The central angle of a hexagon is :
Ф = 360° : 6 = 60°
The hexagon will map onto itself 6 times.
It will turn through angles : 60°, 120°, 180°, 240°, 300° and 360°.
Answer:
π
V-foam = 4r³( 2 - ----- )
3
Step-by-step explanation:
Let the radius of the sphere be r. Then the volume of the sphere is
V = (4/3)(π)(r³).
Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus
V = (2r)³, or 8r³.
Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:
V-foam = 8r³ - (4/3)(π)(r³). This could be factored into
π
V-foam = 4r³( 2 - ----- )
3
Answer:

Step-by-step explanation:
step 1
Find PN
we know that
PN is a diameter
PS is a radius

so

step 2
Find the measure of arc MP



step 3
Find the measure of angle MNP
we know that
The inscribed angle measures half that of the arc comprising

substitute the value

step 4
Find the measure of angle MPN
we know that
The inscribed angle measures half that of the arc comprising

substitute the value

step 5
Find the measure of angle NMP
The sum of the internal angles of a triangle must be equal to 180 degrees


therefore
The triangle MNP is a right triangle
step 6
Find the length MN
In the right triangle MNP

substitute the values


Answer: 8x + 14
Step-by-step explanation:
3x + 2 + 3x + 2 + x + 5 + x + 5 = 2(4x + 7) = 8x + 14