Question

Question 1 (a) Gravel is being dumped from a Conveyor belt at a rate of 30ft/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 is the height of the Pile increasing When the Pile is loft high? (b) Suppose a Water is flowing at Constant rate into the Container shown. Make a rough Sketch on the graph of the water levels versus the time. Make Sure that your Sketch conveys where the graph is Concave up or Concave down and label the y-Coordinates of the inflection Point- 3+ 0 (c) A rectangle is to be inscribed in a right triangle having sides of length 6cm; 8cm and 10cm. Find the dimensions of the rectangle assuming the rectangle is positioned as below to in Bin lin

Answer 1

ta Given d = 30ft/min height = loft A we need to find aber dt h2 volume of the cone = + Ti y²h Here r= 6/2 volume of the cone z f 11 ( 4 ) ² h < - Il bz v - The 12 differenhating wit tine dy z at 3h 12 db de dv 162 db 4 at 깥 at 4 db dt 2 dv वक T62 30x 4 1 x 10² 6 fflmin STI -0.382 ft mins db de C Scanned with CamScanner

het the rectangle length À and width is w 10 w we need to find the with maximum arca. tength and with of the rectangle Using the similarity in the triangle with hergh and base of cow _144) 2 3 Also for the ble with briban w and hep 10-2-2 W 2 } (10-C-~)-6 Substitute value of x in @ Wlo 3.(10---20) 4W 10 - L - 3 3 4wt 10 = 10 L 16w + 9 w 10- (2 1o-L 250 12 CSScanned with CamScanner L2 (0- 25w 12

Area of rectangle, А , Lo 2 (10-a5w)w A low W-25W? defferentiating wit da dw 210 - - 85W 2 O maximum Area da dw Sw= O 10-45o 25w 60 블 62 10- 25 x 1 2 3 10-525 Rectangle length length 25 width bah cscanned with CamScanner