A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is

Question

A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. The area A of the opening may be expressed as the function: A(θ) = 16 sin θ ⋅ (cos θ + 1). If θ = 45°, what is the area of the opening?

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Genesis 6 days 2021-09-15T02:45:19+00:00 1 Answer 0

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    2021-09-15T02:46:26+00:00

    Answer:

    4(2+\sqrt{2})\text{ square unit}

    Step-by-step explanation:

    Given function that shows the area of the opening,

    A(\theta)=16 \sin\theta (\sin \theta + 1)

    If \theta = 45^{\circ}

    Hence, the area of the opening would be,

    A(45^{\circ})=16 \sin 45^{\circ} (\cos 45^{\circ} + 1)

    =16\times \frac{1}{\sqrt{2}}\times (\frac{1}{\sqrt{2}}+1)

    =16(\frac{1}{2}+\frac{1}{\sqrt{2}})

    =8+\frac{16}{\sqrt{2}}

    =8+4\sqrt{2}

    =4(2+\sqrt{2})\text{ square unit}

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