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...
Related questions
Question
![Sure! Here is the transcription of the text as it would appear on an educational website:
---
**4. Solve the inequality:**
\[
\frac{2x}{x^2 - x - 6} \geq 0.
\]
**5. Rationalize the numerator:**
\[
\frac{\sqrt{p} + \sqrt{p^2 - 1}}{\sqrt{p} - \sqrt{p^2 - 1}}.
\]
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee88b8a7-c213-48e1-bed2-7c496e1303f2%2Fbd96c501-6fa5-4aff-b8d0-a4274a5904f0%2Fkip490p_processed.png&w=3840&q=75)
Transcribed Image Text:Sure! Here is the transcription of the text as it would appear on an educational website:
---
**4. Solve the inequality:**
\[
\frac{2x}{x^2 - x - 6} \geq 0.
\]
**5. Rationalize the numerator:**
\[
\frac{\sqrt{p} + \sqrt{p^2 - 1}}{\sqrt{p} - \sqrt{p^2 - 1}}.
\]
---
![**Point-Slope Form of a Line**
**Problem Statement:**
Find the point-slope form of the line passing through the points \((-3, 4)\) and \( (3, -7) \).
**Solution:**
To find the point-slope form of a line, you need a point on the line and the line's slope. The point-slope form is given by:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
1. **Calculate the Slope:**
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plug in the given points \((-3, 4)\) and \( (3, -7) \):
\[
m = \frac{-7 - 4}{3 - (-3)} = \frac{-11}{6}
\]
2. **Use Point-Slope Form:**
Using the point \((-3, 4)\) and the calculated slope \( m = \frac{-11}{6} \), the point-slope form equation is:
\[
y - 4 = \frac{-11}{6}(x + 3)
\]
This represents the equation of the line in point-slope form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee88b8a7-c213-48e1-bed2-7c496e1303f2%2Fbd96c501-6fa5-4aff-b8d0-a4274a5904f0%2Ff8wyq54_processed.png&w=3840&q=75)
Transcribed Image Text:**Point-Slope Form of a Line**
**Problem Statement:**
Find the point-slope form of the line passing through the points \((-3, 4)\) and \( (3, -7) \).
**Solution:**
To find the point-slope form of a line, you need a point on the line and the line's slope. The point-slope form is given by:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.
1. **Calculate the Slope:**
The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Plug in the given points \((-3, 4)\) and \( (3, -7) \):
\[
m = \frac{-7 - 4}{3 - (-3)} = \frac{-11}{6}
\]
2. **Use Point-Slope Form:**
Using the point \((-3, 4)\) and the calculated slope \( m = \frac{-11}{6} \), the point-slope form equation is:
\[
y - 4 = \frac{-11}{6}(x + 3)
\]
This represents the equation of the line in point-slope form.
Expert Solution
Step 1
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Solution Question 4
Given
The inequality
We have to solve the inequality.
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