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Questions and Answers
What is the correct formula for finding the slope, m, of a line with inclination θ?
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?
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?
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?
If (m2-m1)/(1+m1m2) is positive, what can be inferred about the angles θ and φ between the lines?
What is the relation between the slopes m1 and m2 and the angles α1 and α2 of two non-vertical lines L1 and L2?
What is the relation between the slopes m1 and m2 and the angles α1 and α2 of two non-vertical lines L1 and L2?
Which major subdiscipline of modern mathematics is primarily concerned with the study of properties and relationships of numbers?
Which major subdiscipline of modern mathematics is primarily concerned with the study of properties and relationships of numbers?
In modern mathematics, which entities are stipulated to have certain properties and are used as starting points for theories?
In modern mathematics, which entities are stipulated to have certain properties and are used as starting points for theories?
What type of reasoning is primarily used in mathematics to prove properties of abstract objects?
What type of reasoning is primarily used in mathematics to prove properties of abstract objects?
Which area of mathematics is developed in close correlation with its applications in fields such as economics, biology, and political science?
Which area of mathematics is developed in close correlation with its applications in fields such as economics, biology, and political science?
What is the fundamental characteristic of the truths of mathematics in relation to scientific experimentation?
What is the fundamental characteristic of the truths of mathematics in relation to scientific experimentation?
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