The mathematics faculty at a college consists of 4 professors, 10 associate professors,8 assistant professors, and 10 instruc
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Answer:
The approximate are of the inscribed disk using the regular hexagon is
Step-by-step explanation:
we know that
we can divide the regular hexagon into 6 identical equilateral triangles
see the attached figure to better understand the problem
The approximate area of the circle is approximately the area of the six equilateral triangles
Remember that
In an equilateral triangle the interior measurement of each angle is 60 degrees
We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon
Let
M ----> the mid-point of AB
OM ----> the perpendicular bisector of AB
x ----> the measure of angle AOM
In the right triangle OAM
so
we have
substitute
Find the area of six equilateral triangles
simplify
we have
substitute
Therefore
The approximate are of the inscribed disk using the regular hexagon is
<h2>Answer: y = ⁵/₂ x - 13 OR y + 8 = ⁵/₂ x - 5 </h2><h3>Step-by-step explanation:</h3>
<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 <em>negative-reciprocal</em>s of each other.
⇒ if the slope of this line = - ²/₅
then the slope of the perpendicular line (m) = ⁵/₂
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-8) = ⁵/₂ (x - 2)
∴ y + 8 = ⁵/₂ (x - 2)
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 + 8 = ⁵/₂ (x - 2)
y = ⁵/₂ x - 13