A rectangle is bounded by the x and y axes and the graph of the line y= (-1/2)x+3. What length and width should the rectangle have so its area is maximum?

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A rectangle is bounded by the x and y axes and the graph of the line y= (-1/2)x+3. What length and width should the rectangle have so its area is maximum?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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base of rectangle will be \(x\) and height will be \(-\frac{1}{2}x+3\) so area is \[A(x)=x(-\frac{1}{2}x+3)=-\frac{1}{2}x^2+3x\]\]
max will be at the vertex, which is at \(-\frac{b}{2a}=3\)

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oooo a year later c: Heyo humans :D

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