

A: The given question has been solved in detail.

Q: With assuming ideal laboratory conditions, the number of bacteria in a culture grows by the law Q(t)…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  the initial…

Q: Let C(t) be the concentration of a drug in the bloodstream. AS the body eliminates the drug, C(t)…

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Q: According to Hooke’s Law, the force (lb), F, required to hold a spring in place when its…

A: Since it requires 120 lb of force to hold spring 1.5 ft beyond its natural length, therefore F=120…

Q: If a tank holds 4000 gallons of water, which drains from the bottom of the tank in 50 minutes, then…

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Q: According to Newton's law of cooling, the time t needed for an object at an initial temperature To…

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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.