5. A cup of warm coffee at 80°C is cooling off outdoors according to the equation dy = k(y – 20) - dt where y(t) is the temperature (in °C) of the coffee at time t minutes. If the temperature of the coffee is 60°C after 10 minutes, what is (i) the value of k, and (ii) the temperature when t = 15 minutes?

Q: The function p(t)- 20 sin 2xt + 100 models a person's blood pressure while resting, where p(t)…

A:

Q: The rate of change of y with respect to x is one-half times the value of y. Find an equation for y,…

A:

Q: The following equation represents the relationship between hours of TV watched per day (x) and the…

A: Given dataŷ = -0.944x + 24.52x is the hours of TV watched per dayŷ is the number of situpspredicting…

Q: According to the Pew Research Center, the population of Italy for the next thirty years is projected…

A: We will find the answers of all 3 parts as following.

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

A:

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: which is f-1 (x)? f(x)= 1/5x + 3/5

A: Given, fx=15x+35 We have to find f-1x.

Q: The time, in minutes, for a student to run L laps is T(L). What is the meaning of T'(3)=2? O When…

A: It is known that derivative of a function represents the rate of change of the function.

Q: A classmate is building a mathematical model for the temperature in his home during the summer. He…

A: Given function is: Th=-12cosπ12h-1+75 where T is degree in Fahrenheit and h is the number of hours…

Q: The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the…

A: Given that the height of the pebble above the water surface after t seconds is y=285-16t2 and t=2.…

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.