Hey. Why are you so worried. Here is the answer. There is a very small problem.It is that the decimal point is not added.
58 is 50 plus 8. So its 50 and 8.That is for the first one.
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.
Answer:
=6
Step-by-step explanation:
(5×8)×(5-2)/(5×4)
Numerator =40×3
=120
Denominator = 5×4
=20
simplifying 120/20
=6
Answer:
(3/7)^7
Step-by-step explanation:
When multiplying exponents we can use the formula: a^m x a^n = a^m+n.
In this case, we can plug in 3/7 for a, and their respective exponents as m and n.
(3/7)^3 x (3/7)^4= (3/7)^3+4= (3/7)^7
Hope this helps!
:)
