Mathematics, 02.10.2019 19:00 abcrakira

Arain 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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Answer from: isudgyia

For this problem, I think there is no need for the details of 12 inches width and 4 inches length. This is because an equation is already given. It was clearly specified that A as a function of θ represents the area of the opening. Then, we are asked to find exactly that: the area of opening. Moreover, the value of θ was also given. Therefore, I am quite sure that the initial details given are for the purpose of red herring only.

So, all we have to do is substitute θ=45° to the function given.
A = 16 sin 45° ⋅ (cos 45° + 1)

The angle 45° is a special angle in trigonometry. So, it would be easy to remember trigonometric functions of this angle. Sine of 45° is equal to √2/2 while cosine of 45° is also √2/2.

A = 16(√2/2) ⋅ (√2/2 + 1)
A = 8+8√2
A = 19.31 square inches

Answer from: Poohpooh1510

Refer to the diagram shown below which illustrates the problem.

From simple geometry, obtain
a = 4 cosθ
b = 4 sin θ

Therefore the area of the opening is
A = (1/2)*(2a + 4 + 4)*(b)
= (a + 4)*b
= (4a cosθ + 4)*(4a sin θ)
= 16(1+ cosθ)sin θ
This agrees with the given area.

When θ = 45°, sinθ = 1/√2, cos θ = 1/√2.
Therefore
A = 16(1 + 1/√2)*(1/√2)
= 16(1/√2 + 1/2) = 16(√2/2 + 1/2)
= 8(√2 + 1) = 19.3 in²

8(1 + √2) in², or 19.3 in²
Arain gutter is to be constructed of aluminum sheets 12 inches wide. after marking off a length of 4

Arain gutter is to be constructed of aluminum sheets 12 inches wide. after marking off a length of 4

Answer from: Quest

in if you ask questions, the points are taken from your total and given to the one who answered it..

so if i have 30 points and i ask a question for 5 points, then when someone asks a question i will lose 5 points and the answerer earns 5

happy to

Answer from: Quest

answer: the sun

explanation:

water cycle describes the evaporation of water from earth's surface, formation of clouds and precipitation water back onto the surface of earth. seventy percent of the earth is covered with water in the form of seas and oceans. the heat of the sun causes the evaporation of water from the surface of the ocean. the water vapors rise and condense to form water droplets. the collection of these water droplets form clouds which rain down again.

the evaporation of the oceans surface water as part of the water cycle is caused by the sun

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