(y-5) (3,7) 5 units away say find all the valub of y. distance formula use D= √(x²₂³x)² + (Y₂= y)²
(y-5) (3,7) 5 units away say find all the valub of y. distance formula use D= √(x²₂³x)² + (Y₂= y)²
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![### Finding Distance Using the Distance Formula
In this educational example, the task is to find all the values of \( y \) such that the point \( (y-5, 3) \) is 5 units away from the point \( (3, 7) \).
#### Problem Description:
Find all the values of \( y \).
> **Hint:** Use the distance formula.
#### Formula Provided:
The distance formula used in this context is:
\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points, and \( D \) is the distance between them.
#### Steps:
1. Identify the coordinates of the points:
- Point 1 (\( x_1, y_1 \)) = (3, 7)
- Point 2 (\( x, y \)) = (x, y-5)
2. Substitute the values into the distance formula, where \( D = 5 \):
\[
5 = \sqrt{(3 - x)^2 + (7 - (y-5))^2}
\]
3. Simplify the equation:
\[
5 = \sqrt{(3 - 3)^2 + (7 - y + 5)^2}
\]
\[
5 = \sqrt{0 + (12 - y)^2}
\]
4. To find the values of \( y \), we need to solve:
\[
5 = |12 - y|
\]
This will result in two cases:
1. \( 5 = 12 - y \)
2. \( 5 = y - 12 \)
5. Solving these two cases will yield the possible values of \( y \).
Note: While this guide explains the setup and initial process, complete solving to find all \( y \) is left as an exercise for the student.
#### Additional Example:
### Evaluation of Quadratic Expressions
1. **Expression Given:**
\[
3(2)^2 - 4(2)
\]
Simplify Step-By-Step:
\[
3(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87c6590a-3759-4f4e-bb57-64d6c25bd8a3%2Fc83680be-cfa4-4203-9831-48bba5fa3c89%2Fdi5h87d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding Distance Using the Distance Formula
In this educational example, the task is to find all the values of \( y \) such that the point \( (y-5, 3) \) is 5 units away from the point \( (3, 7) \).
#### Problem Description:
Find all the values of \( y \).
> **Hint:** Use the distance formula.
#### Formula Provided:
The distance formula used in this context is:
\[ D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the two points, and \( D \) is the distance between them.
#### Steps:
1. Identify the coordinates of the points:
- Point 1 (\( x_1, y_1 \)) = (3, 7)
- Point 2 (\( x, y \)) = (x, y-5)
2. Substitute the values into the distance formula, where \( D = 5 \):
\[
5 = \sqrt{(3 - x)^2 + (7 - (y-5))^2}
\]
3. Simplify the equation:
\[
5 = \sqrt{(3 - 3)^2 + (7 - y + 5)^2}
\]
\[
5 = \sqrt{0 + (12 - y)^2}
\]
4. To find the values of \( y \), we need to solve:
\[
5 = |12 - y|
\]
This will result in two cases:
1. \( 5 = 12 - y \)
2. \( 5 = y - 12 \)
5. Solving these two cases will yield the possible values of \( y \).
Note: While this guide explains the setup and initial process, complete solving to find all \( y \) is left as an exercise for the student.
#### Additional Example:
### Evaluation of Quadratic Expressions
1. **Expression Given:**
\[
3(2)^2 - 4(2)
\]
Simplify Step-By-Step:
\[
3(
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
