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Pre-Calc Homework Solutions 202

Pre-Calc Homework Solutions 202 - 202 Chapter 4 Review 63...

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61. Step 1: x 5 x -coordinate of point y 5 y -coordinate of point D 5 distance from origin to point Step 2: At the instant in question, x 5 3 and } d d D t } 5 11 units per sec. Step 3: We want to find } d d x t } . Step 4: Since D 2 5 x 2 1 y 2 and y 5 x 3/2 , we have D 5 ˇ x 2 w 1 w x w 3 w for x $ 0. Step 5: } d d D t } 5 } 2 ˇ x 2 w 1 1 w x w 3 w } (2 x 1 3 x 2 ) } d d x t } 5 } 2 2 x x ˇ 1 1 w 3 1 w x 2 x w } } d d x t } 5 } 2 ˇ 3 x 1 w 1 1 w 2 x w } } d d x t } Step 6: 11 5 } 3( 2 3 ˇ ) 1 4 w 2 } } d d x t } } d d x t } 5 4 units per sec 62. (a) Since } h r } 5 } 1 4 0 } , we may write h 5 } 5 2 r } or r 5 } 2 5 h } . (b) Step 1: h 5 depth of water in tank r 5 radius of surface of water V 5 volume of water in tank Step 2: At the instant in question, } d d V t } 5 2 5 ft 3 /min and h 5 6 ft. Step 3: We want to find 2 } d d h t } . Step 4: V 5 } 1 3 } p r 2 h 5 } 7 4 5 } p h 3 Step 5: } d d V t } 5 } 2 4 5 } p h 2 } d d h t } Step 6: 2 5 5 } 2 4 5 } p (6) 2 } d d h t } } d d h t } 5 2 } 1 1 4 2 4 5 p } < 2 0.276 ft/min Since } d d h t } is negative, the water level is dropping at the positive rate of < 0.276 ft/min.
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