Newton’s law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature of the object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroudings. Suppose that a building loses heat in accordance with Newtons law of cooling and that the rate constant k has the value of 0.15 hr^-1 a)write a differential equation for the interior temperature of the building at any time. Assume that the interior tmperature is 20 C when the heating system fails. If the external temperature is -10C, b) How long will take for the interior temperature to fall to 0 C b)

Q: A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential…

A: The surface area of a sphere of radius r is:

Q: A certain RNA molecule replicates every 3 minutes. Find the differential equation for the number…

A:

Q: The population y(t) grows continuously and follows an exponential behavior over time. Its…

A: We have to find the differential equation to describe growth of population y(t).

Q: A tank with a capacity of 250 gal is intended to be used to prepare a sugar solution. The tank…

A: Let the amount of sugar in tank at time t = y(t)

Q: Solve number 3 using first order linear differential equation.

A: We will solve the Differential equation.

Q: A differential equation is considered to be ordinary itit has one independent variable None of the…

A:

Q: The solution to differential equation associated with the path taken by a projectile for which the…

A:

Q: What is a nonhomogeneous differential equation with constant coefficient? Define and illustrate the…

A:

Q: A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its…

A:

Q: One model for the spread of a rumor is that the rate of spread is proportional to the product of the…

A: We will write the Differential equation for this problem.

Q: A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mg/cm3…

A:

Q: Determine which is the pure time differential equation, which is the autonomous differential and…

A: Given equations:  dfdt=e-t2                 ............................(1) y'=3y+y2…

Q: A tank contains 6L (liters) of water in which is dissolved 32 g (grams) of a chemical. A solution…

A:

Q: In differential equation, how to answer family of curves in process and determining the solution of…

A: Given a differential equation, dydx=f1(x)f2(y)

Q: The _____ of a differential equation is the power of the highest order derivative term in the…

A: The solution of above question is written below.

Q: A person planning for her retirement arranges to make continuous deposits into a savings account at…

A:

Q: A dropped ball accelerates downwards at a constant rate 9.8 meters per second squared. Set up the…

A: A dropped ball accelerates downwards at constant rate   9.8m/s2. Initially the ball is at height of…

Q: The population of a certain community is increasing at a rate proportional to the population at any…

A: According to the given problemThe population increase at a rate proportional to the number of people…

Q: A tank contains 6L (Iliters) of water in which is dissolved 32 g (grams) of a chemical. A solution…

A:

Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 5 of…

A: Part(A): Apply the law of conservation of mass, which states that matter is neither created nor…

Q: A falling object weighs 160 lbs. Beginning from the differential equation, find the object's…

A: Given,  a falling object weighs 160 lbs.

Q: Isaac Newton observed that the temperature (in degrees Fahrenheit) of his morning brew (F) changes…

A: Part (a):   According to the question the temperature change of the coffee is directly proportion to…

Q: Assume that a population P of wolves in a region is proportional to the area A of the region. Does…

A: This question is about application of derivative

Q: Sketch the direction or slope field of the differential equation. Be sure to show any “trends" and…

A: Given differential equation is y'=x-2y+1                   (i) Direction field of the given eq. (i)…

Q: A 100,000 liter tank of pure water was accidentally mixed with a 7000 liters of salt with a…

A: 1st we will make a differential equation for amount of salt in the tank and then will solve it to…

Q: A certain drug is being administered intravenously to a hospital patient mg Fluid containing 3 of…

A: A certain drug is being administered intravenously to a hospital patient. Fluid containg 3 mgcm3 of…

Q: Choose the best option that describes this differential equation i) separable ii) linear iii) both…

A: Given differential equation y'=xy+xe-x2

Q: A body weighing 24 lb stretches a vertical spring 1 foot beyond its natural length. The spring is…

A:

Q: A radioactive isotope has a half-life of 25 years. 100 g of it is present. Write the differential…

A:

Q: If x and y are measurements of certain parts of an organism, then the rate of change of y with…

A: Formula used: The differential equation can be equivalently expressed in the form g(y) dy=f(x)dx…

Q: Initially 5 grams of salt are dissolved in 30 liters of water in a tank. Brine with salt…

A: Here Initially, 5 grams of salt are dissolved in 30 liters of water in a tank. Brine with a salt…

Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 5 cm3…

A:

Q: A tank initially contains 100 gal of brine in which 40 lb of salt are dissolved. A brine containing…

A: A tank initially contains 100 gallon of brine with 40lb of dissolved salt. A brine containing…

Q: differential equation

A: Please refer to the image below

Q: Assume that you can contribute $7,000 per year into a retirement fund that grows at a constant rate…

A: Let ,Time = t P = $7,000 Rate = 7% = 0.07 P'(t) = dP/dt (a) Write a first-order linear differential…

Q: A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 2 cm3…

A: A certain drug is being administered intravenously to a hospital patient. Fluid containing 2mgcm3 of…

Q: Solve the Differential Equation by Separation of Variables; and when the Initial-Value Condition is…

A:

Q: independent variables are there in an ordinary differential equation

A: Differential Equation: The equation consists of derivatives of dependent variables (one or more)…

Q: FIND THE GENERAL EQUATION AND INTEGRATING FACTOR OF THE DIFFERENTIAL EQUATION BY METHOD OF…

A:

Q: Show that OW

A: x2+y2-xdx-ydy=0x2+y2-xdx+-ydy=0                 -Equation1Let M=x2+y2-x and N=-y∂M∂y=2y , ∂N∂x=0As…

Q: The rate of change of the population p of bacteria at time t is proportional to the population at…

A:

Q: Assume an object's weight, W, is proportional to its height, H. Does it make sens use differential…

A: This question is about application of derivative

Q: In a certain tropical forest, “litter” [dead vegetation like leaves and vines] forms on the ground…

A:

Q: A 48 gallon tank is filled with pure water. Water which has a concentration of 2g of salt per gallon…

A: Given

Q: Assume that a population P of wolves in a region changes inversely to the area A of the region. Does…

A:

Q: A certain drug is being administered intravenously to a hospital patient. of the drug enters the…

A:

Q: A tank contains 6L (liters) of water in which is dissolved 32 g (grams) of a chemical. A solution…

A:

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.