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Neporo4naja [7]
3 years ago
6

A rain gutter is made from sheets of aluminum that are 16 inches wide by turning up the edges to form right angles. Determine th

e depth of the gutter that will maximize its​ cross- sectional area and allow the greatest amount of water to flow. What is the maximum​ cross-sectional area?
Mathematics
1 answer:
blsea [12.9K]3 years ago
8 0

Answer:

Depth of the rain gutter is 8 inches

Step-by-step explanation:

Let’s assume ‘x’ is the depth of the rain gutter

Then the width of the rain gutter can be written as 16 - 2x

Cross sectional area

A = depth x width

Substitute values

A = x*(16 - 2x)

A = 16x – 2x^2

Now according to axis of symmetry for maximum area x = -b/2a

x = -16/2*(-2)

x = 4 inches depth of rain gutter, substitute the value of x to get

Width of rain gutter 16 – 2(4) = 8 inches

Area of the rain gutter for maximum water flow

A = 4 * 8

A = 32 square inch.

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