84 please Certainly! Below is an educational transcription suitable for a website.---### Section 3.1: Quadratic Functions and Applications#### Exercise 84: Manufacturing ProblemA rain gutter with a rectangular cross-section is to be fabricated by bending up a flat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open.**Diagram Description:** The diagram shows a flat piece of metal with dimensions labeled. The width is marked as "20 - 2x" where "x" is the length of metal bent upwards on each side.**Questions:**a. Write an expression for the cross-sectional area in terms of \( x \), the length of metal which is bent upwards.b. How much metal has to be bent upwards to maximize the cross-sectional area? What is the maximum cross-sectional area?---#### Use the Information Below for Exercises 85 and 86:The quadratic function \( p(x) = -0.387(x - 45)^2 + 2.73(x - 45) - 3.89 \) gives the percentage (in decimal form) of puffin eggs that hatch during a breeding season in terms of \( x \), the mean sea surface temperature of the surrounding area, in degrees Fahrenheit.*(Source: Gjerdrum et al., "Tufted puffin reproduction reveals ocean climate variability," Proceedings of the National Academy of Sciences, August 2003.)***Exercise 85: Ecology**- What is the percentage of puffin eggs that will hatch at 49°F? At 47°F?**Exercise 86: Ecology**- For what mean temperature is the percentage of hatched puffin eggs a maximum? Find the percentage of hatched eggs at this temperature.---#### Supplementary Video**Video Description:** The video features an instructor explaining how to find the maximum mileage using a quadratic function. The whiteboard shows the equation \( m(x) = -0.0108x^2 + 0.91x + 0.05 \) and a graph demonstrating the parabola representing mileage in relation to speed. **Interactive Elements:**- Play options with captions available from Mr. Hampton, Shelby, Breylor, and Julieta.---This section provides students with practical applications of quadratic functions, reinforcing concepts through both algebraic manipulation and real-world contexts like manufacturing and ecology.

Given: Length of the rectangular region is 18 feet. Width of the rectangular region is…

84. Manufacturing A rain gutter with a rectangular cross-section is to be fabricated by bending up a flat piece of metal that is 18 feet long and 20 inches wide. The top of the gutter is open. 20 a. Write an expression for the cross-sectional area in terms of x, the length of metal which is bent upwards. b. How much metal has to be bent upwards to maximize the cross-sectional area? What is the maximum cross-sectional area?