A circular gear turns 60 per hour. through how many radians does it turn in a 24-hour day?
2 answers:
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<h3>Answer: </h3><h3>y + 10 = - 5 (x - 2) [point-slope form] OR</h3><h3>y = - 5 x [slope-intercept form]</h3><h2 /><h3>Step-by-step explanation:</h3>
<u>Identify the slope of the given line</u>
If we rewrite the equation given, we can easily identify the slope
x - 5y = 6
- 5y = - x + 6
y = ¹/₅ x - ⁶/₅
∴ the slope of x - 5y = 6 is ¹/₅
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ since the slope of this line = ¹/₅
then the slope of the perpendicular line (m) = - 5
<u>Determine the equation of perpendicular line</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-10) = - 5 (x - 2)
<h3> ∴ y + 10 = - 5 (x - 2)</h3><h3 />We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y + 10 = - 5 (x - 2)
<h3> y = - 5 x</h3><h3 /><h3>∴ the slope-intercept equation of the perpendicular line is y + 10 = - 5 (x - 2) OR y = - 5 x. </h3><h3 /><h3 /><em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>