121616949-math.132 - 118 Chapter 6 Applications of the...

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118 Chapter 6 Applications of the Derivative to the strength of the source and inversely proportional to the square of the distance from the source. 32. Find the fraction of the area of a triangle that is occupied by the largest rectangle that can be drawn in the triangle (with one of its sides along a side of the triangle). Show that this fraction does not depend on the dimensions of the given triangle. 33. How are your answers to Problem 9 affected if the cost per item for the x items, instead of being simply $2, decreases below $2 in proportion to x (because of economy of scale and volume discounts) by 1 cent for each 25 items produced? 34. You are standing near the side of a large wading pool of uniform depth when you see a child in trouble. You can run at a speed v 1 on land and at a slower speed v 2 in the water. Your perpendicular distance from the side of the pool is a , the child’s perpendicular distance is b ,
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