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Home » Therefore, the remainder is \(\boxed0\). - Databee Business Systems

Therefore, the remainder is \(\boxed0\). - Databee Business Systems

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 \frac{0.205}{4} \approx 0.05125 \Rightarrow b_4 \approx 0.6709 - 0.05125 = 0.61965

📌 So, the value of $ b_4 $ is approximately:

📌 \boxed{0.6197}

📌 Question: A surgical robot arm moves in a rectangular region whose perimeter is 100 units. To maximize precision, the area of the region must be as large as possible. What is the largest possible area?

📌 Solution: Let the rectangle have length $ l $ and width $ w $. The perimeter is:

📌 2l + 2w = 100 \Rightarrow l + w = 50

📌 The area is $ A = lw $. Express $ w = 50 - l $, so:

📌 This is a quadratic in $ l $, opening downward, so maximum occurs at the vertex:

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To find the ratio of the areas, we calculate the area of each shape.
The area \(A\) of a circle with radius \(r\) is given by:
A_{\text{pond}} = \pi r^2
The area \(A\) of a semicircle with radius \(R\) is half the area of a...
A_{\text{semicircle}} = \frac{1}{2} \pi R^2
For the walkway with radius \(5r\):
A_{\text{walkway}} = \frac{1}{2} \pi (5r)^2 = \frac{1}{2} \pi \times 2...
The area of the walkway is the area of the full circle with radius \(5...
A_{\text{walkway only}} = \pi (5r)^2 - \pi r^2 = 25\pi r^2 - \pi r^2 =...
The ratio of the area of the pond to the area of the walkway is:

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