/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 44 Find the angle \(\theta\) (in ra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 44

Find the angle \(\theta\) (in radians and degrees) between the lines. \(3 x-5 y=3\) \(3 x+5 y=12\)

Short Answer

Expert verified
The angle between the two lines, both in degrees and radians, is 0.

Step by step solution

01

Rewriting Equations in Slope Intercept Form

Rewrite the given equations in the slope intercept form \(y = mx + c\), where \(m\) is the slope of the line and \(c\) is the y-intercept. The two equations are \(3x - 5y = 3\) and \(3x + 5y = 12\). Solving for y, we get \(y = \frac{3x - 3}{5}\) and \(y = \frac{3x - 12}{5}\).
02

Finding the Slopes

The coefficients of \(x\) in these equations are the slopes of the lines. This gives us \(\frac{3}{5}\) and \(\frac{3}{5}\).
03

Calculating angle

The formula for finding the angle (\(\theta\)) between two lines is \(\tan\theta = \frac{m_2 - m_1}{1 + m_1 * m_2}\). But in this case, both slopes are equal so the numerator of the fraction is 0. Therefore, the angle is 0.
04

Converting Radians to Degrees

The result is in radians and needs to be converted to degrees. The conversion factor is \(\frac{180}{\pi}\). As angle in radian is 0, multiplying it by this factor still gives 0.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The area of the shaded region in the figure is \(A=\frac{8}{3} p^{1 / 2} b^{3 / 2}\). (a) Find the area when \(p=2\) and \(b=4\). (b) Give a geometric explanation of why the area approaches 0 as \(p\) approaches 0 .

Sketch the graph of the ellipse, using latera recta. \(5 x^{2}+3 y^{2}=15\)

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (5,0),(5,12)\(;\) endpoints of the minor axis: (1,6),(9,6)

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \((x+2)^{2}+\frac{(y+4)^{2}}{1 / 4}=1\)

Use a graphing utility to graph the ellipse. Find the center, foci, and vertices. (Recall that it may be necessary to solve the equation for \(y\) and obtain two equations.) \(12 x^{2}+20 y^{2}-12 x+40 y-37=0\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.