3. [012 Polnts] DETAILS PREVIOUS ANSWERS LARCALC11M 2.6.020. MY NOTES ASK YOUR TEACHER l PRACTIC A trough is 12 meters long and 3 meters across the top (see gure). Its ends are isosceles triangles with altitudes of 3 meters. (a) If water ls being pumped into the trough at 2 cubic meters per mlnute, how fast is the water levei rising when h is 1.5 meters deep? x mm (b) If the water is rlsing at a rate of 2.5 centimeters per minute when h = 2.5, determine the rate at which water is being pumped into the trough. _x mm 10. [-/2 Points] DETAILS LARCALC11M 3.9.041. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The range R of a projectile is shown below, where vo is the initial velocity in meters per second and 0 is the angle of elevation. R = . Vo (sin 20) 9.8 Use differentials to approximate the change in the range when Vo = 700 meters per second and @ is changed from 100 to 150. (Round your answer to the nearest whole number.) m eBook11. [-/2 Points] DETAILS LARCALC11M 3.7.025. MY NOTES ASK YOUR TEACHER PRACTICE AN A rectangle is bounded by the x-axis and the semicircle y = \\ 25 - x2 (see figure). What length and width should the rectangle have so that its area is a maximum? (smaller value) (larger value) 14 12 10 8 y 6 y = qr1(25 - x*2) 4 2 -10 8 6 -4 20 2 8 10 -2 Need Help? Watch It eBook6. [-/2 Points] DETAILS LARCALC11M 3.9.013. MY NOT Use the information to find and compare Ay and dy. (Round your answers to three decimal places.) y = 0.9x x = 1 Ax = dx = 0.1 Ay = dy = Need Help? Watch It eBook Submit Answer 7. [-/2 Points] DETAILS LARCALC11M 3.9.020. MY NOT Find the differential dy of the given function. (Use "dx" for dx.) y = 6x2/3 dy = Need Help? Watch It eBook12. [-12 Points] DETAILS LARCALCHM 3.7.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 34 centimeters (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.) 13. [42 Points] AILS LARCALC11M 3.7.007. ASK YOUR TEACHER PRACTICE ANOTHER Find two positive numbers satisfying the given requirements. The product is 192 and the sum of the rst plus three times the second is a minimum. |:I (rst number) :I (second number) Need Help? .-w...- - ._ .\\ 14. [2/3 Points] DETAILS PREVIOUS ANSWERS LARCALC11M 3.4.023. MY NOTES ASK YOU Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) f(x) = xVx+ 12 ( x, V ) = DNE Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave upward -12,00 concave downward DNE eBook Viewing Saved Work Revert to Last Response5. [0.52 Points] ASKYOUR TEACHER PRACTICE ANOTHER PREVIOUS ANSWERS LARCALU 1 M 2.6.024. A boat is pulled into a dock by means of a winch 2 meters above the deck of the boat. (a) The winch pulls in rope at a late of 1.2 meters per second. Determine the speed of the boat when there is 5.6 meters of rope out. (Round your answer to two decimal places.) x W... What happens to the speed of the boat as it gets closer to the dock? The speed of the boat ' as it approaches the dock. {b} Suppose the boat is moving at a constant rate of 1.2 meters per second. Determine the speed at which the winch pulls in rope when there is a total of 5.6 meters of rope out. (Round your answer to two decimal places.) E x W... What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock? The speed at which the winch pulls in rope approad'ies -4 misec V x B. [-i'2 Points} LARCALCHM 3.9.023. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHI Find the differential 5')! of the glven function. (Use 'dx' for dx.) x + 2 9. [-12 Points] LARCALCHM 3.9.039. MY NOTES ASK YOUR TEACHER | PRACTICE ANOTHI The period of a pendulum is given by the equation shown below, where l. is the length of the pendulum in meters, 9 is the acceleration due to gravity, and Tis the time in seconds. I\". T=2N 9 The pendulum has been subjected to an increase in temperature such that the length has increased by %% (a) Find the approximate percent change in the period. |:| % (b) Using the result in part (a), nd Hie approximaha error in this pendulum dock in 1 day. |:l min