A regular hexagon rotates counterclockwise about its center. It turns through angles greater than 0° and less than or equal to 3
60°. At how many different angles will the hexagon map onto itself?
2 answers:
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If there is such a scalar function <em>f</em>, then
Integrate both sides of the first equation with respect to <em>x</em> :
Differentiate both sides with respect to <em>y</em> :
Integrate both sides with respect to <em>y</em> :
Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :
Integrate both sides with respect to <em>z</em> :
So we end up with
Answer:
x 19/6
Step-by-step explanation:
1. Multiply both sides by 6 (the LCM of 6,3)
5/2 + 3-x <= 2(x-2)
2. Simplify 5/2+3-x to 11/2-x
11/2 - x<=2 (x-2)
3. Expand.
11/2-x<= 2x-4
4. Add x to both sides.
11/2<= 2x-4+x
5. Simplify 2x-4+x to 3x-4.
11/2<=3x-4
6. Add 4 to both sides.
11/2+4<=3x
7. Simplify 11/2+4 to 19/2
19/2<=3x
8. Divide both sides by 3
19/2 /3 <=x
9. Simplify 19/2 /3 to 19/2*3
19/2*3<=x
10. Simplify 2*3 to 6
19/6<=x
11. Switch sides.
x>= 19/6
Hope this helps!
Answer:
The polygon has 9 sides
Step-by-step explanation:
we know that
A regular polygon has equal length sides and equal interior angles
step 1
Find the measure of the interior angle
Remember that
The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)
Let
x ----> the measure of each interior angle in the regular polygon
so
solve for x
step 2
Find the number of sides of the regular polygon
we know that
The measure of each interior angle in a regular polygon is given by the formula
where
n is the number of sides of the polygon
substitute the given values
solve for n
therefore
The polygon has 9 sides