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
_____
<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:
no, the constant n is not divisible by (x-4)
Answer:
$12.85
Step-by-step explanation:
First we need to find the sale price of the CD
Sale price = old price - old price * discount rate
= 17 - 17* .3
= 17 - 5.1
= 11.9
The sale price of the CD is 11.90
Now we need to find the tax
tax = sale price of cd * tax rate
= 11.9 * .08
= .95
The final cost of the CD is sale price of CD plus the tax
Total cost = sale price of CD + tax
= 11.90 + .95
=12.85
I think this is right.. I tried my best. If u get it sorry... I’m very sorry
1. Divide 7.20 by 4 since the 4 are the pencils
2.divide 7.20 by 5 ( 5 represents the erasers )
3. Then finally multiply 1.44 from 7.20/5 and
2 and u get 2.88
