Answer:
Number of sides are 12.
Step-by-step explanation:
Given that smallest angle of rotational symmetry for a regular polygon is 30°.
we have to find the number of sides does the regular polygon have.
If we can rotate a figure around a center point by fewer than 360° and the figure appears unchanged, then the figure has the rotation symmetry.
Now as at the centre the angle is 360 and all the angles at the centre formed equal i.e
Hence, 12 number of sides the polygon have.
9514 1404 393
Answer:
(x, y, z) = (-3, -1, 3)
Step-by-step explanation:
Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.
Use the last equation to write an expression for z.
z = 4 -x +4y
Substitute this into the second equation:
y -4(4 -x +4y) = -13
y -16 +4x -16y = -13
4x -15y -3 = 0
In genera form, the first equation can be written as ...
3x +y +10 = 0
Now, the solution to these two equations can be found to be ...
x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"
y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation
z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z
The solution to the system is (x, y, z) = (-3, -1, 3).
_____
<em>Additional comment</em>
Written as an augmented matrix, the system of equations is ...
Answer:
c=2
Step-by-step explanation:
All polynomials are continuous and differentiable on the set of real numbers.
So we just need to confirm on the given interval that f(1)=f(3).
f(1)=1-12(1)+3(1)^2
f(1)=1-12+3
f(1)=-8
f(3)=1-12(3)+3(3)^2
f(3)=1-36+27
f(3)=-8
So this means there is c in (1,3) such that f'(c)=0.
To solve that equation we must differentiate.
f(x)=1-12x+3x^2
f'(x)=0-12+6x
f'(x)=-12+6x
Remember we need yo solve f'(c)=0 for c.
So we need to solve -12+6c=0.
-12+6c=0
Add 12 on both sides:
6c=12
Divide both sides by 6:
c=2
Answer: Point Three Zero
Step-by-step explanation: