Answer:
an=7n-19
(the last one)
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
So the order of the points is: GHJK
GH = x+10 =JK
HJ=8
JK=2x-4
JK = x+10=2x-4
x+10=2x-4
10+4=2x-x
x=14
GH= 14+10 =24
GJ = GH +HJ = 24+ 8=32
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
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<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.
20 more than what they played or 20 more than what they lost?
