Pre-Calc Homework Solutions 155

Pre-Calc Homework Solutions 155 - Section 4.4 The sum is as...

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The sum is as large as possible when the numbers are } 7 4 9 } and } 1 4 } 1 summing } 7 4 9 } + ! } 1 4 } § 2 , and is as small as possible when the numbers are 0 and 20 (summing 0 + ˇ 2 w 0 w ). Graphical support: [0, 20] by [ 2 10, 25] 2. Let x and y represent the legs of the triangle, and note that 0 , x , 5. Then x 2 1 y 2 5 25, so y 5 ˇ 2 w 5 w 2 w x w 2 w (since y . 0). The area is A 5 } 1 2 } xy 5 } 1 2 } x ˇ 2 w 5 w 2 w x w 2 w , so } d d A x } 5 } 1 2 } x } 2 ˇ 2 w 5 w 1 2 w x w 2 w } ( 2 2 x ) 1 } 1 2 } ˇ 2 w 5 w 2 w x w 2 w 5 } 2 ˇ 25 2 w 2 5 w 2 w 2 x 2 x w 2 w } . The critical point occurs when 25 2 2 x 2 5 0, which means x 5 } ˇ 5 2 w } , (since x . 0). This value corresponds to the largest possible area, since } d d A x } . 0 for 0 , x , } ˇ 5 2 w } and } d d A x } , 0 for } ˇ 5 2 w } , x , 5. When x 5 } ˇ 5 2 w } , we have y 5 ! 2 § 5 § 2 § 1 § } ˇ § 5 2 w } § 2 2 § 5 } ˇ 5 2 w } and A 5 } 1 2 } xy 5 } 1 2 } 1 } ˇ 5 2 w } 2 2 5 } 2 4 5 } . Thus, the largest possible area is
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