According to Newton's Law of Cooling, if a body with temperatureT¡ is placed in surroundings with temperatureTo, different from that ofT1, the body will either cool or warm to temperatureT (t) after t minutes, where: T (t) = To + (T – To) ekt and k is a constant. A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k = -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes.

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

A: Given Newton's law of cooling now we will find the required information as shown below

Q: 4. The temperature of a pan of hot water varies according to Newton's Law of Cooling: T-K(T-A),…

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Q: Suppose that in a certain country the life expectancy at birth of a female is changing at the rate…

A: We have to find the life expectancy.

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: 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: If the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a…

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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: the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a positive…

A:

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

A:

Q: A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be…

A: N(t) = 2t3 + 3t2 − 4t + 1,000 represent the turtle population at the end of the year t.  The turtle…

Q: At any time t seconds, the distance x metres of a particle moving in a straight line from a fixed…

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Q: A turkey is taken out of an oven and cools following Newton's Law of Cooling. The temperature of the…

A: The Newton's law of cooling formula can be denoted as dT/dt = -k( T - Ts), the negative sign…

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

A: we have to use the newtons equation of motion here. let us assume that the initial speed of car be u…

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: 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 ideal gas law is known as PV = nRT Where P, V, n, and T refer to pressure, volume, moles and…

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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: 6 The velocity of an object that moves in a straight line, v m s!. ts after passing through a fixed…

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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: tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound…

A: Let x(t) be the amount of salt at anytime t. Given, x(0)= 10 pounds Volume of tank(constan)= V(t)=…

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: The amount of insulin in microunits per mL in a diabetic patient is given by the function I(t) = 4.5…

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Q: A ball is thrown into the air by a baby cow on a planet in the system alpha centuri with a velocity…

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Q: contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2 pound of salt per…

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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: A particle moves along the x-axis with its position at time t given by x(t) - (t- a)(t - b), where a…

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

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Q: Suppose that in a certain country the life expectancy at birth of a female is changing at the rate…

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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…

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

A: part a) it is given that, P(t)=5+ae-bt . Initial population is P(0)=10,000 Therefore, at t=0,…

Q: A car engine runs at a temperature of 190F. When the engine is turned off, it cools according to…

A: Given that k=0.0341,Ts=60°F,Tt=190°F.

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: A 500 gallon tank is filled with fresh water in which 80 pounds of salt are dissolved. Fresh water…

A: (a) part It is given that the tank holds 500 gallons of fresh water and 80 lbs of salt, the fresh…

Q: Under certain​ conditions, the number of diseased cells​ N(t) at time t increases at a rate…

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Q: 4. A certain volume of a ideal gas satisfies PV = kT , where T is the absolute temperature, P is the…

A: Take the derivative with respect to time t and use the concept of derivative of the form  f = uv

Q: 2. A man with a parachute jumps out of a hovering helicopter at height H. During the fall, the man's…

A: The mathematical model for motion is provided by Newton’s second law, F = ma, with a skydiver of…

Q: -) The concentration of pollutant bacteria (C) in a lake is decreasing according to the following…

A: C=70eat+25ebt To Find: The time required for bacterial concentration to decrease to 9 using…

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

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Q: 4. A stone is thrown from the edge of a bridge that is 48 ft above the ground with an initial…

A: Motion in line

Q: 3. At midnight, the heater inside your house breaks down. The temperature (T) inside your house at…

A: dTdt=-k(T-T0)∫ dT(T-T0)=∫-k dtln(T-T0) =-kt+ln CT=T0 +C e-ktat t=0;T(0)=21°CT0 =-6°C21=-6+CC=27T=T0…

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: 7- The concentration of salt x in a home-made soap maker is given as a function of time by: dx dt =…

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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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Q: 5. A ship started at a certain port and travelled N 48° E at the rate of 32 kph. After 1.5 hours, a…

A: Use the component method to find the result.

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.