1 Points MULTIPLE CHOICE Question 15 The minute hand on a clock is 9 centimeters long. In 10 minutes, how far does the tip of the hand move along the arc it makes?
1 Points MULTIPLE CHOICE Question 15 The minute hand on a clock is 9 centimeters long. In 10 minutes, how far does the tip of the hand move along the arc it makes?
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Please help a brotha figure this one out.
![**Topic: Angle Measure**
**Unit: Trigonometry**
**Angle Measure Review and Quiz**
### Multiple Choice Question
**Question 15:**
The minute hand on a clock is 9 centimeters long.
In 10 minutes, how far does the tip of the hand move along the arc it makes?
**Diagram Description:**
The image displays a clock with a blue circular frame. The clock has a typical circular face with numbers 1 through 12, indicating the hours. The minute and hour hands of the clock are visible, with the minute hand extending to the edge of the clock face. The minute hand is specified to be 9 centimeters in length.
**User Interface Elements:**
- The left sidebar includes navigation options: Dashboard, Learning, Calendar, Community, Directory, Webmail (with 72 unread emails), and Chat.
- The user is identified as "MICHAEL" who is currently "Available."
- The "Learning" section shows the current lesson as "Angle Measure Review for Quiz" with a green check mark, indicating completion. Below it, the "Angle Measure Quiz" is listed.
- A summary at the bottom indicates that 14 out of 15 total questions have been answered.
- There is a "Continue" button at the bottom right for moving forward after answering the question.
- There is also an option to watch a recording related to the unit topic, indicated as "Watch Recording (58min)."
### Explanation:
To solve the question, you can use the formula for the arc length of a circle:
\[ \text{Arc Length} = r \theta \]
where \( r \) is the radius (length of the minute hand) and \( \theta \) is the angle in radians.
Since the minute hand completes one full revolution ( \( 360^\circ \) or \( 2\pi \) radians) in 60 minutes, in 10 minutes, it covers:
\[ \theta = \frac{10}{60} \times 2\pi = \frac{1}{6} \times 2\pi = \frac{\pi}{3} \text{ radians} \]
Now, substituting \( r = 9 \) cm and \( \theta = \frac{\pi}{3} \):
\[ \text{Arc Length} = 9 \times \frac{\pi}{3} = 3\pi \]
Thus, the tip of the minute](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3693de40-daf0-46af-a805-2148b30b96eb%2Ff405bd5d-f9b9-4ebc-bf47-b63b3919276b%2Ftvsprgq_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Angle Measure**
**Unit: Trigonometry**
**Angle Measure Review and Quiz**
### Multiple Choice Question
**Question 15:**
The minute hand on a clock is 9 centimeters long.
In 10 minutes, how far does the tip of the hand move along the arc it makes?
**Diagram Description:**
The image displays a clock with a blue circular frame. The clock has a typical circular face with numbers 1 through 12, indicating the hours. The minute and hour hands of the clock are visible, with the minute hand extending to the edge of the clock face. The minute hand is specified to be 9 centimeters in length.
**User Interface Elements:**
- The left sidebar includes navigation options: Dashboard, Learning, Calendar, Community, Directory, Webmail (with 72 unread emails), and Chat.
- The user is identified as "MICHAEL" who is currently "Available."
- The "Learning" section shows the current lesson as "Angle Measure Review for Quiz" with a green check mark, indicating completion. Below it, the "Angle Measure Quiz" is listed.
- A summary at the bottom indicates that 14 out of 15 total questions have been answered.
- There is a "Continue" button at the bottom right for moving forward after answering the question.
- There is also an option to watch a recording related to the unit topic, indicated as "Watch Recording (58min)."
### Explanation:
To solve the question, you can use the formula for the arc length of a circle:
\[ \text{Arc Length} = r \theta \]
where \( r \) is the radius (length of the minute hand) and \( \theta \) is the angle in radians.
Since the minute hand completes one full revolution ( \( 360^\circ \) or \( 2\pi \) radians) in 60 minutes, in 10 minutes, it covers:
\[ \theta = \frac{10}{60} \times 2\pi = \frac{1}{6} \times 2\pi = \frac{\pi}{3} \text{ radians} \]
Now, substituting \( r = 9 \) cm and \( \theta = \frac{\pi}{3} \):
\[ \text{Arc Length} = 9 \times \frac{\pi}{3} = 3\pi \]
Thus, the tip of the minute
Transcribed Image Text:This page is part of an Algebra 2 lesson on the educational platform Edio, specifically for the unit "Trigonometry" and topic "Angle Measure". The page is titled "Angle Measure Review and Quiz," marked as section 10.1.4. It features the following elements:
1. **Video Resource:** A recording titled "Watch Recording (58min)" is available as a resource for the lesson.
2. **Contents of the Lesson:**
- **Angle Measure Review for Quiz:** This segment appears to be a review section to help students prepare for a quiz on angle measures.
- **Angle Measure Quiz:** This is the quiz section where students answer questions to test their understanding of angle measures.
3. **Student Dashboard:**
- **Left Sidebar:**
- Options include Dashboard, Learning, Calendar, Community, Directory, and Webmail.
- An inbox showing 72 unread messages.
- A chat icon showing 4 new messages.
- Profile section displaying the student's name "Michael," marked as "Available."
- **Progress Tracking:**
- Shows that the student has finished 1 out of 2 items (50% complete).
4. **Question and Answer Section:**
- Displays a problem involving angle measures, illustrated by a clock face. The clock appears to be part of the problem, but specific details about the question are not visible.
- Below the illustration, there are multiple-choice options:
- Option A: \(6\pi\) centimeters
- Option B: \(3\pi\) centimeters
- Option C: \(\frac{\pi}{3}\) centimeters
- Option D: \(\frac{2\pi}{3}\) centimeters (highlighted).
5. **Student Progress Bar:**
- Indicates that 14 of 15 total questions have been answered.
- The progress is depicted with green checkmarks for completed questions and circles for remaining questions.
6. **Navigation Controls:**
- Located at the bottom right of the page are navigation buttons. The "Continue" button is enabled for moving forward.
This educational platform seems to integrate a mixture of instructional video content, quizzes, progress tracking, and interactive elements to facilitate student learning.
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!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education