Answer: C) 78 in2
Step-by-step explanation:
The polygon is divided into two trapezoids with equal measurements.
Area of a trapezoid:
1
2
(b1 + b2)h
Since the area of the hexagon equals the area of two trapezoids with equal measurements, do not multiply by 1/2.
(b1 + b2)h
(10 + 16)3
26(3)
78 in2
The answer is CD = √3
This is because of the fact that a 30-60-90 right triangle has proportions of 1-√3-2 based on the length opposite of the angle. Since we are given the segment opposite to the right angle as 2, we know that we can use the base numbers for the proportions to find the rest. Since CD is opposite of the 60 degree angle, it must be √3.
It is 33.33 Percent greater than $135.00
The differential equation

has characteristic equation
<em>r</em> ⁴ - <em>n </em>² <em>r</em> ² = <em>r</em> ² (<em>r</em> ² - <em>n </em>²) = <em>r</em> ² (<em>r</em> - <em>n</em>) (<em>r</em> + <em>n</em>) = 0
with roots <em>r</em> = 0 (multiplicity 2), <em>r</em> = -1, and <em>r</em> = 1, so the characteristic solution is

For the non-homogeneous equation, reduce the order by substituting <em>u(x)</em> = <em>y''(x)</em>, so that <em>u''(x)</em> is the 4th derivative of <em>y</em>, and

Solve for <em>u</em> by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by <em>u₁ </em>and <em>u₂</em>. Now we look for a particular solution of the form

where


where <em>W</em> (<em>u₁</em>, <em>u₂</em>) is the Wronskian of <em>u₁ </em>and <em>u₂</em>. We have

and so


So we have

and hence

Finally, integrate both sides twice to solve for <em>y</em> :

All you have to do is multiply 3 with 25 to get 75 (: