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noname [10]
2 years ago
5

7 digit number 8,920,000 when rounded to nearest 10 thousand. Digits in tens & hundreds are the least & same value. Valu

e of thousand digit is double that of ten thousand digit. Sum of all digits is 24
Mathematics
1 answer:
kirill [66]2 years ago
8 0
First we can conclude that the number is:
8,9 x x, x x x ( 7-digit number ) and the value of ten thousand digit it 1 or 2. But if value of thousand digits must be the double of the value of ten thousand digits, then the number is:
8,924, x x x ( because it can not be 8,912, x x x - that number should be 8,910,000 rounded to a ten thousand digit ).
Then tens and hundreds are same and the least value. That value is zero.
8,924,00 x.
Finally, we add up all values and subtract it from 24.
24 - ( 8 + 9 + 2 + 4 + 0 + 0 ) = 24 - 23 = 1
Answer:
This number is 8,924,001.  
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A prism, bases of which are equilateral triangles, circumscribes a sphere of radius 6. What is the volume of the prism?
koban [17]

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.

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