At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To determine the area of a rectangle when given the length and width as functions of [tex]\( x \)[/tex], we simply multiply these functions together.
Given:
- [tex]\( L(x) = 5x \)[/tex] (Length as a function of [tex]\( x \)[/tex])
- [tex]\( W(x) = 2x^2 - 4x + 13 \)[/tex] (Width as a function of [tex]\( x \)[/tex])
The area [tex]\( A(x) \)[/tex] of the rectangle as a function of [tex]\( x \)[/tex] is given by:
[tex]\[ A(x) = L(x) \times W(x) \][/tex]
Step-by-Step Solution:
1. Substitute the expressions for [tex]\( L(x) \)[/tex] and [tex]\( W(x) \)[/tex] into the area function:
[tex]\[ A(x) = (5x) \times (2x^2 - 4x + 13) \][/tex]
2. Distribute [tex]\( 5x \)[/tex] to each term inside the parentheses:
[tex]\[ A(x) = 5x \times 2x^2 + 5x \times (-4x) + 5x \times 13 \][/tex]
3. Multiply the terms:
[tex]\[ 5x \times 2x^2 = 10x^3 \][/tex]
[tex]\[ 5x \times (-4x) = -20x^2 \][/tex]
[tex]\[ 5x \times 13 = 65x \][/tex]
4. Combine the results:
[tex]\[ A(x) = 10x^3 - 20x^2 + 65x \][/tex]
Thus, the area of the rectangle in terms of [tex]\( x \)[/tex] is:
[tex]\[ 10x^3 - 20x^2 + 65x \][/tex]
So, the correct answer is:
[tex]\[ W(x) = 10x^3 - 20x^2 + 65x \][/tex]
Given:
- [tex]\( L(x) = 5x \)[/tex] (Length as a function of [tex]\( x \)[/tex])
- [tex]\( W(x) = 2x^2 - 4x + 13 \)[/tex] (Width as a function of [tex]\( x \)[/tex])
The area [tex]\( A(x) \)[/tex] of the rectangle as a function of [tex]\( x \)[/tex] is given by:
[tex]\[ A(x) = L(x) \times W(x) \][/tex]
Step-by-Step Solution:
1. Substitute the expressions for [tex]\( L(x) \)[/tex] and [tex]\( W(x) \)[/tex] into the area function:
[tex]\[ A(x) = (5x) \times (2x^2 - 4x + 13) \][/tex]
2. Distribute [tex]\( 5x \)[/tex] to each term inside the parentheses:
[tex]\[ A(x) = 5x \times 2x^2 + 5x \times (-4x) + 5x \times 13 \][/tex]
3. Multiply the terms:
[tex]\[ 5x \times 2x^2 = 10x^3 \][/tex]
[tex]\[ 5x \times (-4x) = -20x^2 \][/tex]
[tex]\[ 5x \times 13 = 65x \][/tex]
4. Combine the results:
[tex]\[ A(x) = 10x^3 - 20x^2 + 65x \][/tex]
Thus, the area of the rectangle in terms of [tex]\( x \)[/tex] is:
[tex]\[ 10x^3 - 20x^2 + 65x \][/tex]
So, the correct answer is:
[tex]\[ W(x) = 10x^3 - 20x^2 + 65x \][/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.