Find the length of the arc, s, on a circle of radius r intercepted by a central angle 0. Express the arc length in terms of t. Then round your answer to two decimal places. Radius, r = 5 inches; Central angle, 0 = 120°
Find the length of the arc, s, on a circle of radius r intercepted by a central angle 0. Express the arc length in terms of t. Then round your answer to two decimal places. Radius, r = 5 inches; Central angle, 0 = 120°
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...
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![**Question: 1 pt**
Find the length of the arc, \( s \), on a circle of radius \( r \) intercepted by a central angle \( \theta \). Express the arc length in terms of \(\pi\). Then round your answer to two decimal places.
- **Radius, \( r \) = 5 inches; Central angle, \(\theta\) = 120°**
\[ s = \_\_\_\_ \text{ inches} \]
(Simplify your answer. Type your answer in terms of \(\pi\). Use integers or fractions for any numbers in the expression.)
\[ s = \_\_\_\_ \text{ inches} \]
(Type your answer rounded to two decimal places.)
---
**Instructions:**
Enter your answer in each of the answer boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81a44892-e725-436e-9c8e-21f599a0ba84%2F79da9419-eb06-4ac5-a5e9-5267be66dbf9%2Fibp6h6s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question: 1 pt**
Find the length of the arc, \( s \), on a circle of radius \( r \) intercepted by a central angle \( \theta \). Express the arc length in terms of \(\pi\). Then round your answer to two decimal places.
- **Radius, \( r \) = 5 inches; Central angle, \(\theta\) = 120°**
\[ s = \_\_\_\_ \text{ inches} \]
(Simplify your answer. Type your answer in terms of \(\pi\). Use integers or fractions for any numbers in the expression.)
\[ s = \_\_\_\_ \text{ inches} \]
(Type your answer rounded to two decimal places.)
---
**Instructions:**
Enter your answer in each of the answer boxes.
![**Matrix Inversion Problem**
Use the fact that if \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), then
\[ A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \]
to find the inverse of the matrix, if possible. Check that \( AA^{-1} = I_2 \) and \( A^{-1}A = I_2 \).
Given:
\[ A = \begin{bmatrix} -1 & -4 \\ 3 & -5 \end{bmatrix} \]
---
**Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- \( \bigcirc \) **A.** \( A^{-1} = \begin{bmatrix} \_\_ & \_\_ \\ \_\_ & \_\_ \end{bmatrix} \) (Type an integer or a simplified fraction for each matrix element.)
- \( \bigcirc \) **B.** The matrix does not have an inverse.
---
**Instructions:** Click to select and enter your answer(s).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81a44892-e725-436e-9c8e-21f599a0ba84%2F79da9419-eb06-4ac5-a5e9-5267be66dbf9%2F1clgspo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Inversion Problem**
Use the fact that if \( A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \), then
\[ A^{-1} = \frac{1}{ad-bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix} \]
to find the inverse of the matrix, if possible. Check that \( AA^{-1} = I_2 \) and \( A^{-1}A = I_2 \).
Given:
\[ A = \begin{bmatrix} -1 & -4 \\ 3 & -5 \end{bmatrix} \]
---
**Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- \( \bigcirc \) **A.** \( A^{-1} = \begin{bmatrix} \_\_ & \_\_ \\ \_\_ & \_\_ \end{bmatrix} \) (Type an integer or a simplified fraction for each matrix element.)
- \( \bigcirc \) **B.** The matrix does not have an inverse.
---
**Instructions:** Click to select and enter your answer(s).
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