### Designing an Optimal Rain GutterA rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle $ \theta $. How should $ \theta $ be chosen so that the gutter will carry the maximum amount of water?#### Diagram Explanation:The diagram illustrates a top view of the metal sheet after it has been bent to form a rain gutter. The total width of the metal sheet is 30 cm, and it has been divided into three equal parts, each measuring 10 cm in width. The side parts have been bent upwards to form the sides of the gutter. The angle of the bend is denoted by $ \theta $.- $ \theta $ is the angle formed between the initially flat metal sheet and the bent-up side portions of the gutter.- The diagram shows the dimensions and how the bending occurs symmetrically on both sides of the gutter.The key here is to determine the optimal angle $ \theta $ in radians so that the gutter can carry the maximum amount of water.#### Interactive Element:Below the diagram is an interactive input field where students can input their calculated or chosen value for $ \theta $ in radians.\[ \theta = \text{ } \boxed{\phantom{\rule{4cm}{0.5pt}}} \text { radians} \] By inputting different values for $ \theta $, students can explore how the shape and capacity of the rain gutter changes with varying angles, leading to discussions and calculations about optimizing gutter design.

We use the Given find the maximum amount of water. We are use the width one- third part is 10 cm.

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle 0. How should 0 be chosen so that the gutter will carry the maximum amount of water? E 10 cm -– 10 cm →- 10 cm radians

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle 0. How should 0 be chosen so that the gutter will carry the maximum amount of water? E 10 cm -– 10 cm →- 10 cm radians

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: 4 45° 4/2 :: 4 :: 2 2/2 :: ::

Q: Two sides of a triangle are 3 m and 5 m respectively. If the included angle is changing at the rate…

Q: SET 1 Match each equation in Column I with the appropriate right triangle in Column II. In each…

Q: 50° J 80° 1. marcML marcJLM. 3. marcJK marcMIJ 5. marcMI

A: We have to find arc

Q: Date: 1. Directions: Find the missing side or an 2. X 24 Per 47° ** Thi

Q: Find m2R. 1209 S R 140%

A: Solving the problem by finding the value of Angele R.

Q: While sitting in class doing homework, Mr. T decides to take his pen and spin it around. The length…

A: Solve for angular velocity

Q: nswer the following questions. a. If Laura has traveled 1.4 km along the ski trail then the angle…

Q: (1+7i) а. 2i(4-i)

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 70 35° 35

Q: A 109°105° D C B

A: Here we use linear pair Theorem

Q: Let a = ci + j and b = 16i + 12j. Find c π so that the angle between a and b is 6

Q: A hunter aims a shotgun at a mourning dove at the top of a tree standing 350 feet away. He pulls the…

A: Distance between Hunter and tree = 350 feet

Q: 16 15

Q: Eratosthenes noticed that the shadow’s length was 1/8 the pole’s height. Suppose the pole’s height…

A: We are only allow to do first question Dear student if you need rest of answere please upload…

Q: 18 25

A: We need to find value of x.

Q: A drone operator has his drone take off and then start flying due north. The drone flies 45.3 meters…

A: Step 1: Step 2: Step 3: Step 4:

Q: 3. Evaluate the following: (1+7i) а. 2430° b. 12-120° 2i(4-i) 5. с. (4е С. d. (22175°)(6450°)

A: Since you have posted a question with multiple subparts according to guildlines I will solve first…

Q: Solve the problem with a complete step-by-step process or solution Find the angle to which a 10…

A: In this question we have to find the angle.

Q: Step 3 Take the square root of both sides. Round your answer to one decimal place. a2 x 4864.54 a z…

A: Law of sines,sin(A)a=sin(B)b=sin(C)c

Q: Let a - ci +j and b- 9i + 12j. Find c so that the a %3D Round your answers to four decimal places…

A: Use dot product

Q: Solve Triangle ABC if given a=15.4, c=27.2 and B =75 degrees. This is using Cosine Law.

A: Given: Triangle ABC a = 15.4 c = 27.2 B = 75°

Question

### Designing an Optimal Rain Gutter

A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle $ \theta $. How should $ \theta $ be chosen so that the gutter will carry the maximum amount of water?

#### Diagram Explanation:
The diagram illustrates a top view of the metal sheet after it has been bent to form a rain gutter. The total width of the metal sheet is 30 cm, and it has been divided into three equal parts, each measuring 10 cm in width. The side parts have been bent upwards to form the sides of the gutter. The angle of the bend is denoted by $ \theta $.

- $ \theta $ is the angle formed between the initially flat metal sheet and the bent-up side portions of the gutter.
- The diagram shows the dimensions and how the bending occurs symmetrically on both sides of the gutter.

The key here is to determine the optimal angle $ \theta $ in radians so that the gutter can carry the maximum amount of water.

#### Interactive Element:
Below the diagram is an interactive input field where students can input their calculated or chosen value for $ \theta $ in radians.

\[ \theta = \text{ } \boxed{\phantom{\rule{4cm}{0.5pt}}} \text { radians} \]

By inputting different values for $ \theta $, students can explore how the shape and capacity of the rain gutter changes with varying angles, leading to discussions and calculations about optimizing gutter design.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Law of Cosines$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

1
A radar follows a plane moving overhead. When the radar has an angle of π/6 with the ground the distance from the radar to the plane is 50 km and the rate the radar is moving is π/30 radians per minute upward. If the altitude and speed of the aircraft are constant, find the aircraft's speed and altitude.
A = 50° 51' a = 46° 30' b = 53° 51' Find B.
b = 125, A = 91.5°, c = 151 B 3D C = a 3= Additional Materials eBook
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match each sine or cosine value to its equivalent measure.
answer as soon as possiblesolve and convert to rectangular form
Two sides of a triangle are 3 m and 5 m respectively. If the included angle is changing at the rate of 2 radian per second, at what rate is the third side changing when the included angle is 30°?
Two students are standing 15 feet apart. Between them is a wall. The angle of the student’s foot and the top of the wall is 20° and then 40° to the other student’s foot. How tall is the wall? Round to the nearest hundredth.
Camera 43°F Mostly cloudy 11/ Samuel needs to make 300 milliliters of a solution that is 35% sulfuric acid for science class. In the cabinet there is a 30% sulfuric acid solution and a 40% sulfuric acid solution. How much of the 30% solution and how much of the 40% solution does Samuel need? Round to the nearest milliliter if necessary. Show your work here O Search O 1/1 0 7:10 PM 1/17/2023 X
The angle of elevation θ of the sun in the sky at any latitude L is calculated with the formula sinθ=cosDcosLcosω+sinDsinL. ω is the number of radians that the Earth has rotated through since noon when ω=0. D is the declination of the sun. Westville has latitude L=37.9°. Find the angle of elevation θ in degrees of the sun at 3 PM on February 29, 2012, where at that time D≈−0.1425 and
In a right triangle, a and b represent legs and c represents the hypotenuse. Determine the measure of side c if a =28.2 cm and b= 12.8 cm. Express the answer to the nearest tenth centimeter. cm Type here to search 44°F Cloudy ^ E O A 0) T DELL prt sc home end insert delete DII F12 F7 F8 F9 F10 F11 F2 F3 F4 F5 F6 24 & backspace 080 3 4. P R Y H. K F.
Two planes leave from the same airport at the same time. One flies at a bearing of N25°W with a speed of 450 mi/hr. The other at a bearing of S55°W at a speed of 500mi/hr. If both planes fly at the same altitude, how far apart are they after 2 hours?Use either the Law of Sines or Cosines and include a detailed diagram.