Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
_____
<em>Comment on the geometry</em>
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
Answer:
f
(
x
)
=
5
x
2
−
2
x
+
3
g
(
x
)
=
4
x
2
+
7
x
−
5
f
(
g
(
x
)
)
=
5
(
4
x
2
+
7
x
−
5
)
2
−
2
(
4
x
2
+
7
x
−
5
)
+
3
=
80
x
4
+
280
x
3
+
45
x
2
−
350
x
+
125
−
8
x
2
−
14
x
+
10
+
3
=
80
x
4
+
280
x
3
+
45
x
2
−
8
x
2
−
350
x
−
14
x
+
125
+
10
+
3
f
(
g
(
x
)
)
=
80
x
4
+
280
x
3
+
37
x
2
−
364
x
+
138
The answer is
f
(
g
(
x
)
)
=
80
x
4
+
280
x
3
+
37
x
2
−
364
x
+
138
.
Step-by-step explanation:
Answer:
(2, 7 )
Step-by-step explanation:
Given the 2 equations
y = 2x + 3 → (1)
y = 3x + 1 → (2)
Substitute y = 3x + 1 into (1)
3x + 1 = 2x + 3 ( subtract 2x from both sides )
x + 1 = 3 ( subtract 1 from both sides )
x = 2
Substitute x = 2 into either of the 2 equations for corresponding value of y
Substituting x = 2 into (1)
y = 2(2) + 3 = 4 + 3 = 7
Solution is (2, 7 )
Answer:
you can just type out like 30 degrees, 50 degrees, and 100 degrees or something like that
Step-by-step explanation:
-10 + a = 6a - 7a
Rearrange the left hand side
a - 10 = 6a - 7a
Simplify 6a - 7a
a - 10 = -a
Add a on both sides
2a - 10 = 0
Add 10 on both sides
2a = 10
Divide by 2 on both sides
a = 5
