Lorelei uses a large oval-shaped tank to feed her horses. Due to recent thunderstorms the tank is completely full of dirty water that needs to be removed. At time t = 0, Lorelei starts to drain the tank at a rate modeled by g(t), measured in gallons per hour, where g is given by the piecewise function: (t-2)(3t+2)/t-2 0 < t < 2
g(t) = k 2 < t < 4
ae^0.49t 4 < t < 5
a. What values of k and a make g(x) continuous at both t = 2 and t = 4?
b. The average acceleration of the draining water from time a to time a + h is given by:
average acceleration = g(a + h) - g(a)/h
Is the average acceleration of g(t) higher from t = 0 to t = 1 or from t = 4 to t = 5?
c. The cylindrical horse feeder in the neighboring pasture is also full of water. At time t = 0, Lorelei's friend starts to drain the water from this feeder at a rate modeled by s(t).
s (t) = 3t
Let h(t) = g(t) - s(t). Apply the Intermediate Value Theorem to the function h on the interval 0 < t < 5 to justify that there exists a time t, 0 < t < 5, at which the heights of water in the two feeders are changing at the same rate.

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1.3.4 practice : modeling: solving linear equations in this assignment, you may work alone, with a partner, or in a small group. discuss the results of your work and/or any lingering questions with your teacher. your assignment: road trip you're taking a scenic road trip down ca-highway 1 from san jose, california, to los angeles. you plan to split the drive into two days, stopping for one night. choose one town to stop in, and find the driving distance for the second day. 1. circle the town you chose to stop in. (1 point) santa barbara: an image of palm trees san luis obispo: an image of a church 2. why did you choose this town? (1 point) 3.what do you know? .what do you want to find out? .what kind of answer do you expect? define the variable. 4. what is the variable x for this problem? (1 point) write the equation. 5. write an equation showing that the distance traveled on the first day plus the distance traveled on the second day is equal to 425 miles. (4 points: 2 points for each side of the equation) isolate the variable. 6. what inverse operation do you need to perform on both sides to isolate x in the equation? (2 points: 1 point for the correct number, 1 point for the correct operation) solve the equation. 7. solve the equation for x. interpret the answer in terms of the problem. (2 points: 1 point for the solution, 1 point for the interpretation) check your solution. 8. to confirm that your answer is correct, add the two days' distances. this should equal the total distance from san jose to los angeles. show your work as an equation. (3 points: 1 point for the setup, 2 points for the correct answer)