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A planning engineer for a new alum plant must present some estimates to his company regarding the capacity of a silo designed to contain bauxite ore until it is processed into alum. The ore resembles pink talcum powder and is poured from a conveyor at the top of the silo. The silo is a cylinder 100 ft high with a radius of 200 ft. The conveyor carries ore at a rate of 60,000π ft3/h and the ore maintains a conical shape whose radius is 1.5 times its height.
(a) If, at a certain time t, the pile is 60 ft high, how long will it take for the pile to reach the top of the silo?
(b) Management wants to know how much room will be left in the floor area of the silo when the pile is 60 ft high. How fast is the floor area of the pile growing at that height?
(c) Suppose a loader starts removing the ore at the rate of 20,000π ft3/h when the height of the pile reaches 90 ft. Suppose, also, that the pile continues to maintain its shape. How long will it take for the pile to reach the top of the silo under these conditions?
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Chapter 9 Solutions
Calculus (MindTap Course List)
- Please refer belowarrow_forward(1) (16 points) Let f(x, y) = 2x + 3y + In(xy) (a) (6 points) Calculate the gradient field Vf(x, y) and determine all points (x, y) where ▼f(x, y) = (0, 0). (b) (4 points) Calculate the second derivative matrix D²f(x,y).arrow_forwardLet f(x, y) = 2x + 3y+ In(xy)arrow_forward
- (3) (16 points) Let D = [0, π/2] × [0, 7/6]. Define T: DCR2 R3 by → T(0, 4) = (2 sin cos 0, 2 sin sin 0, 2 cos x). Let S be the surface parametrized by T. (a) (8 points) Determine the normal, call it n(p), for the tangent plane TS at an arbitrary point p = T(0, 4). (b) (4 points) Show that n(p) parallel to the position vector T(0, 4) determined by p? Do the two vectors have the same direction or opposite direction? Explain. (c) (4 points) At which points p, if any, is TS parallel to the xy-plane?arrow_forward5:19 0 TEMU TEMU >>> 49 95% University at Albany - Single Sig... L Lumen OHM D2L HW4- AMAT100-Precal HW4 Score: 12.99/21 Answered: 18/21 × Question 16 Score on last try: 0 of 1 pts. See Details for more. > Next question Get a similar question You can retry this question below Find the inverse for the function k(x) = √√7x+12 k-¹(x) = Question Help: Video Message instructor Submit Question esc ||| F1 80 ୮ (x) = tarrow_forwarduse components when solvingarrow_forward
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