Answer:
Euler's Formula states that:
V -E +F = 2 meaning that the vertices minus the edges plus the faces of a convex polyhedron will always equal two.
So, for the initial question, we have 40 edges and 24 faces.
So, vertices = 2 + Edges -Faces
Vertices = 2 + 40 - 24
Vertices = 18
Source: https://www.1728.org/platonic.htm
Step-by-step explanation:
Answer:
108pi
Step-by-step explanation:
We do not need to know the height and radius, as the formula for the volume of a cone is just a third of the volume of a cylinder. So we have 36pi * 3 or 108pi.
3x + 34
x = 4
Substitute x:
3 times 4 = 12
12 + 34 = 46
The answer is 46.
Hope this helped
Answer:
m∠JKP = 31.5°
Step-by-step explanation:
Incenter of a triangle is the point where all the bisectors of interior angles intersect each other.
JN is the angle bisector of ∠KJL.
Therefore, m∠KJN = m∠LJN
(7x - 6) = (5x + 4)
7x - 5x = 6 + 4
2x = 10
x = 5
m∠KJN = (7x - 6)
= 7(5) - 6
= 35 - 6
= 29°
In ΔKJN,
m∠JKN + m∠KNJ + m∠NJK = 180°
m∠JKN + 90° + 29° = 180°
m∠JKN = 180°- 119° = 61°
Since KO is the angle bisector of ∠JKN,
m∠JKP = 
= 
= 30.5°
9514 1404 393
Answer:
√35 +3√7 -6 . . . square units
Step-by-step explanation:
The area can be figured a number of ways. The figure can be divided into parts, and the areas of those parts added.
Or, the area of the enclosing rectangle can be found, and the rectangle at upper right that is not shaded can be subtracted from that. We choose the latter.
The overall width is the sum of the given partial widths:
width = (√7 -2) + (2) = √7
Then the area of the bounding rectangle is ...
A = LW = (√5 +3)(√7) = √35 +3√7
The area of the upper right empty-space is ...
A = LW = (3)(2) = 6
Then The area of the shaded figure is ...
√35 +3√7 -6
