Newton's law of cooling is , where is the temperature of an object, is in hours, is a constant ambient temperature, and is a positive constant. Suppose a building loses heat in accordance with Newton's law of cooling. Suppose that the rate constant has the value Assume that the interior temperature is , when the heating system fails. If the external temperature is , how long will it take for the interior temperature to fall to

Complete Question

The complete question is shown on the first uploaded image

The time taken  is  

 

Explanation:

From the question we are told that

       The value of  

       The  the interior temperature is  

         The external temperature is  

          The required interior temperature is  

      The newton cooling law is

                     

=>                

  Now integrate both sides we have  

                 

                       

Since c is a constant lnC = c   will also give a constant so

                     

       =>      

     =>          

          substituting value

                 

                 

Hence

       

       

=>    

         

 

Answertraveling around a circular trackexplanation"traveling around a circular track" is the best answer as you could be traveling around a circular track at a constant speed. your velocity would therefore have the same magnitude but will always be constantly direction. since acceleration is the rate of change of velocity, the rate of change will only involve the direction of velocity and not the magnitude.wrong choices: "an object at rest" does not accelerate at all"increasing speed while traveling around a curve" means that the acceleration will not be constant due to only change in direction; it will be constant due to both magnitude and direction"an object in free fall" does not necessarily change direction