number 18 please
4 1 2 1 &l r1B &/ 1 414 44 41441 1W 0 wden2 when cach edge is ( 16. Surface Area All edges of a cube are ex rate of 6 centimeters per second. How fast is te area changing when each edge is (a) 2 centime (b) Consider the trian ladder, and the of the triangle 7 feet from the wdee r S (c) Find the rate a wall of the ho (b) aden a 1 (b) 10 centimeters? de whena3y4 17. Height At a sand and gravel plant, sand is fallin is 7 feet from (a) conveyor and onto a conical pile at a rate of 10 cubic minute. The diameter of the base of the cone is appr three times the altitude. At what rate is the height of t changing when the pile is 15 feet high? (Hint: The fom the volume of a cone is V = nrh.) 18. Height The volume of oil in a cylindrical comu increasing at a rate of 150 cubic inches per second. The of the cylinder is approximately ten times the radius. A rate is the height of the oil changing when the oil is 35 m high? (Hint: The formula for the volume of a cylne V= nr?h.) -2 (b) whenx = 4y3 Point In Exercises 7-10, a point is along the graph of the given function at rd. Find dy dt for the given values of x. 2 centimeters per second )r0 (c) x = 1 Figure for 21 5 inches per second FOR FU on the mathe x 0 (c) x 2 (c) x=2 Ladder Para 19. Depth A swimming pool is 12 meters long, 6 meters I meter deep at the shallow end, and 3 meters dep deep end (see figure). Water is being pumped into the p cubic meter per minute, and there is 1 meter of water The Colleg et per second MathArticle 22. Cons plank of a r * 4 (c) x 0 deep end. mtimeters per second oppo wall (c) 1 m 0.1S alo
Given,
dV 150 cubic inches per second dt h=10r
Consider the volume of the cylinger,
V Trh h hh=10r] 10 V = 7 V = 100
Now differentiating with r...
dV dh -.3h2 dt dt 100 Злh dh 150 dV =150 dt 100 dt When h 35 inches, we get Зл (35) dh = 150 dt 100 dh 150x100 di 3л-(35)* 1.2992 inches per second.
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