Answer:
-89 +4i sqrt (3)
Step-by-step explanation:
sqrt(-48) - 89
sqrt(-1) sqrt(48) - 89
We know that sqrt(-1) = ±i
±i sqrt(48) - 89
±i sqrt(16)sqrt(3) - 89
±4i sqrt(3) - 89
Taking the principal square root
-89 +4i sqrt (3)
1,009.479 just add themmmm
$0.70 for 2 lollipops
X for 94 lollipops
So, 2X=94*0.70
X= (94*0.70)/2 = 65.8/2
X= $32.9
The answer is YES. They are charging enough money to get $32.90 after selling 94 lollipops on sale for buy one and get one for free.
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.
