Let f(t) be the temperature (in degrees Celsius) of a liquid at time t (in hours)....

 

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Let f(t) be the temperature (in degrees Celsius) of a liquid at time t (in hours). Listed below are typical questions about f(t) and its rate of change at various points and a list of typical methods of solution. For each question, pick the correct method of solution and explain why it is the correct method of solution. Questions: (a) What is the temperature of the liquid after 6 hours? (b) When is the temperature rising at a rate of 6 degrees per hour? (c) How much did the temperature increase during the first 6 hours? (d) When is the liquid's temperature 6C? (e) How fast is the temperature changing after 6 hours? (f) What is the average rate of increase in the temperature during the first 6 hours? Methods of Solution: (1) Compute f(6). (2) Set f(t)=6 and solve for t. (3) Compute [f(6)-f(0)]/6. (4) Compute f'(6). (5) Set f'(t) = 6 and solve for t. (6) Compute f(6)-f(0). Acceleration is the rate that velocity is changing. (a) Explain why acceleration is the second derivative of the position function. (b) Let p(t) be the position function, v(t) be the velocity function, and a(t) be the acceleration function for an object moving on a standard number line. Also remember that speed is the absolute value of velocity. i. You know p(2)=4. v(2) is positive, and a(2) is positive. Which direction is the object moving? Is it speeding up or slowing down? Why? ii. You know p(8) - 10, v(8) is positive, and a(8) is negative. Which direction is the object moving? Is it speeding up or slowing down? Why? iii. You know p(15)=-5, v(15) is negative, and a(15) is positive. Which direction is the object moving? Is it speeding up or slowing down? Why? iv. You know p(27) = 0, e(27) is negative, and a(27) is negative. Which direction is the object moving? Is it speeding up or slowing down? Why? Let f(t) be the temperature (in degrees Celsius) of a liquid at time t (in hours). Listed below are typical questions about f(t) and its rate of change at various points and a list of typical methods of solution. For each question, pick the correct method of solution and explain why it is the correct method of solution. Questions: (a) What is the temperature of the liquid after 6 hours? (b) When is the temperature rising at a rate of 6 degrees per hour? (c) How much did the temperature increase during the first 6 hours? (d) When is the liquid's temperature 6C? (e) How fast is the temperature changing after 6 hours? (f) What is the average rate of increase in the temperature during the first 6 hours? Methods of Solution: (1) Compute f(6). (2) Set f(t)=6 and solve for t. (3) Compute [f(6)-f(0)]/6. (4) Compute f'(6). (5) Set f'(t) = 6 and solve for t. (6) Compute f(6)-f(0). Acceleration is the rate that velocity is changing. (a) Explain why acceleration is the second derivative of the position function. (b) Let p(t) be the position function, v(t) be the velocity function, and a(t) be the acceleration function for an object moving on a standard number line. Also remember that speed is the absolute value of velocity. i. You know p(2)=4. v(2) is positive, and a(2) is positive. Which direction is the object moving? Is it speeding up or slowing down? Why? ii. You know p(8) - 10, v(8) is positive, and a(8) is negative. Which direction is the object moving? Is it speeding up or slowing down? Why? iii. You know p(15)=-5, v(15) is negative, and a(15) is positive. Which direction is the object moving? Is it speeding up or slowing down? Why? iv. You know p(27) = 0, e(27) is negative, and a(27) is negative. Which direction is the object moving? Is it speeding up or slowing down? Why?

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a After six hours what is the liquids temperature Approach to Solution Calculate 6 f 6 The explanation is as follows Since we wish to know the temperature at a given time 6 hours we just need to plug ... View the full answer