Newton's law of cooling states that the rate of change of temperature of an object in a surrounding medium is proportional to the difference of the temperature of the medium and the temperature of the object. suppose a metal bar, initially at temperature 30 degrees celsius, is placed in a room which is held at the constant temperature of 10 degrees celsius. one minute later the bar has cooled to 10.99574 degrees . write the differential equation that models the temperature in the bar (in degrees celsius) as a function of time (in minutes). hint: you will need to find the constant of proportionality. start by calling the constant k and solving the initial value problem to obtain the temperature as a function of k and t . then use the observed temperature after one minute to solve for k .

dt/dt = 3(10-t) correct: your answer is correct.

so what i got is only dt/dt=k(tm-to)=k(10-to)

can some one explain how do they get the value of k as 3?

For this option, you will work individually. the pythagorean theorem can be used in many real-world scenarios. part 1 write your own real-world scenario where the pythagorean theorem can be applied to find a missing piece. you may choose to write a problem that is two- or three-dimensional in nature. be sure that you will be able to draw a diagram of your scenario. write out your problem and submit it for part 1. be sure to end your scenario with a question. part 2 draw a diagram of the scenario you created in part 1. you may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. be sure to label all parts and dimensions of the drawing. part 3 solve the question that you posed in part 1. show all of your steps in answering the question. for this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps. * note that your instructor is looking for your own original idea. while it is acceptable to use the internet for research and inspiration, academic integrity policies apply.