7. [l1 Points] DETAILS SCALCETQ 3.9.035. 0/50 Submissions Used MY NOTES ASK YOUR TEACHER A ladder 10 ft long rests against a vertical wall If the bottom of the ladder slides away from the wall at a rate of l tft/s, how fast (in rad/'5) is the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is find the angles rate of Change when the bottom of the ladder is 8 ft from the wall.) Wall l0 1 Ground (D Em Need Heir)a 3. [l1 Points] SCALCET9 3.9.047. 0/50 Submissions Used ASK YOUR TEACHER A plane flies horizontally at an altitude of 4 km and passes directly over a tracking telescope on the ground. When the angle of elevation is 3, this angle is decreasing at a rate ofE rad/min. How fast is the 4 4 plane traveling (in km/rnin) at that time? (Round your answer to two decimal places.) km/min 5. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.9.025. 1/50 Submissions Used MY NOTES ASK YOUR TEACHER Water is leaking out of an inverted conical tank at a rate of 7,000 cm/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate (in cm /min) at which water is being pumped into the tank. (Round your answer to the nearest integer.) -1.02 * cm3/min Enhanced Feedback Please try again. Note that the radius r of the cross section at hight h can be obtained using similar triangles. Indeed, Tadius at the top = freight of the talk. Using the given values of the radius (half of the h diameter) at the top and the height of the water tank in this relation, you can solve for r. Next, you need to use the formula for the volume of a conical cylinder of height h and base radius r: V = _ n r2 h, and plug in the expression for r to write V as a function of h. Finally, differentiate with respect to t using the Chain Rule to obtain the relation between - and . Let C = (rate water is pumped in). Then dt dt dv - = C - (rate water is pumped out). Now, you can obtain the value of C. Need Help? Read It Watch It 6. [-/1 Points] DETAILS SCALCET9 3.9.029. 0/50 Submissions Used MY NOTES ASK YOUR TEACHER Gravel is being dumped from a conveyor belt at a rate of 25 fts/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast (in ft/min) is the height of the pile increasing when the pile is 14 ft high? (Round your answer to two decimal places.) ft/min Need Help? Read It Watch It3. [-/1 Points] DETAILS SCALCET9 3.9.016. 0/50 Submissions Used MY NOTES ASK YOUR TEACHER At noon, ship A is 150 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.? (Round your answer to three decimal places.) km/h Need Help? Read It Submit Answer 4. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.9.022.MI. 3/50 Submissions Used MY NOTES ASK YOUR TEACHER A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at a rate of 1 m/s, how fast (in m/s) is the boat approaching the dock when it is 5 m from the dock? (Round your answer to two decimal places.) -1.02 x m/s