Please make sure to answer all three questions. 1. A piece of wire of length 10m

Question

Please make sure to answer all three questions.

1. A piece of wire of length 10m is bent into the shape of a rectangle. Which dimensions produce the rectangle of maximum area? Your task is to build a road a ranch to a highway that enables drivers to reach the city in the shortest time. How should this be done if the speed limit is 60 km/h on the road and 110 km/h on the highway. The perpendicular distance from the ranch to the highway? The perpendicular distance from the ranch to the highway is 30 km, and the city is 50 km down the highway. What is the maximum area of a rectangle inscribed in a right triangle with legs of length 3 and 4 as in figure. The sides of the rectangle are parallel to the legs of the triangle. 2. 3. 4 ho nhnne nf a semicircle on top of a

Explanation / Answer

1. Let the side of the rectangles are x and y

So 2x+2y =10

x+y=5

x = 5-y

Area = x y = (5-y)y = 5y-y2

A ' = 5-2y

A ' =0

5-2y=0

y=2.5m

x = 5-y = 5-2.5 = 2.5 m

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