Answer :
To solve the given problem, we need to determine various expressions using the provided polynomials for the dimensions of the solar panels and the height of the coop. Let's go through this step by step:
1. Width of the Solar Panel: The width of the solar panel is represented by the polynomial [tex]\(4c^2 + 5c\)[/tex]. This gives us a quadratic expression in terms of [tex]\(c\)[/tex].
2. Length of the Solar Panel: The length of the solar panel is represented by the polynomial [tex]\(7c - 3\)[/tex]. This is a linear expression in terms of [tex]\(c\)[/tex].
3. Height of the Coop: The coop's height is represented by the polynomial [tex]\(2c + 6d\)[/tex]. This is also a linear expression, but it involves both [tex]\(c\)[/tex] and [tex]\(d\)[/tex].
4. Area of the Solar Panel: To find the area of the solar panel, we multiply the width by the length. This means we calculate the product of [tex]\(4c^2 + 5c\)[/tex] and [tex]\(7c - 3\)[/tex].
[tex]\[
\text{Area} = (4c^2 + 5c) \times (7c - 3)
\][/tex]
While we're not performing the calculation here, we know this expression represents the polynomial for the area of the solar panel in terms of [tex]\(c\)[/tex].
These expressions reflect the aspects of the problem from the dimensions provided:
- The width and length polynomials help understand how changes in [tex]\(c\)[/tex] affect the size of the solar panel.
- The height polynomial shows how [tex]\(c\)[/tex] and [tex]\(d\)[/tex] affect the height of the coop.
This step-by-step guide outlines how these polynomial expressions are used to understand the dimensions and potential calculations involving the solar panels and the coop.
1. Width of the Solar Panel: The width of the solar panel is represented by the polynomial [tex]\(4c^2 + 5c\)[/tex]. This gives us a quadratic expression in terms of [tex]\(c\)[/tex].
2. Length of the Solar Panel: The length of the solar panel is represented by the polynomial [tex]\(7c - 3\)[/tex]. This is a linear expression in terms of [tex]\(c\)[/tex].
3. Height of the Coop: The coop's height is represented by the polynomial [tex]\(2c + 6d\)[/tex]. This is also a linear expression, but it involves both [tex]\(c\)[/tex] and [tex]\(d\)[/tex].
4. Area of the Solar Panel: To find the area of the solar panel, we multiply the width by the length. This means we calculate the product of [tex]\(4c^2 + 5c\)[/tex] and [tex]\(7c - 3\)[/tex].
[tex]\[
\text{Area} = (4c^2 + 5c) \times (7c - 3)
\][/tex]
While we're not performing the calculation here, we know this expression represents the polynomial for the area of the solar panel in terms of [tex]\(c\)[/tex].
These expressions reflect the aspects of the problem from the dimensions provided:
- The width and length polynomials help understand how changes in [tex]\(c\)[/tex] affect the size of the solar panel.
- The height polynomial shows how [tex]\(c\)[/tex] and [tex]\(d\)[/tex] affect the height of the coop.
This step-by-step guide outlines how these polynomial expressions are used to understand the dimensions and potential calculations involving the solar panels and the coop.
