I am stuck on this math problem:  Suppose a cup of coffee is at 100 degrees Celsius at time t = 0, it is at 70 degrees at t = 10 minutes, and it is at 50 degrees at t = 20 minutes. Compute the ambient temperature. In the book, I got the differential equation of Newton's Cooling which is dT/dt = k(A-T). T is the temperature, A is the ambient temperature, t is the time in minutes, k is a constant. By separating the variables and integrating both sides, I got T= A + e^c * e^kt. I tried to solve for A using the available values, but can't seem to solve for A.

Q: A turkey is cooked to an internal temperature, I(t), of 180 degrees Fahrenheit, and then is the…

A: Given that , Internal temperature =180°F what is the differential equation to solve for It.

Q: The median value of a home in a particular market is decreasing exponentially. If the value of a…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: A tank initially contains 50 gallons of brine, with 30 pounds of salt in solution. Water runs into…

A: This question is related to differrential equations, We will solve it using given information.

Q: This is a differential equation problem. A thermometer is removed from a 70-degree F room and is…

A:

Q: The rate of change of the temperatu

A: Given, the rate of change of the temperature, T, of a cooling object is proportional to the…

Q: A thermometer is moved from a room where the temperature is 68 °F to a freezer where the temperature…

A: (a) The thermometer is moved to the freezer, so the surrounding temperature is 12°F

Q: A watering system holds 500 gallons of water. Water is added into the system at a rate of 8 gallons…

A:

Q: During the first few years of life, the rate at which a baby gains weight is proportional to the…

A:

Q: A particle moves according to the formula s = 6 to + 63 t-15 where distance s is measured in meters…

A:

Q: Take x = 2.5 as a first approximation to the root of the equation e* – 4x = 0 and apply Newton's…

A:

Q: The rate of change of the time it takes to mow a lawn is inversely proportional to the square of the…

A:

Q: We are given this situation to model using a differential equation: Snow is falling at a constant…

A: An autonomous differential equation is an equation of the formdydt=f(y)." data-mce-style="margin:…

Q: Write the differential equation (unlimited, limited, or logistic) that applies to the situation…

A: Given that, the initial cases are N0=14. "It is known that, the formula for the exponential growth…

Q: 4) You are visiting a beach, and the tides for the day of your visit are given by: Tt h(t) = 3+3 sin…

A: As given the sin function in the height of the tide. ht=3+3sinπ6t Use the definition when the sin…

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.