Straight Lines Quiz
10 Questions
1 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the correct formula for finding the slope, m, of a line with inclination θ?

  • $m = \frac{1 - \tan \theta}{1 + \tan \theta}$
  • $m = \frac{\tan \theta}{1 + \tan \theta}$
  • $m = \frac{1 + \tan \theta}{1 - \tan \theta}$
  • $m = \tan \theta$ (correct)

    • If the slope of the y-axis is not defined, what is the slope of the x-axis?

  • One
  • Zero (correct)
  • Undefined
  • Infinity

    • What is the formula for finding the angle φ between two lines with slopes m1 and m2?

  • $\tan \phi = (m2+m1)/(1-m1m2)$
  • $\tan \phi = -(m2+m1)/(1-m1m2)$
  • $\tan \phi = -(m2-m1)/(1+m1m2)$ (correct)
  • $\tan \phi = (m2-m1)/(1+m1m2)$

    • If (m2-m1)/(1+m1m2) is positive, what can be inferred about the angles θ and φ between the lines?

    <p>θ will be acute and φ will be obtuse</p> Signup and view all the answers

    What is the relation between the slopes m1 and m2 and the angles α1 and α2 of two non-vertical lines L1 and L2?

    <p>$m1 = \tan \alpha1$, $m2 = \tan \alpha2$</p> Signup and view all the answers

    Which major subdiscipline of modern mathematics is primarily concerned with the study of properties and relationships of numbers?

    <p>Number theory</p> Signup and view all the answers

    In modern mathematics, which entities are stipulated to have certain properties and are used as starting points for theories?

    <p>Abstract objects with certain properties called axioms</p> Signup and view all the answers

    What type of reasoning is primarily used in mathematics to prove properties of abstract objects?

    <p>Pure reason</p> Signup and view all the answers

    Which area of mathematics is developed in close correlation with its applications in fields such as economics, biology, and political science?

    <p>Statistics</p> Signup and view all the answers

    What is the fundamental characteristic of the truths of mathematics in relation to scientific experimentation?

    <p>Independent from any scientific experimentation</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser