Problem 2: The function that will convert Fahrenheit to Celsius is 9 F(C) = = C+32 %3D where C and F are the temperature readings in Celsius and in Fahrenheit, respectively. Derive this expression knowing that The freezing point of water is measured to be 0°C and 32°F. The boiling point of water is measured to be 100°C and 212 F. The Fahrenheit and Celsius scales show a linearrelationship.

Q: If C = 100, k = 0.1, and t is time in minutes, how long will it take a hot cup of coffee to cool to…

A: From Newton’s Law of Cooling, we know that T(t) = Ts + Cekt Given C = 100, k = 0.1 Consider freshly…

Q: . An alloy at temperature 100°C is brought into a medium whose temperature is kept at 80°C. After 20…

A: We can use Newton's law of cooling/ heating formula and its general solution to solve this problem.

Q: 1. You are an engineer and you know that the time (T) it takes to build a bridge varies directly as…

A:

Q: The quantity relative for 1980 with 1960 as base was 105 whilst the quantity relative for 1980 with…

A: Definition:A quantity relative is the ratio of the quantity of a specific product in one period to…

Q: The number of citizens of a certain modern city is known to increase at a rate proportional to the…

A:

Q: If one earthquake has a magnitude of 5 on the Richter scale and a second earthquake has a magnitude…

A: We have to determine the relationship between the intensities of the two earthquakes .

Q: combined

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: A dead body was found within a closed room of a house where the temperature was a constant 70° F. At…

A: Given A dead body was found with in a closed room of a house where temperature was a constant 70∘F .…

Q: A body of an unknown temperature is placed in a room which is held at a constant temperature of 30 .…

A: Given that, A body of an unknown temperature is placed in a room which is held at a constant…

Q: A 100-gal tank initially contains 25% dye solution. A 40% dye solution is allowed to enter at a rate…

A:

Q: Early Monday morning, the temperature in the lecture hall has fallen to 41°F, the same as the…

A: We will use the formula , where Ku=K1−K.Here, T(t) represents the temperature inside the…

Q: Ohm’s law says that the current, I, (in amps) obeys the formula I =V/R where V represents the…

A:

Q: Early Monday morning, the temperature in the lecture hall has fallen to 42°F, the same as the…

A: We will use the formula , where Ku=K1−K.Here, T(t) represents the temperature inside the…

Q: The average cupcake temperature at a bakery is 75 degrees celsius. You buy a cupcake, and after 1…

A: Newton's of cooling

Q: A tank contains 3000 gallons of pure water. Polluted water containing 2 lb of sludge per gallon…

A: To find a formula for the concentration of pollutants at time t in the tank.

Q: Answer 2

A: Please refer to the image below

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.