14. [OIZ Points] DETAILS PREVIOUS ANSWERS SCALC8 2.8.048. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTH Two people start from the same point. One walks east at 6 mi/h and the other walks northeast at 1 mi/h. How fast is the distance between the people changing after 15 minutes? (Round your answer to three decimal places.) 2. 834 x mi/h Submit Answer 15. [0/3 Points] DETAILS PREVIOUS ANSWERS SCALCS 2.7.502.XP. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTH If a ball is given a push so that it has an initial velocity of 3 m/s down a certain inclined plane, then the distance it has rolled after tseconds is given by the following equation. 5(t) = 3t + 4t2 (a) Find the velocity after 2 seconds. x m/s (b) )How long does it take for the velocity to reach 40 m/s? (Round your answer to two decimal places.) _xs 16. [-/3 Points] DETAILS SCALC8 3.1.512.XP. Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x2 - 32x + 5, [0, 9] absolute minimum value absolute maximum value20. [15 Points] DETAILS SCALC8 3.7.011. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHER Consider the following problem: A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? (a) Draw several diagrams illustrating the situation, some with shallow, wide pens and some with deep, narrow pens. Find the total areas of these congurations. Does it appearthat there is a maximum area? If so, estimate it. (b) Draw a diagram illustrating the general situation. Let X denote the length of each of two sides and three dividers. Let y denote the length of the other two sides. (c) Write an expression for the total area A in terms of both x and y. A: (d) Use the given information to write an equation that relates the variables. (e) Use part (d) to write the total area as a function of one variable. A(X) = (f) Finish solving the problem by finding the largest area. :W 24. [-/6 Mains] D TAILS SCALC8 4.2.008. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHER 9 The table gives the values of a function obtained from an experiment. Use them to estimate f x) dx using three equal subintervals with right endpoints, left endpoints, 3 and midpoints. X 3 4 5 6 7 8 9 f(x) 3.4 2.2 0.7 0.3 0.7 1.5 1.7 9 (a) Estimate ] f(x) dx using tiree equal subintervals with right endpoints. 3 If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? 0 less than 0 greater than 0 one cannot say 9 (b) Estimate 1 f(x) dX using three equal subintervals with left endpoints. 3 L3 = If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? 0 less than 0 greater than 0 one cannot say 9 ((2) Estimate / f(x) dx using three equal subintervals with midpoints, 3 M3 = :1 If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? 0 less than 0 greater than 0 one cannot say 27. [OIG Points] DETAILS PREVIOUS ANSWERS SCALCB 4.5.022.MI.SA. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER This question has several parts that must be completed sequentially. If you skip a pant of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Evaluate the indefinite integral. f cosgn/X'm) dx X41 We must decide what to choose for u. If u = f(x), then du = f'(x) dx, and so it is helpful to look for some expression for which the derivative is also present, though perhaps missing a constant factor. We can re-write f cos(%) dx=fcos(%) ( L41) dx. x $1 We see that i is part of this integral, and the derivative of i is >6") x40 31. [1.58/3 Points] DETAILS PREVIOUS ANSWERS SCALC8 5.2.510.XP. MY NOTES Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = _, x=8, x =16, y = 0; about the x-axis X V = X