Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Discover detailed and accurate answers to your questions from our knowledgeable and dedicated community members.
Sagot :
Answer:
[tex]\displaystyle \frac{dA}{dt} = 102 \ m^2/day[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right
Geometry
Area of a Rectangle: A = lw
- l is length
- w is width
Calculus
Derivatives
Derivative Notation
Implicit Differentiation
Differentiation with respect to time
Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle l = 10 \ meters[/tex]
[tex]\displaystyle \frac{dl}{dt} = 4 \ m/day[/tex]
[tex]\displaystyle w = 23 \ meters[/tex]
[tex]\displaystyle \frac{dw}{dt} = 1 \ m/day[/tex]
Step 2: Differentiate
- [Area of Rectangle] Product Rule: [tex]\displaystyle \frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]
Step 3: Solve
- [Rate] Substitute in variables [Derivative]: [tex]\displaystyle \frac{dA}{dt} = (10 \ m)(1 \ m/day) + (23 \ m)(4 \ m/day)[/tex]
- [Rate] Multiply: [tex]\displaystyle \frac{dA}{dt} = 10 \ m^2/day + 92 \ m^2/day[/tex]
- [Rate] Add: [tex]\displaystyle \frac{dA}{dt} = 102 \ m^2/day[/tex]
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Implicit Differentiation
Book: College Calculus 10e
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.