Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
Representing a situation as an algebraic equation using variables can be used to solve complex problems
The correct option as option for the depth of the gutter that will allow a cross-sectional area of 54 square inches as option d.
d. y ≈ 2.4 in. and y ≈ 11.1 in.
The reason the selected option is correct is as follows:
The given parameters of the rain gutter are;
The width of the aluminum sheets from which the rain gutter is made = 27 inches
The angle to which the edges are turned up to form right angles = Right angles (90 degrees)
Required:
To determine the depth of the gutter allowing a cross-sectional area of 54 square inches
Method:
Form an equation that describe the area of the gutter, taking note that the gutter does not have a cover (top) and therefore only three sides are required
Solution:
Let y represent the length of the sides (depth) of the rain gutter, and let x represent the width, we have;
2·y + x = 27...(1) (The total with of the gutter; 2 sides and a base)
The cross sectional area of the gutter, A = y × x...(2)
Where;
y = The depth of the gutter
x = The width of the gutter
From equation (1), we have;
x = 27 - 2·y
Therefore, in equation (2), we have;
A = y × (27 - 2·y)
The desired cross-sectional area, A = 54 in.²
∴ A = 54 = y × (27 - 2·y) = 27·y - 2·y²
Which gives;
2·y² - 27·y + 54 = 0
From which we get;
[tex]y = \dfrac{27 \pm \sqrt{(-27)^2 - 4 \times 2 \times 54} }{2 \times 2} = \dfrac{27 \pm 3\times \sqrt{33} }{4}[/tex]
Therefore;
y ≈ 2.4 and/or y ≈ 11.1
Which gives the depth of the gutter that will allow a cross-sectional area of 54 square inches as y ≈ 2.4 in. and y ≈ 11.1 in.
Learn more about algebraic equations here:
https://brainly.com/question/21464859
https://brainly.com/question/19864285
https://brainly.com/question/23206107
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
