Answer:
9.65-9.74
Those numbers and anything between them.
tan(x) = 10/60
tan(x) = 1/6
tan(x) = a -> x = arctan(a) + πn
x = arctan(1/6) + πn
x = 0.165 + πn
Best of Luck!
=3(3z)2-3
=3(9z2)-3
=27z^2-3
=3(9z^2-1)
=3(3z+1)(3z-1)
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.
Sin(theta)=√3/2, 0≤theta≤360
In a unit circle, sin is y/r, r is always positive, y is positive in the first and second quadrant only.
sin60=√3/2, sin120=√3/2
so theta is 60 or 120
